Noordzij, Marlies; Dekker, Friedo W; Zoccali, Carmine; Jager, Kitty J
2011-01-01
The sample size is the number of patients or other experimental units that need to be included in a study to answer the research question. Pre-study calculation of the sample size is important; if a sample size is too small, one will not be able to detect an effect, while a sample that is too large may be a waste of time and money. Methods to calculate the sample size are explained in statistical textbooks, but because there are many different formulas available, it can be difficult for investigators to decide which method to use. Moreover, these calculations are prone to errors, because small changes in the selected parameters can lead to large differences in the sample size. This paper explains the basic principles of sample size calculations and demonstrates how to perform such a calculation for a simple study design.
Considerations when calculating the sample size for an inequality test
2016-01-01
Click here for Korean Translation. Calculating the sample size is a vital step during the planning of a study in order to ensure the desired power for detecting clinically meaningful differences. However, estimating the sample size is not always straightforward. A number of key components should be considered to calculate a suitable sample size. In this paper, general considerations for conducting sample size calculations for inequality tests are summarized. PMID:27482308
Considerations when calculating the sample size for an inequality test.
In, Junyong
2016-08-01
Click here for Korean Translation. Calculating the sample size is a vital step during the planning of a study in order to ensure the desired power for detecting clinically meaningful differences. However, estimating the sample size is not always straightforward. A number of key components should be considered to calculate a suitable sample size. In this paper, general considerations for conducting sample size calculations for inequality tests are summarized.
On power and sample size calculation in ethnic sensitivity studies.
Zhang, Wei; Sethuraman, Venkat
2011-01-01
In ethnic sensitivity studies, it is of interest to know whether the same dose has the same effect over populations in different regions. Glasbrenner and Rosenkranz (2006) proposed a criterion for ethnic sensitivity studies in the context of different dose-exposure models. Their method is liberal in the sense that their sample size will not achieve the target power. We will show that the power function can be easily calculated by numeric integration, and the sample size can be determined by bisection.
Sample size calculation for comparing two negative binomial rates.
Zhu, Haiyuan; Lakkis, Hassan
2014-02-10
Negative binomial model has been increasingly used to model the count data in recent clinical trials. It is frequently chosen over Poisson model in cases of overdispersed count data that are commonly seen in clinical trials. One of the challenges of applying negative binomial model in clinical trial design is the sample size estimation. In practice, simulation methods have been frequently used for sample size estimation. In this paper, an explicit formula is developed to calculate sample size based on the negative binomial model. Depending on different approaches to estimate the variance under null hypothesis, three variations of the sample size formula are proposed and discussed. Important characteristics of the formula include its accuracy and its ability to explicitly incorporate dispersion parameter and exposure time. The performance of the formula with each variation is assessed using simulations.
Power and Sample Size Calculations for Contrast Analysis in ANCOVA.
Shieh, Gwowen
2017-01-01
Analysis of covariance (ANCOVA) is commonly used in behavioral and educational research to reduce the error variance and improve the power of analysis of variance by adjusting the covariate effects. For planning and evaluating randomized ANCOVA designs, a simple sample-size formula has been proposed to account for the variance deflation factor in the comparison of two treatment groups. The objective of this article is to highlight an overlooked and potential problem of the exiting approximation and to provide an alternative and exact solution of power and sample size assessments for testing treatment contrasts. Numerical investigations are conducted to reveal the relative performance of the two procedures as a reliable technique to accommodate the covariate features that make ANCOVA design particularly distinctive. The described approach has important advantages over the current method in general applicability, methodological justification, and overall accuracy. To enhance the practical usefulness, computer algorithms are presented to implement the recommended power calculations and sample-size determinations.
GLIMMPSE Lite: Calculating Power and Sample Size on Smartphone Devices
Munjal, Aarti; Sakhadeo, Uttara R.; Muller, Keith E.; Glueck, Deborah H.; Kreidler, Sarah M.
2014-01-01
Researchers seeking to develop complex statistical applications for mobile devices face a common set of difficult implementation issues. In this work, we discuss general solutions to the design challenges. We demonstrate the utility of the solutions for a free mobile application designed to provide power and sample size calculations for univariate, one-way analysis of variance (ANOVA), GLIMMPSE Lite. Our design decisions provide a guide for other scientists seeking to produce statistical software for mobile platforms. PMID:25541688
Muhm, J M; Olshan, A F
1989-01-01
A program for the Hewlett Packard 41 series programmable calculator that determines sample size, power, and least detectable relative risk for comparative studies with independent groups is described. The user may specify any ratio of cases to controls (or exposed to unexposed subjects) and, if calculating least detectable relative risks, may specify whether the study is a case-control or cohort study.
Sample size calculation for the one-sample log-rank test.
Schmidt, René; Kwiecien, Robert; Faldum, Andreas; Berthold, Frank; Hero, Barbara; Ligges, Sandra
2015-03-15
An improved method of sample size calculation for the one-sample log-rank test is provided. The one-sample log-rank test may be the method of choice if the survival curve of a single treatment group is to be compared with that of a historic control. Such settings arise, for example, in clinical phase-II trials if the response to a new treatment is measured by a survival endpoint. Present sample size formulas for the one-sample log-rank test are based on the number of events to be observed, that is, in order to achieve approximately a desired power for allocated significance level and effect the trial is stopped as soon as a certain critical number of events are reached. We propose a new stopping criterion to be followed. Both approaches are shown to be asymptotically equivalent. For small sample size, though, a simulation study indicates that the new criterion might be preferred when planning a corresponding trial. In our simulations, the trial is usually underpowered, and the aspired significance level is not exploited if the traditional stopping criterion based on the number of events is used, whereas a trial based on the new stopping criterion maintains power with the type-I error rate still controlled.
How to calculate sample size for different study designs in medical research?
Charan, Jaykaran; Biswas, Tamoghna
2013-04-01
Calculation of exact sample size is an important part of research design. It is very important to understand that different study design need different method of sample size calculation and one formula cannot be used in all designs. In this short review we tried to educate researcher regarding various method of sample size calculation available for different study designs. In this review sample size calculation for most frequently used study designs are mentioned. For genetic and microbiological studies readers are requested to read other sources.
Sample size calculation for the one-sample log-rank test.
Wu, Jianrong
2015-01-01
In this paper, an exact variance of the one-sample log-rank test statistic is derived under the alternative hypothesis, and a sample size formula is proposed based on the derived exact variance. Simulation results showed that the proposed sample size formula provides adequate power to design a study to compare the survival of a single sample with that of a standard population.
Sample Size Calculations for Precise Interval Estimation of the Eta-Squared Effect Size
ERIC Educational Resources Information Center
Shieh, Gwowen
2015-01-01
Analysis of variance is one of the most frequently used statistical analyses in the behavioral, educational, and social sciences, and special attention has been paid to the selection and use of an appropriate effect size measure of association in analysis of variance. This article presents the sample size procedures for precise interval estimation…
Vallejo, Adriana; Muniesa, Ana; Ferreira, Chelo; de Blas, Ignacio
2013-10-01
Nowadays the formula to calculate the sample size for estimate a proportion (as prevalence) is based on the Normal distribution, however it would be based on a Binomial distribution which confidence interval was possible to be calculated using the Wilson Score method. By comparing the two formulae (Normal and Binomial distributions), the variation of the amplitude of the confidence intervals is relevant in the tails and the center of the curves. In order to calculate the needed sample size we have simulated an iterative sampling procedure, which shows an underestimation of the sample size for values of prevalence closed to 0 or 1, and also an overestimation for values closed to 0.5. Attending to these results we proposed an algorithm based on Wilson Score method that provides similar values for the sample size than empirically obtained by simulation.
SAMPLE SIZE/POWER CALCULATION FOR STRATIFIED CASE-COHORT DESIGN
Hu, Wenrong; Cai, Jianwen; Zeng, Donglin
2014-01-01
The Case-cohort (CC) study design usually has been used for risk factor assessment in epidemiologic studies or disease prevention trials for rare diseases. The sample size/power calculation for the CC design is given in Cai and Zeng [1]. However, the sample size/power calculation for a stratified case-cohort (SCC) design has not been addressed before. This article extends the results of Cai and Zeng [1] to the SCC design. Simulation studies show that the proposed test for the SCC design utilizing small sub-cohort sampling fractions is valid and efficient for situations where the disease rate is low. Furthermore, optimization of sampling in the SCC design is discussed and compared with proportional and balanced sampling techniques. An epidemiological study is provided to illustrate the sample size calculation under the SCC design. PMID:24889145
Power and sample size calculations for Mendelian randomization studies using one genetic instrument.
Freeman, Guy; Cowling, Benjamin J; Schooling, C Mary
2013-08-01
Mendelian randomization, which is instrumental variable analysis using genetic variants as instruments, is an increasingly popular method of making causal inferences from observational studies. In order to design efficient Mendelian randomization studies, it is essential to calculate the sample sizes required. We present formulas for calculating the power of a Mendelian randomization study using one genetic instrument to detect an effect of a given size, and the minimum sample size required to detect effects for given levels of significance and power, using asymptotic statistical theory. We apply the formulas to some example data and compare the results with those from simulation methods. Power and sample size calculations using these formulas should be more straightforward to carry out than simulation approaches. These formulas make explicit that the sample size needed for Mendelian randomization study is inversely proportional to the square of the correlation between the genetic instrument and the exposure and proportional to the residual variance of the outcome after removing the effect of the exposure, as well as inversely proportional to the square of the effect size.
Sample size calculation for stepped wedge and other longitudinal cluster randomised trials.
Hooper, Richard; Teerenstra, Steven; de Hoop, Esther; Eldridge, Sandra
2016-11-20
The sample size required for a cluster randomised trial is inflated compared with an individually randomised trial because outcomes of participants from the same cluster are correlated. Sample size calculations for longitudinal cluster randomised trials (including stepped wedge trials) need to take account of at least two levels of clustering: the clusters themselves and times within clusters. We derive formulae for sample size for repeated cross-section and closed cohort cluster randomised trials with normally distributed outcome measures, under a multilevel model allowing for variation between clusters and between times within clusters. Our formulae agree with those previously described for special cases such as crossover and analysis of covariance designs, although simulation suggests that the formulae could underestimate required sample size when the number of clusters is small. Whether using a formula or simulation, a sample size calculation requires estimates of nuisance parameters, which in our model include the intracluster correlation, cluster autocorrelation, and individual autocorrelation. A cluster autocorrelation less than 1 reflects a situation where individuals sampled from the same cluster at different times have less correlated outcomes than individuals sampled from the same cluster at the same time. Nuisance parameters could be estimated from time series obtained in similarly clustered settings with the same outcome measure, using analysis of variance to estimate variance components. Copyright © 2016 John Wiley & Sons, Ltd.
Sample size/power calculation for stratified case-cohort design.
Hu, Wenrong; Cai, Jianwen; Zeng, Donglin
2014-10-15
The case-cohort (CC) study design usually has been used for risk factor assessment in epidemiologic studies or disease prevention trials for rare diseases. The sample size/power calculation for a stratified CC (SCC) design has not been addressed before. This article derives such result based on a stratified test statistic. Simulation studies show that the proposed test for the SCC design utilizing small sub-cohort sampling fractions is valid and efficient for situations where the disease rate is low. Furthermore, optimization of sampling in the SCC design is discussed and compared with proportional and balanced sampling techniques. An epidemiological study is provided to illustrate the sample size calculation under the SCC design.
Kaiser, Reinhard; Woodruff, Bradley A; Bilukha, Oleg; Spiegel, Paul B; Salama, Peter
2006-06-01
A good estimate of the design effect is critical for calculating the most efficient sample size for cluster surveys. We reviewed the design effects for seven nutrition and health outcomes from nine population-based cluster surveys conducted in emergency settings. Most of the design effects for outcomes in children, and one-half of the design effects for crude mortality, were below two. A reassessment of mortality data from Kosovo and Badghis, Afghanistan revealed that, given the same number of clusters, changing sample size had a relatively small impact on the precision of the estimate of mortality. We concluded that, in most surveys, assuming a design effect of 1.5 for acute malnutrition in children and two or less for crude mortality would produce a more efficient sample size. In addition, enhancing the sample size in cluster surveys without increasing the number of clusters may not result in substantial improvements in precision.
Krishnamoorthy, K; Xia, Yanping
2008-01-01
The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to carry out one-sided tests (null hypothesis may involve a nonzero value for the multiple correlation coefficient) to attain a specified power is given. Sample size calculation for computing confidence intervals for the squared multiple correlation coefficient with a specified expected width is also provided. Sample sizes for powers and confidence intervals are tabulated for a wide range of parameter configurations and dimensions. The results are illustrated using the empirical data from Timm (1975) that related scores from the Peabody Picture Vocabulary Test to four proficiency measures.
[On the impact of sample size calculation and power in clinical research].
Held, Ulrike
2014-10-01
The aim of a clinical trial is to judge the efficacy of a new therapy or drug. In the planning phase of the study, the calculation of the necessary sample size is crucial in order to obtain a meaningful result. The study design, the expected treatment effect in outcome and its variability, power and level of significance are factors which determine the sample size. It is often difficult to fix these parameters prior to the start of the study, but related papers from the literature can be helpful sources for the unknown quantities. For scientific as well as ethical reasons it is necessary to calculate the sample size in advance in order to be able to answer the study question.
CHI-B: Sample Size Calculation for Chi-Square Tests
ERIC Educational Resources Information Center
Pohl, Norval F.; Tsai, San-Yun W.
1978-01-01
The nature of the approximate chi-square test for hypotheses concerning multinomial probabilities is reviewed. Also, a BASIC computer program for calculating the sample size necessary to control for both Type I and Type II errors in chi-square tests for hypotheses concerning multinomial probabilities is described.
Power and Sample Size Calculations for Logistic Regression Tests for Differential Item Functioning
ERIC Educational Resources Information Center
Li, Zhushan
2014-01-01
Logistic regression is a popular method for detecting uniform and nonuniform differential item functioning (DIF) effects. Theoretical formulas for the power and sample size calculations are derived for likelihood ratio tests and Wald tests based on the asymptotic distribution of the maximum likelihood estimators for the logistic regression model.…
Sample Size Calculation for Estimating or Testing a Nonzero Squared Multiple Correlation Coefficient
ERIC Educational Resources Information Center
Krishnamoorthy, K.; Xia, Yanping
2008-01-01
The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to…
[Sample size calculation in clinical post-marketing evaluation of traditional Chinese medicine].
Fu, Yingkun; Xie, Yanming
2011-10-01
In recent years, as the Chinese government and people pay more attention on the post-marketing research of Chinese Medicine, part of traditional Chinese medicine breed has or is about to begin after the listing of post-marketing evaluation study. In the post-marketing evaluation design, sample size calculation plays a decisive role. It not only ensures the accuracy and reliability of post-marketing evaluation. but also assures that the intended trials will have a desired power for correctly detecting a clinically meaningful difference of different medicine under study if such a difference truly exists. Up to now, there is no systemic method of sample size calculation in view of the traditional Chinese medicine. In this paper, according to the basic method of sample size calculation and the characteristic of the traditional Chinese medicine clinical evaluation, the sample size calculation methods of the Chinese medicine efficacy and safety are discussed respectively. We hope the paper would be beneficial to medical researchers, and pharmaceutical scientists who are engaged in the areas of Chinese medicine research.
Exact Power and Sample Size Calculations for the Two One-Sided Tests of Equivalence.
Shieh, Gwowen
2016-01-01
Equivalent testing has been strongly recommended for demonstrating the comparability of treatment effects in a wide variety of research fields including medical studies. Although the essential properties of the favorable two one-sided tests of equivalence have been addressed in the literature, the associated power and sample size calculations were illustrated mainly for selecting the most appropriate approximate method. Moreover, conventional power analysis does not consider the allocation restrictions and cost issues of different sample size choices. To extend the practical usefulness of the two one-sided tests procedure, this article describes exact approaches to sample size determinations under various allocation and cost considerations. Because the presented features are not generally available in common software packages, both R and SAS computer codes are presented to implement the suggested power and sample size computations for planning equivalence studies. The exact power function of the TOST procedure is employed to compute optimal sample sizes under four design schemes allowing for different allocation and cost concerns. The proposed power and sample size methodology should be useful for medical sciences to plan equivalence studies.
Exact Power and Sample Size Calculations for the Two One-Sided Tests of Equivalence
Shieh, Gwowen
2016-01-01
Equivalent testing has been strongly recommended for demonstrating the comparability of treatment effects in a wide variety of research fields including medical studies. Although the essential properties of the favorable two one-sided tests of equivalence have been addressed in the literature, the associated power and sample size calculations were illustrated mainly for selecting the most appropriate approximate method. Moreover, conventional power analysis does not consider the allocation restrictions and cost issues of different sample size choices. To extend the practical usefulness of the two one-sided tests procedure, this article describes exact approaches to sample size determinations under various allocation and cost considerations. Because the presented features are not generally available in common software packages, both R and SAS computer codes are presented to implement the suggested power and sample size computations for planning equivalence studies. The exact power function of the TOST procedure is employed to compute optimal sample sizes under four design schemes allowing for different allocation and cost concerns. The proposed power and sample size methodology should be useful for medical sciences to plan equivalence studies. PMID:27598468
Tavernier, Elsa; Trinquart, Ludovic; Giraudeau, Bruno
2016-01-01
Sample sizes for randomized controlled trials are typically based on power calculations. They require us to specify values for parameters such as the treatment effect, which is often difficult because we lack sufficient prior information. The objective of this paper is to provide an alternative design which circumvents the need for sample size calculation. In a simulation study, we compared a meta-experiment approach to the classical approach to assess treatment efficacy. The meta-experiment approach involves use of meta-analyzed results from 3 randomized trials of fixed sample size, 100 subjects. The classical approach involves a single randomized trial with the sample size calculated on the basis of an a priori-formulated hypothesis. For the sample size calculation in the classical approach, we used observed articles to characterize errors made on the formulated hypothesis. A prospective meta-analysis of data from trials of fixed sample size provided the same precision, power and type I error rate, on average, as the classical approach. The meta-experiment approach may provide an alternative design which does not require a sample size calculation and addresses the essential need for study replication; results may have greater external validity. PMID:27362939
Sample size calculation for testing differences between cure rates with the optimal log-rank test.
Wu, Jianrong
2017-01-01
In this article, sample size calculations are developed for use when the main interest is in the differences between the cure rates of two groups. Following the work of Ewell and Ibrahim, the asymptotic distribution of the weighted log-rank test is derived under the local alternative. The optimal log-rank test under the proportional distributions alternative is discussed, and sample size formulas for the optimal and standard log-rank tests are derived. Simulation results show that the proposed formulas provide adequate sample size estimation for trial designs and that the optimal log-rank test is more efficient than the standard log-rank test, particularly when both cure rates and percentages of censoring are small.
Sample size calculations in pediatric clinical trials conducted in an ICU: a systematic review.
Nikolakopoulos, Stavros; Roes, Kit C B; van der Lee, Johanna H; van der Tweel, Ingeborg
2014-07-08
At the design stage of a clinical trial, several assumptions have to be made. These usually include guesses about parameters that are not of direct interest but must be accounted for in the analysis of the treatment effect and also in the sample size calculation (nuisance parameters, e.g. the standard deviation or the control group event rate). We conducted a systematic review to investigate the impact of misspecification of nuisance parameters in pediatric randomized controlled trials conducted in intensive care units. We searched MEDLINE through PubMed. We included all publications concerning two-arm RCTs where efficacy assessment was the main objective. We included trials with pharmacological interventions. Only trials with a dichotomous or a continuous outcome were included. This led to the inclusion of 70 articles describing 71 trials. In 49 trial reports a sample size calculation was reported. Relative misspecification could be calculated for 28 trials, 22 with a dichotomous and 6 with a continuous primary outcome. The median [inter-quartile range (IQR)] overestimation was 6.9 [-12.1, 57.8]% for the control group event rate in trials with dichotomous outcomes and -1.5 [-15.3, 5.1]% for the standard deviation in trials with continuous outcomes. Our results show that there is room for improvement in the clear reporting of sample size calculations in pediatric clinical trials conducted in ICUs. Researchers should be aware of the importance of nuisance parameters in study design and in the interpretation of the results.
Sample size and power calculations for correlations between bivariate longitudinal data.
Comulada, W Scott; Weiss, Robert E
2010-11-30
The analysis of a baseline predictor with a longitudinally measured outcome is well established and sample size calculations are reasonably well understood. Analysis of bivariate longitudinally measured outcomes is gaining in popularity and methods to address design issues are required. The focus in a random effects model for bivariate longitudinal outcomes is on the correlations that arise between the random effects and between the bivariate residuals. In the bivariate random effects model, we estimate the asymptotic variances of the correlations and we propose power calculations for testing and estimating the correlations. We compare asymptotic variance estimates to variance estimates obtained from simulation studies and compare our proposed power calculations for correlations on bivariate longitudinal data to power calculations for correlations on cross-sectional data.
Tosteson, Tor D; Buzas, Jeffrey S; Demidenko, Eugene; Karagas, Margaret
2003-04-15
Covariate measurement error is often a feature of scientific data used for regression modelling. The consequences of such errors include a loss of power of tests of significance for the regression parameters corresponding to the true covariates. Power and sample size calculations that ignore covariate measurement error tend to overestimate power and underestimate the actual sample size required to achieve a desired power. In this paper we derive a novel measurement error corrected power function for generalized linear models using a generalized score test based on quasi-likelihood methods. Our power function is flexible in that it is adaptable to designs with a discrete or continuous scalar covariate (exposure) that can be measured with or without error, allows for additional confounding variables and applies to a broad class of generalized regression and measurement error models. A program is described that provides sample size or power for a continuous exposure with a normal measurement error model and a single normal confounder variable in logistic regression. We demonstrate the improved properties of our power calculations with simulations and numerical studies. An example is given from an ongoing study of cancer and exposure to arsenic as measured by toenail concentrations and tap water samples.
Sample size calculations in pediatric clinical trials conducted in an ICU: a systematic review
2014-01-01
At the design stage of a clinical trial, several assumptions have to be made. These usually include guesses about parameters that are not of direct interest but must be accounted for in the analysis of the treatment effect and also in the sample size calculation (nuisance parameters, e.g. the standard deviation or the control group event rate). We conducted a systematic review to investigate the impact of misspecification of nuisance parameters in pediatric randomized controlled trials conducted in intensive care units. We searched MEDLINE through PubMed. We included all publications concerning two-arm RCTs where efficacy assessment was the main objective. We included trials with pharmacological interventions. Only trials with a dichotomous or a continuous outcome were included. This led to the inclusion of 70 articles describing 71 trials. In 49 trial reports a sample size calculation was reported. Relative misspecification could be calculated for 28 trials, 22 with a dichotomous and 6 with a continuous primary outcome. The median [inter-quartile range (IQR)] overestimation was 6.9 [-12.1, 57.8]% for the control group event rate in trials with dichotomous outcomes and -1.5 [-15.3, 5.1]% for the standard deviation in trials with continuous outcomes. Our results show that there is room for improvement in the clear reporting of sample size calculations in pediatric clinical trials conducted in ICUs. Researchers should be aware of the importance of nuisance parameters in study design and in the interpretation of the results. PMID:25004909
Sample size calculations for the design of cluster randomized trials: A summary of methodology.
Gao, Fei; Earnest, Arul; Matchar, David B; Campbell, Michael J; Machin, David
2015-05-01
Cluster randomized trial designs are growing in popularity in, for example, cardiovascular medicine research and other clinical areas and parallel statistical developments concerned with the design and analysis of these trials have been stimulated. Nevertheless, reviews suggest that design issues associated with cluster randomized trials are often poorly appreciated and there remain inadequacies in, for example, describing how the trial size is determined and the associated results are presented. In this paper, our aim is to provide pragmatic guidance for researchers on the methods of calculating sample sizes. We focus attention on designs with the primary purpose of comparing two interventions with respect to continuous, binary, ordered categorical, incidence rate and time-to-event outcome variables. Issues of aggregate and non-aggregate cluster trials, adjustment for variation in cluster size and the effect size are detailed. The problem of establishing the anticipated magnitude of between- and within-cluster variation to enable planning values of the intra-cluster correlation coefficient and the coefficient of variation are also described. Illustrative examples of calculations of trial sizes for each endpoint type are included.
Sample size calculation for recurrent events data in one-arm studies.
Rebora, Paola; Galimberti, Stefania
2012-01-01
In some exceptional circumstances, as in very rare diseases, nonrandomized one-arm trials are the sole source of evidence to demonstrate efficacy and safety of a new treatment. The design of such studies needs a sound methodological approach in order to provide reliable information, and the determination of the appropriate sample size still represents a critical step of this planning process. As, to our knowledge, no method exists for sample size calculation in one-arm trials with a recurrent event endpoint, we propose here a closed sample size formula. It is derived assuming a mixed Poisson process, and it is based on the asymptotic distribution of the one-sample robust nonparametric test recently developed for the analysis of recurrent events data. The validity of this formula in managing a situation with heterogeneity of event rates, both in time and between patients, and time-varying treatment effect was demonstrated with exhaustive simulation studies. Moreover, although the method requires the specification of a process for events generation, it seems to be robust under erroneous definition of this process, provided that the number of events at the end of the study is similar to the one assumed in the planning phase. The motivating clinical context is represented by a nonrandomized one-arm study on gene therapy in a very rare immunodeficiency in children (ADA-SCID), where a major endpoint is the recurrence of severe infections.
ERIC Educational Resources Information Center
Luh, Wei-Ming; Guo, Jiin-Huarng
2011-01-01
Sample size determination is an important issue in planning research. In the context of one-way fixed-effect analysis of variance, the conventional sample size formula cannot be applied for the heterogeneous variance cases. This study discusses the sample size requirement for the Welch test in the one-way fixed-effect analysis of variance with…
Zhang, Song; Cao, Jing; Ahn, Chul
2017-02-20
We investigate the estimation of intervention effect and sample size determination for experiments where subjects are supposed to contribute paired binary outcomes with some incomplete observations. We propose a hybrid estimator to appropriately account for the mixed nature of observed data: paired outcomes from those who contribute complete pairs of observations and unpaired outcomes from those who contribute either pre-intervention or post-intervention outcomes. We theoretically prove that if incomplete data are evenly distributed between the pre-intervention and post-intervention periods, the proposed estimator will always be more efficient than the traditional estimator. A numerical research shows that when the distribution of incomplete data is unbalanced, the proposed estimator will be superior when there is moderate-to-strong positive within-subject correlation. We further derive a closed-form sample size formula to help researchers determine how many subjects need to be enrolled in such studies. Simulation results suggest that the calculated sample size maintains the empirical power and type I error under various design configurations. We demonstrate the proposed method using a real application example. Copyright © 2016 John Wiley & Sons, Ltd.
Larson, Michael J; Carbine, Kaylie A
2017-01-01
There is increasing focus across scientific fields on adequate sample sizes to ensure non-biased and reproducible effects. Very few studies, however, report sample size calculations or even the information needed to accurately calculate sample sizes for grants and future research. We systematically reviewed 100 randomly selected clinical human electrophysiology studies from six high impact journals that frequently publish electroencephalography (EEG) and event-related potential (ERP) research to determine the proportion of studies that reported sample size calculations, as well as the proportion of studies reporting the necessary components to complete such calculations. Studies were coded by the two authors blinded to the other's results. Inter-rater reliability was 100% for the sample size calculations and kappa above 0.82 for all other variables. Zero of the 100 studies (0%) reported sample size calculations. 77% utilized repeated-measures designs, yet zero studies (0%) reported the necessary variances and correlations among repeated measures to accurately calculate future sample sizes. Most studies (93%) reported study statistical values (e.g., F or t values). Only 40% reported effect sizes, 56% reported mean values, and 47% reported indices of variance (e.g., standard deviations/standard errors). Absence of such information hinders accurate determination of sample sizes for study design, grant applications, and meta-analyses of research and whether studies were adequately powered to detect effects of interest. Increased focus on sample size calculations, utilization of registered reports, and presenting information detailing sample size calculations and statistics for future researchers are needed and will increase sample size-related scientific rigor in human electrophysiology research.
Testing bioequivalence for multiple formulations with power and sample size calculations.
Zheng, Cheng; Wang, Jixian; Zhao, Lihui
2012-01-01
Bioequivalence (BE) trials play an important role in drug development for demonstrating the BE between test and reference formulations. The key statistical analysis for BE trials is the use of two one-sided tests (TOST), which is equivalent to showing that the 90% confidence interval of the relative bioavailability is within a given range. Power and sample size calculations for the comparison between one test formulation and the reference formulation has been intensively investigated, and tables and software are available for practical use. From a statistical and logistical perspective, it might be more efficient to test more than one formulation in a single trial. However, approaches for controlling the overall type I error may be required. We propose a method called multiplicity-adjusted TOST (MATOST) combining multiple comparison adjustment approaches, such as Hochberg's or Dunnett's method, with TOST. Because power and sample size calculations become more complex and are difficult to solve analytically, efficient simulation-based procedures for this purpose have been developed and implemented in an R package. Some numerical results for a range of scenarios are presented in the paper. We show that given the same overall type I error and power, a BE crossover trial designed to test multiple formulations simultaneously only requires a small increase in the total sample size compared with a simple 2 × 2 crossover design evaluating only one test formulation. Hence, we conclude that testing multiple formulations in a single study is generally an efficient approach. The R package MATOST is available at https://sites.google.com/site/matostbe/.
Abdulatif, M; Mukhtar, A; Obayah, G
2015-11-01
We have evaluated the pitfalls in reporting sample size calculation in randomized controlled trials (RCTs) published in the 10 highest impact factor anaesthesia journals.Superiority RCTs published in 2013 were identified and checked for the basic components required for sample size calculation and replication. The difference between the reported and replicated sample size was estimated. The sources used for estimating the expected effect size (Δ) were identified, and the difference between the expected and observed effect sizes (Δ gap) was estimated.We enrolled 194 RCTs. Sample size calculation was reported in 91.7% of studies. Replication of sample size calculation was possible in 80.3% of studies. The original and replicated sample sizes were identical in 67.8% of studies. The difference between the replicated and reported sample sizes exceeded 10% in 28.7% of studies. The expected and observed effect sizes were comparable in RCTs with positive outcomes (P=0.1). Studies with negative outcome tended to overestimate the effect size (Δ gap 42%, 95% confidence interval 32-51%), P<0.001. Post hoc power of negative studies was 20.2% (95% confidence interval 13.4-27.1%). Studies using data derived from pilot studies for sample size calculation were associated with the smallest Δ gaps (P=0.008).Sample size calculation is frequently reported in anaesthesia journals, but the details of basic elements for calculation are not consistently provided. In almost one-third of RCTs, the reported and replicated sample sizes were not identical and the assumptions for the expected effect size and variance were not supported by relevant literature or pilot studies.
Mandava, Pitchaiah; Krumpelman, Chase S.; Shah, Jharna N.; White, Donna L.; Kent, Thomas A.
2013-01-01
provide the user with programs to calculate and incorporate errors into sample size estimation. PMID:23861800
Hirakawa, Akihiro; Hamada, Chikuma; Yoshimura, Isao
2012-01-01
When identifying the differentially expressed genes (DEGs) in microarray data, we often observe heteroscedasticity between groups and dependence among genes. Incorporating these factors is necessary for sample size calculation in microarray experiments. A penalized t-statistic is widely used to improve the identifiability of DEGs. We develop a formula to calculate sample size with dependence adjustment for the penalized t-statistic. Sample size is determined on the basis of overall power under certain conditions to maintain a certain false discovery rate. The usefulness of the proposed method is demonstrated by numerical studies using both simulated data and real data.
Shieh, Gwowen
2013-03-01
Effect size reporting and interpreting practices have been extensively recommended in academic journals when primary outcomes of all empirical studies have been analyzed. This article presents an alternative approach to constructing confidence intervals of the weighted eta-squared effect size within the context of one-way heteroscedastic ANOVA models. It is shown that the proposed interval procedure has advantages over an existing method in its theoretical justification, computational simplicity, and numerical performance. For design planning, the corresponding sample size procedures for precise interval estimation of the weighted eta-squared association measure are also delineated. Specifically, the developed formulas compute the necessary sample sizes with respect to the considerations of expected confidence interval width and tolerance probability of interval width within a designated value. Supplementary computer programs are provided to aid the implementation of the suggested techniques in practical applications of ANOVA designs when the assumption of homogeneous variances is not tenable.
Sample size calculations for noninferiority trials with Poisson distributed count data.
Stucke, Kathrin; Kieser, Meinhard
2013-03-01
Clinical trials with Poisson distributed count data as the primary outcome are common in various medical areas such as relapse counts in multiple sclerosis trials or the number of attacks in trials for the treatment of migraine. In this article, we present approximate sample size formulae for testing noninferiority using asymptotic tests which are based on restricted or unrestricted maximum likelihood estimators of the Poisson rates. The Poisson outcomes are allowed to be observed for unequal follow-up schemes, and both the situations that the noninferiority margin is expressed in terms of the difference and the ratio are considered. The exact type I error rates and powers of these tests are evaluated and the accuracy of the approximate sample size formulae is examined. The test statistic using the restricted maximum likelihood estimators (for the difference test problem) and the test statistic that is based on the logarithmic transformation and employs the maximum likelihood estimators (for the ratio test problem) show favorable type I error control and can be recommended for practical application. The approximate sample size formulae show high accuracy even for small sample sizes and provide power values identical or close to the aspired ones. The methods are illustrated by a clinical trial example from anesthesia.
Bayesian sample size calculation for estimation of the difference between two binomial proportions.
Pezeshk, Hamid; Nematollahi, Nader; Maroufy, Vahed; Marriott, Paul; Gittins, John
2013-12-01
In this study, we discuss a decision theoretic or fully Bayesian approach to the sample size question in clinical trials with binary responses. Data are assumed to come from two binomial distributions. A Dirichlet distribution is assumed to describe prior knowledge of the two success probabilities p1 and p2. The parameter of interest is p = p1 - p2. The optimal size of the trial is obtained by maximising the expected net benefit function. The methodology presented in this article extends previous work by the assumption of dependent prior distributions for p1 and p2.
Jun, Jae Kwan; Kim, Mi Jin; Choi, Kui Son; Suh, Mina; Jung, Kyu-Won
2012-01-01
Mammographic breast density is a known risk factor for breast cancer. To conduct a survey to estimate the distribution of mammographic breast density in Korean women, appropriate sampling strategies for representative and efficient sampling design were evaluated through simulation. Using the target population from the National Cancer Screening Programme (NCSP) for breast cancer in 2009, we verified the distribution estimate by repeating the simulation 1,000 times using stratified random sampling to investigate the distribution of breast density of 1,340,362 women. According to the simulation results, using a sampling design stratifying the nation into three groups (metropolitan, urban, and rural), with a total sample size of 4,000, we estimated the distribution of breast density in Korean women at a level of 0.01% tolerance. Based on the results of our study, a nationwide survey for estimating the distribution of mammographic breast density among Korean women can be conducted efficiently.
Exact calculation of power and sample size in bioequivalence studies using two one-sided tests.
Shen, Meiyu; Russek-Cohen, Estelle; Slud, Eric V
2015-01-01
The number of subjects in a pharmacokinetic two-period two-treatment crossover bioequivalence study is typically small, most often less than 60. The most common approach to testing for bioequivalence is the two one-sided tests procedure. No explicit mathematical formula for the power function in the context of the two one-sided tests procedure exists in the statistical literature, although the exact power based on Owen's special case of bivariate noncentral t-distribution has been tabulated and graphed. Several approximations have previously been published for the probability of rejection in the two one-sided tests procedure for crossover bioequivalence studies. These approximations and associated sample size formulas are reviewed in this article and compared for various parameter combinations with exact power formulas derived here, which are computed analytically as univariate integrals and which have been validated by Monte Carlo simulations. The exact formulas for power and sample size are shown to improve markedly in realistic parameter settings over the previous approximations.
ERIC Educational Resources Information Center
Lambert, Richard; Flowers, Claudia; Sipe, Theresa; Idleman, Lynda
This paper discusses three software packages that offer unique features and options that greatly simplify the research package for conducting surveys. The first package, EPSILON, from Resource Group, Ltd. of Dallas (Texas) is designed to perform a variety of sample size calculations covering most of the commonly encountered survey research…
Sugimoto, Tomoyuki; Sozu, Takashi; Hamasaki, Toshimitsu
2012-01-01
The clinical efficacy of a new treatment may often be better evaluated by two or more co-primary endpoints. Recently, in pharmaceutical drug development, there has been increasing discussion regarding establishing statistically significant favorable results on more than one endpoint in comparisons between treatments, which is referred to as a problem of multiple co-primary endpoints. Several methods have been proposed for calculating the sample size required to design a trial with multiple co-primary correlated endpoints. However, because these methods require users to have considerable mathematical sophistication and knowledge of programming techniques, their application and spread may be restricted in practice. To improve the convenience of these methods, in this paper, we provide a useful formula with accompanying numerical tables for sample size calculations to design clinical trials with two treatments, where the efficacy of a new treatment is demonstrated on continuous co-primary endpoints. In addition, we provide some examples to illustrate the sample size calculations made using the formula. Using the formula and the tables, which can be read according to the patterns of correlations and effect size ratios expected in multiple co-primary endpoints, makes it convenient to evaluate the required sample size promptly.
Divine, George; Norton, H James; Hunt, Ronald; Dienemann, Jacqueline
2013-09-01
When a study uses an ordinal outcome measure with unknown differences in the anchors and a small range such as 4 or 7, use of the Wilcoxon rank sum test or the Wilcoxon signed rank test may be most appropriate. However, because nonparametric methods are at best indirect functions of standard measures of location such as means or medians, the choice of the most appropriate summary measure can be difficult. The issues underlying use of these tests are discussed. The Wilcoxon-Mann-Whitney odds directly reflects the quantity that the rank sum procedure actually tests, and thus it can be a superior summary measure. Unlike the means and medians, its value will have a one-to-one correspondence with the Wilcoxon rank sum test result. The companion article appearing in this issue of Anesthesia & Analgesia ("Aromatherapy as Treatment for Postoperative Nausea: A Randomized Trial") illustrates these issues and provides an example of a situation for which the medians imply no difference between 2 groups, even though the groups are, in fact, quite different. The trial cited also provides an example of a single sample that has a median of zero, yet there is a substantial shift for much of the nonzero data, and the Wilcoxon signed rank test is quite significant. These examples highlight the potential discordance between medians and Wilcoxon test results. Along with the issues surrounding the choice of a summary measure, there are considerations for the computation of sample size and power, confidence intervals, and multiple comparison adjustment. In addition, despite the increased robustness of the Wilcoxon procedures relative to parametric tests, some circumstances in which the Wilcoxon tests may perform poorly are noted, along with alternative versions of the procedures that correct for such limitations.
45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations
Code of Federal Regulations, 2011 CFR
2011-10-01
... Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... Follow-Up Populations 1. Using Finite Population Correction The Finite Population Correction (FPC) is applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more...
45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations
Code of Federal Regulations, 2013 CFR
2013-10-01
... Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... Follow-Up Populations 1. Using Finite Population Correction The Finite Population Correction (FPC) is applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more...
45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations
Code of Federal Regulations, 2014 CFR
2014-10-01
... Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... Follow-Up Populations 1. Using Finite Population Correction The Finite Population Correction (FPC) is applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more...
45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations
Code of Federal Regulations, 2012 CFR
2012-10-01
... Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... Follow-Up Populations 1. Using Finite Population Correction The Finite Population Correction (FPC) is applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more...
45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations
Code of Federal Regulations, 2010 CFR
2010-10-01
... Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... Follow-Up Populations 1. Using Finite Population Correction The Finite Population Correction (FPC) is applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more...
Reich, Nicholas G; Myers, Jessica A; Obeng, Daniel; Milstone, Aaron M; Perl, Trish M
2012-01-01
In recent years, the number of studies using a cluster-randomized design has grown dramatically. In addition, the cluster-randomized crossover design has been touted as a methodological advance that can increase efficiency of cluster-randomized studies in certain situations. While the cluster-randomized crossover trial has become a popular tool, standards of design, analysis, reporting and implementation have not been established for this emergent design. We address one particular aspect of cluster-randomized and cluster-randomized crossover trial design: estimating statistical power. We present a general framework for estimating power via simulation in cluster-randomized studies with or without one or more crossover periods. We have implemented this framework in the clusterPower software package for R, freely available online from the Comprehensive R Archive Network. Our simulation framework is easy to implement and users may customize the methods used for data analysis. We give four examples of using the software in practice. The clusterPower package could play an important role in the design of future cluster-randomized and cluster-randomized crossover studies. This work is the first to establish a universal method for calculating power for both cluster-randomized and cluster-randomized clinical trials. More research is needed to develop standardized and recommended methodology for cluster-randomized crossover studies.
Hardouin, Jean-Benoit; Amri, Sarah; Feddag, Mohand-Larbi; Sébille, Véronique
2012-05-20
Evaluation of patient-reported outcomes (PRO) is increasingly performed in health sciences. PRO differs from other measurements because such patient characteristics cannot be directly observed. Item response theory (IRT) is an attractive way for PRO analysis. However, in the framework of IRT, sample size justification is rarely provided or ignores the fact that PRO measures are latent variables with the use of formulas developed for observed variables. It might therefore be inappropriate and might provide inadequately sized studies. The objective was to develop valid sample size methodology for the comparison of PRO in two groups of patients using IRT. The proposed approach takes into account questionnaire's items parameters, the difference of the latent variables means, and its variance whose derivation is approximated using Cramer-Rao bound (CRB). We also computed the associated power. We realized a simulation study taking into account sample size, number of items, and value of the group effect. We compared power obtained from CRB with the one obtained from simulations (SIM) and with the power based on observed variables (OBS). For a given sample size, powers using CRB and SIM were similar and always lower than OBS. We observed a strong impact of the number of items for CRB and SIM, the power increasing with the questionnaire's length but not for OBS. In the context of latent variables, it seems important to use an adapted sample size formula because the formula developed for observed variables seems to be inadequate and leads to an underestimated study size.
Neumann, Christoph; Taub, Margaret A; Younkin, Samuel G; Beaty, Terri H; Ruczinski, Ingo; Schwender, Holger
2014-11-01
Case-parent trio studies considering genotype data from children affected by a disease and their parents are frequently used to detect single nucleotide polymorphisms (SNPs) associated with disease. The most popular statistical tests for this study design are transmission/disequilibrium tests (TDTs). Several types of these tests have been developed, for example, procedures based on alleles or genotypes. Therefore, it is of great interest to examine which of these tests have the highest statistical power to detect SNPs associated with disease. Comparisons of the allelic and the genotypic TDT for individual SNPs have so far been conducted based on simulation studies, since the test statistic of the genotypic TDT was determined numerically. Recently, however, it has been shown that this test statistic can be presented in closed form. In this article, we employ this analytic solution to derive equations for calculating the statistical power and the required sample size for different types of the genotypic TDT. The power of this test is then compared with the one of the corresponding score test assuming the same mode of inheritance as well as the allelic TDT based on a multiplicative mode of inheritance, which is equivalent to the score test assuming an additive mode of inheritance. This is, thus, the first time the power of these tests are compared based on equations, yielding instant results and omitting the need for time-consuming simulation studies. This comparison reveals that these tests have almost the same power, with the score test being slightly more powerful.
ERIC Educational Resources Information Center
Dong, Nianbo; Maynard, Rebecca
2013-01-01
This paper and the accompanying tool are intended to complement existing supports for conducting power analysis tools by offering a tool based on the framework of Minimum Detectable Effect Sizes (MDES) formulae that can be used in determining sample size requirements and in estimating minimum detectable effect sizes for a range of individual- and…
Guo, Qing; Thabane, Lehana; Hall, Geoffrey; McKinnon, Margaret; Goeree, Ron; Pullenayegum, Eleanor
2014-02-01
Anecdotal evidence suggests that functional magnetic resonance imaging (fMRI) studies rarely consider statistical power when setting a sample size. This raises concerns since undersized studies may fail to detect effects of interest and encourage data dredging. Although sample size methodology in this field exists, implementation requires specifications of estimated effect size and variance components. We therefore systematically evaluated how often estimates of effect size and variance components were reported in observational fMRI studies involving clinical human participants published in six leading journals between January 2010 and December 2011. A random sample of 100 eligible articles was included in data extraction and analyses. Two independent reviewers assessed the reporting of sample size calculations and the data components required to perform the calculations in the fMRI literature. One article (1%) reported sample size calculations. The reporting of parameter estimates for effect size (8%), between-subject variance (4%), within-subject variance (1%) and temporal autocorrelation matrix (0%) was uncommon. Three articles (3%) reported Cohen's d or F effect sizes. The majority (83%) reported peak or average t, z or F statistics. The inter-rater agreement was very good, with a prevalence-adjusted bias-adjusted kappa (PABAK) value greater than 0.88. We concluded that sample size calculations were seldom reported in fMRI studies. Moreover, omission of parameter estimates for effect size, between- and within-subject variances, and temporal autocorrelation matrix could limit investigators' ability to perform power analyses for new studies. We suggest routine reporting of these quantities, and recommend strategies for reducing bias in their reported values.
Jiang, Zhiwei; Wang, Ling; Li, Chanjuan; Xia, Jielai; Jia, Hongxia
2012-01-01
Group sequential design has been widely applied in clinical trials in the past few decades. The sample size estimation is a vital concern of sponsors and investigators. Especially in the survival group sequential trials, it is a thorny question because of its ambiguous distributional form, censored data and different definition of information time. A practical and easy-to-use simulation-based method is proposed for multi-stage two-arm survival group sequential design in the article and its SAS program is available. Besides the exponential distribution, which is usually assumed for survival data, the Weibull distribution is considered here. The incorporation of the probability of discontinuation in the simulation leads to the more accurate estimate. The assessment indexes calculated in the simulation are helpful to the determination of number and timing of the interim analysis. The use of the method in the survival group sequential trials is illustrated and the effects of the varied shape parameter on the sample size under the Weibull distribution are explored by employing an example. According to the simulation results, a method to estimate the shape parameter of the Weibull distribution is proposed based on the median survival time of the test drug and the hazard ratio, which are prespecified by the investigators and other participants. 10+ simulations are recommended to achieve the robust estimate of the sample size. Furthermore, the method is still applicable in adaptive design if the strategy of sample size scheme determination is adopted when designing or the minor modifications on the program are made.
Hanson, R L; Looker, H C; Ma, L; Muller, Y L; Baier, L J; Knowler, W C
2006-05-01
Association (e.g. case-control) studies are often used to finely map loci identified by linkage analysis. We investigated the influence of various parameters on power and sample size requirements for such a study. Calculations were performed for various values of a high-risk functional allele (fA), frequency of a marker allele associated with the high risk allele (f1), degree of linkage disquilibrium between functional and marker alleles (D') and trait heritability attributable to the functional locus (h2). The calculations show that if cases and controls are selected from equal but opposite extreme quantiles of a quantitative trait, the primary determinants of power are h2 and the specific quantiles selected. For a dichotomous trait, power also depends on population prevalence. Power is optimal if functional alleles are studied (fA= f1 and D'= 1.0) and can decrease substantially as D' diverges from 1.0 or as f(1) diverges from fA. These analyses suggest that association studies to finely map loci are most powerful if potential functional polymorphisms are identified a priori or if markers are typed to maximize haplotypic diversity. In the absence of such information, expected minimum power at a given location for a given sample size can be calculated by specifying a range of potential frequencies for fA (e.g. 0.1-0.9) and determining power for all markers within the region with specification of the expected D' between the markers and the functional locus. This method is illustrated for a fine-mapping project with 662 single nucleotide polymorphisms in 24 Mb. Regions differed by marker density and allele frequencies. Thus, in some, power was near its theoretical maximum and little additional information is expected from additional markers, while in others, additional markers appear to be necessary. These methods may be useful in the analysis and interpretation of fine-mapping studies.
Sample Size for Correlation Estimates
1989-09-01
graphs, and computer programs are developed to find the sample number needed for a desired confidence interval size. Nonparametric measures of...correlation (Spearman’s ra and Kendall’s tau) are also examined for appropriate sample numbers when a specific confidence interval size desired.
van Velthoven, Michelle Helena; Li, Ye; Wang, Wei; Du, Xiaozhen; Chen, Li; Wu, Qiong; Majeed, Azeem; Zhang, Yanfeng; Car, Josip
2013-01-01
Background An important issue for mHealth evaluation is the lack of information for sample size calculations. Objective To explore factors that influence sample size calculations for mHealth–based studies and to suggest strategies for increasing the participation rate. Methods We explored factors influencing recruitment and follow–up of participants (caregivers of children) in an mHealth text messaging data collection cross–over study. With help of village doctors, we recruited 1026 (25%) caregivers of children under five out of the 4170 registered. To explore factors influencing recruitment and provide recommendations for improving recruitment, we conducted semi–structured interviews with village doctors. Of the 1014 included participants, 662 (65%) responded to the first question about willingness to participate, 538 (53%) responded to the first survey question and 356 (35%) completed the text message survey. To explore factors influencing follow–up and provide recommendations for improving follow–up, we conducted interviews with participants. We added views from the researchers who were involved in the study to contextualize the findings. Results We found several factors influencing recruitment related to the following themes: experiences with recruitment, village doctors’ work, village doctors’ motivations, caregivers’ characteristics, caregivers’ motivations. Village doctors gave several recommendations for ways to recruit more caregivers and we added our views to these. We found the following factors influencing follow–up: mobile phone usage, ability to use mobile phone, problems with mobile phone, checking mobile phone, available time, paying back text message costs, study incentives, subjective norm, culture, trust, perceived usefulness of process, perceived usefulness of outcome, perceived ease of use, attitude, behavioural intention to use, and actual use. From our perspective, factors influencing follow–up were: different
Biostatistics Series Module 5: Determining Sample Size
Hazra, Avijit; Gogtay, Nithya
2016-01-01
Determining the appropriate sample size for a study, whatever be its type, is a fundamental aspect of biomedical research. An adequate sample ensures that the study will yield reliable information, regardless of whether the data ultimately suggests a clinically important difference between the interventions or elements being studied. The probability of Type 1 and Type 2 errors, the expected variance in the sample and the effect size are the essential determinants of sample size in interventional studies. Any method for deriving a conclusion from experimental data carries with it some risk of drawing a false conclusion. Two types of false conclusion may occur, called Type 1 and Type 2 errors, whose probabilities are denoted by the symbols σ and β. A Type 1 error occurs when one concludes that a difference exists between the groups being compared when, in reality, it does not. This is akin to a false positive result. A Type 2 error occurs when one concludes that difference does not exist when, in reality, a difference does exist, and it is equal to or larger than the effect size defined by the alternative to the null hypothesis. This may be viewed as a false negative result. When considering the risk of Type 2 error, it is more intuitive to think in terms of power of the study or (1 − β). Power denotes the probability of detecting a difference when a difference does exist between the groups being compared. Smaller α or larger power will increase sample size. Conventional acceptable values for power and α are 80% or above and 5% or below, respectively, when calculating sample size. Increasing variance in the sample tends to increase the sample size required to achieve a given power level. The effect size is the smallest clinically important difference that is sought to be detected and, rather than statistical convention, is a matter of past experience and clinical judgment. Larger samples are required if smaller differences are to be detected. Although the
Sample size verification for clinical trials.
Shuster, Jonathan J
2014-02-01
In this paper, we shall provide simple methods where nonstatisticians can evaluate sample size calculations for most large simple trials, as an important part of the peer review process, whether a grant, an Institutional Review Board review, an internal scientific review committee, or a journal referee. Through the methods of the paper, not only can readers determine if there is a major disparity, but they can readily determine the correct sample size. It will be of comfort to find in most cases that the sample size computation is correct, but the implications can be major for the minority where serious errors occur. We shall provide three real examples, one where the sample size need was seriously overestimated, one (HIP PRO-test of a device to prevent hip fractures) where the sample size need was dramatically underestimated, and one where the sample size was correct. The HIP PRO case is especially troubling as it went through an NIH study section and two peer reviewed journal reports without anyone catching this sample size error of a factor of more than five-fold.
[Clinical research V. Sample size].
Talavera, Juan O; Rivas-Ruiz, Rodolfo; Bernal-Rosales, Laura Paola
2011-01-01
In clinical research it is impossible and inefficient to study all patients with a specific pathology, so it is necessary to study a sample of them. The estimation of the sample size before starting a study guarantees the stability of the results and allows us to foresee the feasibility of the study depending on the availability of patients and cost. The basic structure of sample size estimation is based on the premise that seeks to demonstrate, among other cases, that the observed difference between two or more maneuvers in the subsequent state is real. Initially, it requires knowing the value of the expected difference (δ) and its data variation (standard deviation). These data are usually obtained from previous studies. Then, other components must be considered: a (alpha), percentage of error in the assertion that the difference between means is real, usually 5 %; and β, error rate accepting the claim that the no-difference between the means is real, usually ranging from 15 to 20 %. Finally, these values are substituted into the formula or in an electronic program for estimating sample size. While summary and dispersion measures vary with the type of variable according to the outcome, the basic structure is the same.
Improving your Hypothesis Testing: Determining Sample Sizes.
ERIC Educational Resources Information Center
Luftig, Jeffrey T.; Norton, Willis P.
1982-01-01
This article builds on an earlier discussion of the importance of the Type II error (beta) and power to the hypothesis testing process (CE 511 484), and illustrates the methods by which sample size calculations should be employed so as to improve the research process. (Author/CT)
Improved sample size determination for attributes and variables sampling
Stirpe, D.; Picard, R.R.
1985-01-01
Earlier INMM papers have addressed the attributes/variables problem and, under conservative/limiting approximations, have reported analytical solutions for the attributes and variables sample sizes. Through computer simulation of this problem, we have calculated attributes and variables sample sizes as a function of falsification, measurement uncertainties, and required detection probability without using approximations. Using realistic assumptions for uncertainty parameters of measurement, the simulation results support the conclusions: (1) previously used conservative approximations can be expensive because they lead to larger sample sizes than needed; and (2) the optimal verification strategy, as well as the falsification strategy, are highly dependent on the underlying uncertainty parameters of the measurement instruments. 1 ref., 3 figs.
Sample size recalculation in sequential diagnostic trials.
Tang, Liansheng Larry; Liu, Aiyi
2010-01-01
Before a comparative diagnostic trial is carried out, maximum sample sizes for the diseased group and the nondiseased group need to be obtained to achieve a nominal power to detect a meaningful difference in diagnostic accuracy. Sample size calculation depends on the variance of the statistic of interest, which is the difference between receiver operating characteristic summary measures of 2 medical diagnostic tests. To obtain an appropriate value for the variance, one often has to assume an arbitrary parametric model and the associated parameter values for the 2 groups of subjects under 2 tests to be compared. It becomes more tedious to do so when the same subject undergoes 2 different tests because the correlation is then involved in modeling the test outcomes. The calculated variance based on incorrectly specified parametric models may be smaller than the true one, which will subsequently result in smaller maximum sample sizes, leaving the study underpowered. In this paper, we develop a nonparametric adaptive method for comparative diagnostic trials to update the sample sizes using interim data, while allowing early stopping during interim analyses. We show that the proposed method maintains the nominal power and type I error rate through theoretical proofs and simulation studies.
How Sample Size Affects a Sampling Distribution
ERIC Educational Resources Information Center
Mulekar, Madhuri S.; Siegel, Murray H.
2009-01-01
If students are to understand inferential statistics successfully, they must have a profound understanding of the nature of the sampling distribution. Specifically, they must comprehend the determination of the expected value and standard error of a sampling distribution as well as the meaning of the central limit theorem. Many students in a high…
Stepwise two-stage sample size adaptation.
Wan, Hong; Ellenberg, Susan S; Anderson, Keaven M
2015-01-15
Several adaptive design methods have been proposed to reestimate sample size using the observed treatment effect after an initial stage of a clinical trial while preserving the overall type I error at the time of the final analysis. One unfortunate property of the algorithms used in some methods is that they can be inverted to reveal the exact treatment effect at the interim analysis. We propose using a step function with an inverted U-shape of observed treatment difference for sample size reestimation to lessen the information on treatment effect revealed. This will be referred to as stepwise two-stage sample size adaptation. This method applies calculation methods used for group sequential designs. We minimize expected sample size among a class of these designs and compare efficiency with the fully optimized two-stage design, optimal two-stage group sequential design, and designs based on promising conditional power. The trade-off between efficiency versus the improved blinding of the interim treatment effect will be discussed.
NASA Astrophysics Data System (ADS)
Heckmann, Tobias; Gegg, Katharina; Becht, Michael
2013-04-01
Statistical approaches to landslide susceptibility modelling on the catchment and regional scale are used very frequently compared to heuristic and physically based approaches. In the present study, we deal with the problem of the optimal sample size for a logistic regression model. More specifically, a stepwise approach has been chosen in order to select those independent variables (from a number of derivatives of a digital elevation model and landcover data) that explain best the spatial distribution of debris flow initiation zones in two neighbouring central alpine catchments in Austria (used mutually for model calculation and validation). In order to minimise problems arising from spatial autocorrelation, we sample a single raster cell from each debris flow initiation zone within an inventory. In addition, as suggested by previous work using the "rare events logistic regression" approach, we take a sample of the remaining "non-event" raster cells. The recommendations given in the literature on the size of this sample appear to be motivated by practical considerations, e.g. the time and cost of acquiring data for non-event cases, which do not apply to the case of spatial data. In our study, we aim at finding empirically an "optimal" sample size in order to avoid two problems: First, a sample too large will violate the independent sample assumption as the independent variables are spatially autocorrelated; hence, a variogram analysis leads to a sample size threshold above which the average distance between sampled cells falls below the autocorrelation range of the independent variables. Second, if the sample is too small, repeated sampling will lead to very different results, i.e. the independent variables and hence the result of a single model calculation will be extremely dependent on the choice of non-event cells. Using a Monte-Carlo analysis with stepwise logistic regression, 1000 models are calculated for a wide range of sample sizes. For each sample size
Requirements for Minimum Sample Size for Sensitivity and Specificity Analysis
Adnan, Tassha Hilda
2016-01-01
Sensitivity and specificity analysis is commonly used for screening and diagnostic tests. The main issue researchers face is to determine the sufficient sample sizes that are related with screening and diagnostic studies. Although the formula for sample size calculation is available but concerning majority of the researchers are not mathematicians or statisticians, hence, sample size calculation might not be easy for them. This review paper provides sample size tables with regards to sensitivity and specificity analysis. These tables were derived from formulation of sensitivity and specificity test using Power Analysis and Sample Size (PASS) software based on desired type I error, power and effect size. The approaches on how to use the tables were also discussed. PMID:27891446
Adjustment for unbalanced sample size for analytical biosimilar equivalence assessment.
Dong, Xiaoyu Cassie; Weng, Yu-Ting; Tsong, Yi
2017-01-06
Large sample size imbalance is not uncommon in the biosimilar development. At the beginning of a product development, sample sizes of a biosimilar and a reference product may be limited. Thus, a sample size calculation may not be feasible. During the development stage, more batches of reference products may be added at a later stage to have a more reliable estimate of the reference variability. On the other hand, we also need a sufficient number of biosimilar batches in order to have a better understanding of the product. Those challenges lead to a potential sample size imbalance. In this paper, we show that large sample size imbalance may increase the power of the equivalence test in an unfavorable way, giving higher power for less similar products when the sample size of biosimilar is much smaller than that of the reference product. Thus, it is necessary to make some sample size imbalance adjustments to motivate sufficient sample size for biosimilar as well. This paper discusses two adjustment methods for the equivalence test in analytical biosimilarity studies. Please keep in mind that sufficient sample sizes for both biosimilar and reference products (if feasible) are desired during the planning stage.
Rock sampling. [apparatus for controlling particle size
NASA Technical Reports Server (NTRS)
Blum, P. (Inventor)
1971-01-01
An apparatus for sampling rock and other brittle materials and for controlling resultant particle sizes is described. The device includes grinding means for cutting grooves in the rock surface and to provide a grouping of thin, shallow, parallel ridges and cutter means to reduce these ridges to a powder specimen. Collection means is provided for the powder. The invention relates to rock grinding and particularly to the sampling of rock specimens with good size control.
[Effect sizes, statistical power and sample sizes in "the Japanese Journal of Psychology"].
Suzukawa, Yumi; Toyoda, Hideki
2012-04-01
This study analyzed the statistical power of research studies published in the "Japanese Journal of Psychology" in 2008 and 2009. Sample effect sizes and sample statistical powers were calculated for each statistical test and analyzed with respect to the analytical methods and the fields of the studies. The results show that in the fields like perception, cognition or learning, the effect sizes were relatively large, although the sample sizes were small. At the same time, because of the small sample sizes, some meaningful effects could not be detected. In the other fields, because of the large sample sizes, meaningless effects could be detected. This implies that researchers who could not get large enough effect sizes would use larger samples to obtain significant results.
Experimental determination of size distributions: analyzing proper sample sizes
NASA Astrophysics Data System (ADS)
Buffo, A.; Alopaeus, V.
2016-04-01
The measurement of various particle size distributions is a crucial aspect for many applications in the process industry. Size distribution is often related to the final product quality, as in crystallization or polymerization. In other cases it is related to the correct evaluation of heat and mass transfer, as well as reaction rates, depending on the interfacial area between the different phases or to the assessment of yield stresses of polycrystalline metals/alloys samples. The experimental determination of such distributions often involves laborious sampling procedures and the statistical significance of the outcome is rarely investigated. In this work, we propose a novel rigorous tool, based on inferential statistics, to determine the number of samples needed to obtain reliable measurements of size distribution, according to specific requirements defined a priori. Such methodology can be adopted regardless of the measurement technique used.
Kühberger, Anton; Fritz, Astrid; Scherndl, Thomas
2014-01-01
Background The p value obtained from a significance test provides no information about the magnitude or importance of the underlying phenomenon. Therefore, additional reporting of effect size is often recommended. Effect sizes are theoretically independent from sample size. Yet this may not hold true empirically: non-independence could indicate publication bias. Methods We investigate whether effect size is independent from sample size in psychological research. We randomly sampled 1,000 psychological articles from all areas of psychological research. We extracted p values, effect sizes, and sample sizes of all empirical papers, and calculated the correlation between effect size and sample size, and investigated the distribution of p values. Results We found a negative correlation of r = −.45 [95% CI: −.53; −.35] between effect size and sample size. In addition, we found an inordinately high number of p values just passing the boundary of significance. Additional data showed that neither implicit nor explicit power analysis could account for this pattern of findings. Conclusion The negative correlation between effect size and samples size, and the biased distribution of p values indicate pervasive publication bias in the entire field of psychology. PMID:25192357
Sample Size Determination for Clustered Count Data
Amatya, A.; Bhaumik, D.; Gibbons, R.D.
2013-01-01
We consider the problem of sample size determination for count data. Such data arise naturally in the context of multi-center (or cluster) randomized clinical trials, where patients are nested within research centers. We consider cluster-specific and population-average estimators (maximum likelihood based on generalized mixed-effects regression and generalized estimating equations respectively) for subject-level and cluster-level randomized designs respectively. We provide simple expressions for calculating number of clusters when comparing event rates of two groups in cross-sectional studies. The expressions we derive have closed form solutions and are based on either between-cluster variation or inter-cluster correlation for cross-sectional studies. We provide both theoretical and numerical comparisons of our methods with other existing methods. We specifically show that the performance of the proposed method is better for subject-level randomized designs, whereas the comparative performance depends on the rate ratio for the cluster-level randomized designs. We also provide a versatile method for longitudinal studies. Results are illustrated by three real data examples. PMID:23589228
Size safety valve discharge piping with a programmable calculator
D'ambra, A.
1982-10-01
Discussed is a program that will aid in the proper sizing of steam safety valve discharge piping frequently encountered in steam distribution systems. Basis for calculation is the ASME/ANSI Power Piping Code. Code reference is not necessary for running the program. Presented is a safety valve installation schematic, the program listing, data registers, constants, and a sample problem. The calculation done by this program is a fluid momentum check to assure that selected pipe sizes yield velocities and back pressures such that the steam blowing out of the safety valve is driven up the stack and not backwards out of the clearance. Back pressure should not exceed safety valve manufacturers' limits to realize full design capacity of the installation.
Heidel, R. Eric
2016-01-01
Statistical power is the ability to detect a significant effect, given that the effect actually exists in a population. Like most statistical concepts, statistical power tends to induce cognitive dissonance in hepatology researchers. However, planning for statistical power by an a priori sample size calculation is of paramount importance when designing a research study. There are five specific empirical components that make up an a priori sample size calculation: the scale of measurement of the outcome, the research design, the magnitude of the effect size, the variance of the effect size, and the sample size. A framework grounded in the phenomenon of isomorphism, or interdependencies amongst different constructs with similar forms, will be presented to understand the isomorphic effects of decisions made on each of the five aforementioned components of statistical power. PMID:27073717
Sample size of the reference sample in a case-augmented study.
Ghosh, Palash; Dewanji, Anup
2017-03-13
The case-augmented study, in which a case sample is augmented with a reference (random) sample from the source population with only covariates information known, is becoming popular in different areas of applied science such as pharmacovigilance, ecology, and econometrics. In general, the case sample is available from some source (for example, hospital database, case registry, etc.); however, the reference sample is required to be drawn from the corresponding source population. The required minimum size of the reference sample is an important issue in this regard. In this work, we address the minimum sample size calculation and discuss related issues. Copyright © 2017 John Wiley & Sons, Ltd.
Exploratory Factor Analysis with Small Sample Sizes
ERIC Educational Resources Information Center
de Winter, J. C. F.; Dodou, D.; Wieringa, P. A.
2009-01-01
Exploratory factor analysis (EFA) is generally regarded as a technique for large sample sizes ("N"), with N = 50 as a reasonable absolute minimum. This study offers a comprehensive overview of the conditions in which EFA can yield good quality results for "N" below 50. Simulations were carried out to estimate the minimum required "N" for different…
Sample size considerations for clinical research studies in nuclear cardiology.
Chiuzan, Cody; West, Erin A; Duong, Jimmy; Cheung, Ken Y K; Einstein, Andrew J
2015-12-01
Sample size calculation is an important element of research design that investigators need to consider in the planning stage of the study. Funding agencies and research review panels request a power analysis, for example, to determine the minimum number of subjects needed for an experiment to be informative. Calculating the right sample size is crucial to gaining accurate information and ensures that research resources are used efficiently and ethically. The simple question "How many subjects do I need?" does not always have a simple answer. Before calculating the sample size requirements, a researcher must address several aspects, such as purpose of the research (descriptive or comparative), type of samples (one or more groups), and data being collected (continuous or categorical). In this article, we describe some of the most frequent methods for calculating the sample size with examples from nuclear cardiology research, including for t tests, analysis of variance (ANOVA), non-parametric tests, correlation, Chi-squared tests, and survival analysis. For the ease of implementation, several examples are also illustrated via user-friendly free statistical software.
Predicting sample size required for classification performance
2012-01-01
Background Supervised learning methods need annotated data in order to generate efficient models. Annotated data, however, is a relatively scarce resource and can be expensive to obtain. For both passive and active learning methods, there is a need to estimate the size of the annotated sample required to reach a performance target. Methods We designed and implemented a method that fits an inverse power law model to points of a given learning curve created using a small annotated training set. Fitting is carried out using nonlinear weighted least squares optimization. The fitted model is then used to predict the classifier's performance and confidence interval for larger sample sizes. For evaluation, the nonlinear weighted curve fitting method was applied to a set of learning curves generated using clinical text and waveform classification tasks with active and passive sampling methods, and predictions were validated using standard goodness of fit measures. As control we used an un-weighted fitting method. Results A total of 568 models were fitted and the model predictions were compared with the observed performances. Depending on the data set and sampling method, it took between 80 to 560 annotated samples to achieve mean average and root mean squared error below 0.01. Results also show that our weighted fitting method outperformed the baseline un-weighted method (p < 0.05). Conclusions This paper describes a simple and effective sample size prediction algorithm that conducts weighted fitting of learning curves. The algorithm outperformed an un-weighted algorithm described in previous literature. It can help researchers determine annotation sample size for supervised machine learning. PMID:22336388
Statistical Analysis Techniques for Small Sample Sizes
NASA Technical Reports Server (NTRS)
Navard, S. E.
1984-01-01
The small sample sizes problem which is encountered when dealing with analysis of space-flight data is examined. Because of such a amount of data available, careful analyses are essential to extract the maximum amount of information with acceptable accuracy. Statistical analysis of small samples is described. The background material necessary for understanding statistical hypothesis testing is outlined and the various tests which can be done on small samples are explained. Emphasis is on the underlying assumptions of each test and on considerations needed to choose the most appropriate test for a given type of analysis.
Sample size and optimal sample design in tuberculosis surveys
Sánchez-Crespo, J. L.
1967-01-01
Tuberculosis surveys sponsored by the World Health Organization have been carried out in different communities during the last few years. Apart from the main epidemiological findings, these surveys have provided basic statistical data for use in the planning of future investigations. In this paper an attempt is made to determine the sample size desirable in future surveys that include one of the following examinations: tuberculin test, direct microscopy, and X-ray examination. The optimum cluster sizes are found to be 100-150 children under 5 years of age in the tuberculin test, at least 200 eligible persons in the examination for excretors of tubercle bacilli (direct microscopy) and at least 500 eligible persons in the examination for persons with radiological evidence of pulmonary tuberculosis (X-ray). Modifications of the optimum sample size in combined surveys are discussed. PMID:5300008
Information Conversion, Effective Samples, and Parameter Size
Lin, Xiaodong; Pittman, Jennifer; Clarke, Bertrand
2008-01-01
Consider the relative entropy between a posterior density for a parameter given a sample and a second posterior density for the same parameter, based on a different model and a different data set. Then the relative entropy can be minimized over the second sample to get a virtual sample that would make the second posterior as close as possible to the first in an informational sense. If the first posterior is based on a dependent dataset and the second posterior uses an independence model, the effective inferential power of the dependent sample is transferred into the independent sample by the optimization. Examples of this optimization are presented for models with nuisance parameters, finite mixture models, and models for correlated data. Our approach is also used to choose the effective parameter size in a Bayesian hierarchical model. PMID:19079764
The cost of large numbers of hypothesis tests on power, effect size and sample size.
Lazzeroni, L C; Ray, A
2012-01-01
Advances in high-throughput biology and computer science are driving an exponential increase in the number of hypothesis tests in genomics and other scientific disciplines. Studies using current genotyping platforms frequently include a million or more tests. In addition to the monetary cost, this increase imposes a statistical cost owing to the multiple testing corrections needed to avoid large numbers of false-positive results. To safeguard against the resulting loss of power, some have suggested sample sizes on the order of tens of thousands that can be impractical for many diseases or may lower the quality of phenotypic measurements. This study examines the relationship between the number of tests on the one hand and power, detectable effect size or required sample size on the other. We show that once the number of tests is large, power can be maintained at a constant level, with comparatively small increases in the effect size or sample size. For example at the 0.05 significance level, a 13% increase in sample size is needed to maintain 80% power for ten million tests compared with one million tests, whereas a 70% increase in sample size is needed for 10 tests compared with a single test. Relative costs are less when measured by increases in the detectable effect size. We provide an interactive Excel calculator to compute power, effect size or sample size when comparing study designs or genome platforms involving different numbers of hypothesis tests. The results are reassuring in an era of extreme multiple testing.
Calculation of the size of ice hummocks
Kozitskii, I.E.
1985-03-01
Ice hummocks are often seen during the breakup of water bodies and are the result of shifting of the ice cover during spring movements and are confined both to the shore slope, or exposed stretches of the bottom, and to shallow waters. At the same time, the shore is often used for needs of construction, transportation, power engineering and economic purposes, and cases of damage to structures and disruption of operations by ice hummocks are known. The authors therefore study here the character and extent of the phenomenon as it affects the design of shore engineering structures. They add that existing standards do not fully reflect the composition of ice loads on structures, in connection with which it is expedient to theorize as regards the expected size of ice hummocks.
Conservative Sample Size Determination for Repeated Measures Analysis of Covariance.
Morgan, Timothy M; Case, L Douglas
2013-07-05
In the design of a randomized clinical trial with one pre and multiple post randomized assessments of the outcome variable, one needs to account for the repeated measures in determining the appropriate sample size. Unfortunately, one seldom has a good estimate of the variance of the outcome measure, let alone the correlations among the measurements over time. We show how sample sizes can be calculated by making conservative assumptions regarding the correlations for a variety of covariance structures. The most conservative choice for the correlation depends on the covariance structure and the number of repeated measures. In the absence of good estimates of the correlations, the sample size is often based on a two-sample t-test, making the 'ultra' conservative and unrealistic assumption that there are zero correlations between the baseline and follow-up measures while at the same time assuming there are perfect correlations between the follow-up measures. Compared to the case of taking a single measurement, substantial savings in sample size can be realized by accounting for the repeated measures, even with very conservative assumptions regarding the parameters of the assumed correlation matrix. Assuming compound symmetry, the sample size from the two-sample t-test calculation can be reduced at least 44%, 56%, and 61% for repeated measures analysis of covariance by taking 2, 3, and 4 follow-up measures, respectively. The results offer a rational basis for determining a fairly conservative, yet efficient, sample size for clinical trials with repeated measures and a baseline value.
Sample size estimation and power analysis for clinical research studies
Suresh, KP; Chandrashekara, S
2012-01-01
Determining the optimal sample size for a study assures an adequate power to detect statistical significance. Hence, it is a critical step in the design of a planned research protocol. Using too many participants in a study is expensive and exposes more number of subjects to procedure. Similarly, if study is underpowered, it will be statistically inconclusive and may make the whole protocol a failure. This paper covers the essentials in calculating power and sample size for a variety of applied study designs. Sample size computation for single group mean, survey type of studies, 2 group studies based on means and proportions or rates, correlation studies and for case-control for assessing the categorical outcome are presented in detail. PMID:22870008
40 CFR 80.127 - Sample size guidelines.
Code of Federal Regulations, 2011 CFR
2011-07-01
... attest engagement, the auditor shall sample relevant populations to which agreed-upon procedures will be... population; and (b) Sample size shall be determined using one of the following options: (1) Option 1. Determine the sample size using the following table: Sample Size, Based Upon Population Size No....
(Sample) Size Matters! An Examination of Sample Size from the SPRINT Trial
Bhandari, Mohit; Tornetta, Paul; Rampersad, Shelly-Ann; Sprague, Sheila; Heels-Ansdell, Diane; Sanders, David W.; Schemitsch, Emil H.; Swiontkowski, Marc; Walter, Stephen
2012-01-01
Introduction Inadequate sample size and power in randomized trials can result in misleading findings. This study demonstrates the effect of sample size in a large, clinical trial by evaluating the results of the SPRINT (Study to Prospectively evaluate Reamed Intramedullary Nails in Patients with Tibial fractures) trial as it progressed. Methods The SPRINT trial evaluated reamed versus unreamed nailing of the tibia in 1226 patients, as well as in open and closed fracture subgroups (N=400 and N=826, respectively). We analyzed the re-operation rates and relative risk comparing treatment groups at 50, 100 and then increments of 100 patients up to the final sample size. Results at various enrollments were compared to the final SPRINT findings. Results In the final analysis, there was a statistically significant decreased risk of re-operation with reamed nails for closed fractures (relative risk reduction 35%). Results for the first 35 patients enrolled suggested reamed nails increased the risk of reoperation in closed fractures by 165%. Only after 543 patients with closed fractures were enrolled did the results reflect the final advantage for reamed nails in this subgroup. Similarly, the trend towards an increased risk of re-operation for open fractures (23%) was not seen until 62 patients with open fractures were enrolled. Conclusions Our findings highlight the risk of conducting a trial with insufficient sample size and power. Such studies are not only at risk of missing true effects, but also of giving misleading results. Level of Evidence N/A PMID:23525086
Cusp Catastrophe Polynomial Model: Power and Sample Size Estimation
Chen, Ding-Geng(Din); Chen, Xinguang(Jim); Lin, Feng; Tang, Wan; Lio, Y. L.; Guo, (Tammy) Yuanyuan
2016-01-01
Guastello’s polynomial regression method for solving cusp catastrophe model has been widely applied to analyze nonlinear behavior outcomes. However, no statistical power analysis for this modeling approach has been reported probably due to the complex nature of the cusp catastrophe model. Since statistical power analysis is essential for research design, we propose a novel method in this paper to fill in the gap. The method is simulation-based and can be used to calculate statistical power and sample size when Guastello’s polynomial regression method is used to cusp catastrophe modeling analysis. With this novel approach, a power curve is produced first to depict the relationship between statistical power and samples size under different model specifications. This power curve is then used to determine sample size required for specified statistical power. We verify the method first through four scenarios generated through Monte Carlo simulations, and followed by an application of the method with real published data in modeling early sexual initiation among young adolescents. Findings of our study suggest that this simulation-based power analysis method can be used to estimate sample size and statistical power for Guastello’s polynomial regression method in cusp catastrophe modeling. PMID:27158562
Effect size estimates: current use, calculations, and interpretation.
Fritz, Catherine O; Morris, Peter E; Richler, Jennifer J
2012-02-01
The Publication Manual of the American Psychological Association (American Psychological Association, 2001, American Psychological Association, 2010) calls for the reporting of effect sizes and their confidence intervals. Estimates of effect size are useful for determining the practical or theoretical importance of an effect, the relative contributions of factors, and the power of an analysis. We surveyed articles published in 2009 and 2010 in the Journal of Experimental Psychology: General, noting the statistical analyses reported and the associated reporting of effect size estimates. Effect sizes were reported for fewer than half of the analyses; no article reported a confidence interval for an effect size. The most often reported analysis was analysis of variance, and almost half of these reports were not accompanied by effect sizes. Partial η2 was the most commonly reported effect size estimate for analysis of variance. For t tests, 2/3 of the articles did not report an associated effect size estimate; Cohen's d was the most often reported. We provide a straightforward guide to understanding, selecting, calculating, and interpreting effect sizes for many types of data and to methods for calculating effect size confidence intervals and power analysis.
Public Opinion Polls, Chicken Soup and Sample Size
ERIC Educational Resources Information Center
Nguyen, Phung
2005-01-01
Cooking and tasting chicken soup in three different pots of very different size serves to demonstrate that it is the absolute sample size that matters the most in determining the accuracy of the findings of the poll, not the relative sample size, i.e. the size of the sample in relation to its population.
7 CFR 52.3757 - Standard sample unit size.
Code of Federal Regulations, 2014 CFR
2014-01-01
... Ripe Olives 1 Product Description, Types, Styles, and Grades § 52.3757 Standard sample unit size... following standard sample unit size for the applicable style: (a) Whole and pitted—50 olives. (b)...
7 CFR 52.3757 - Standard sample unit size.
Code of Federal Regulations, 2013 CFR
2013-01-01
... Ripe Olives 1 Product Description, Types, Styles, and Grades § 52.3757 Standard sample unit size... following standard sample unit size for the applicable style: (a) Whole and pitted—50 olives. (b)...
[Unconditioned logistic regression and sample size: a bibliographic review].
Ortega Calvo, Manuel; Cayuela Domínguez, Aurelio
2002-01-01
Unconditioned logistic regression is a highly useful risk prediction method in epidemiology. This article reviews the different solutions provided by different authors concerning the interface between the calculation of the sample size and the use of logistics regression. Based on the knowledge of the information initially provided, a review is made of the customized regression and predictive constriction phenomenon, the design of an ordinal exposition with a binary output, the event of interest per variable concept, the indicator variables, the classic Freeman equation, etc. Some skeptical ideas regarding this subject are also included.
The Relationship between Sample Sizes and Effect Sizes in Systematic Reviews in Education
ERIC Educational Resources Information Center
Slavin, Robert; Smith, Dewi
2009-01-01
Research in fields other than education has found that studies with small sample sizes tend to have larger effect sizes than those with large samples. This article examines the relationship between sample size and effect size in education. It analyzes data from 185 studies of elementary and secondary mathematics programs that met the standards of…
Optimal flexible sample size design with robust power.
Zhang, Lanju; Cui, Lu; Yang, Bo
2016-08-30
It is well recognized that sample size determination is challenging because of the uncertainty on the treatment effect size. Several remedies are available in the literature. Group sequential designs start with a sample size based on a conservative (smaller) effect size and allow early stop at interim looks. Sample size re-estimation designs start with a sample size based on an optimistic (larger) effect size and allow sample size increase if the observed effect size is smaller than planned. Different opinions favoring one type over the other exist. We propose an optimal approach using an appropriate optimality criterion to select the best design among all the candidate designs. Our results show that (1) for the same type of designs, for example, group sequential designs, there is room for significant improvement through our optimization approach; (2) optimal promising zone designs appear to have no advantages over optimal group sequential designs; and (3) optimal designs with sample size re-estimation deliver the best adaptive performance. We conclude that to deal with the challenge of sample size determination due to effect size uncertainty, an optimal approach can help to select the best design that provides most robust power across the effect size range of interest. Copyright © 2016 John Wiley & Sons, Ltd.
7 CFR 52.775 - Sample unit size.
Code of Federal Regulations, 2014 CFR
2014-01-01
... Cherries 1 Sample Unit Size § 52.775 Sample unit size. Compliance with requirements for the size and the..., color, pits, and character—20 ounces of drained cherries. (b) Defects (other than harmless extraneous material)—100 cherries. (c) Harmless extraneous material—The total contents of each container in the...
7 CFR 52.803 - Sample unit size.
Code of Federal Regulations, 2010 CFR
2010-01-01
... PROCESSED FRUITS AND VEGETABLES, PROCESSED PRODUCTS THEREOF, AND CERTAIN OTHER PROCESSED FOOD PRODUCTS 1 United States Standards for Grades of Frozen Red Tart Pitted Cherries Sample Unit Size § 52.803 Sample unit size. Compliance with requirements for size and the various quality factors is based on...
7 CFR 52.803 - Sample unit size.
Code of Federal Regulations, 2011 CFR
2011-01-01
... PROCESSED FRUITS AND VEGETABLES, PROCESSED PRODUCTS THEREOF, AND CERTAIN OTHER PROCESSED FOOD PRODUCTS 1 United States Standards for Grades of Frozen Red Tart Pitted Cherries Sample Unit Size § 52.803 Sample unit size. Compliance with requirements for size and the various quality factors is based on...
7 CFR 52.803 - Sample unit size.
Code of Federal Regulations, 2012 CFR
2012-01-01
... PROCESSED FRUITS AND VEGETABLES, PROCESSED PRODUCTS THEREOF, AND CERTAIN OTHER PROCESSED FOOD PRODUCTS 1 United States Standards for Grades of Frozen Red Tart Pitted Cherries Sample Unit Size § 52.803 Sample unit size. Compliance with requirements for size and the various quality factors is based on...
7 CFR 52.775 - Sample unit size.
Code of Federal Regulations, 2013 CFR
2013-01-01
... Cherries 1 Sample Unit Size § 52.775 Sample unit size. Compliance with requirements for the size and the..., color, pits, and character—20 ounces of drained cherries. (b) Defects (other than harmless extraneous material)—100 cherries. (c) Harmless extraneous material—The total contents of each container in the...
Are Sample Sizes Clear and Justified in RCTs Published in Dental Journals?
Koletsi, Despina; Fleming, Padhraig S.; Seehra, Jadbinder; Bagos, Pantelis G.; Pandis, Nikolaos
2014-01-01
Sample size calculations are advocated by the CONSORT group to justify sample sizes in randomized controlled trials (RCTs). The aim of this study was primarily to evaluate the reporting of sample size calculations, to establish the accuracy of these calculations in dental RCTs and to explore potential predictors associated with adequate reporting. Electronic searching was undertaken in eight leading specific and general dental journals. Replication of sample size calculations was undertaken where possible. Assumed variances or odds for control and intervention groups were also compared against those observed. The relationship between parameters including journal type, number of authors, trial design, involvement of methodologist, single-/multi-center study and region and year of publication, and the accuracy of sample size reporting was assessed using univariable and multivariable logistic regression. Of 413 RCTs identified, sufficient information to allow replication of sample size calculations was provided in only 121 studies (29.3%). Recalculations demonstrated an overall median overestimation of sample size of 15.2% after provisions for losses to follow-up. There was evidence that journal, methodologist involvement (OR = 1.97, CI: 1.10, 3.53), multi-center settings (OR = 1.86, CI: 1.01, 3.43) and time since publication (OR = 1.24, CI: 1.12, 1.38) were significant predictors of adequate description of sample size assumptions. Among journals JCP had the highest odds of adequately reporting sufficient data to permit sample size recalculation, followed by AJODO and JDR, with 61% (OR = 0.39, CI: 0.19, 0.80) and 66% (OR = 0.34, CI: 0.15, 0.75) lower odds, respectively. Both assumed variances and odds were found to underestimate the observed values. Presentation of sample size calculations in the dental literature is suboptimal; incorrect assumptions may have a bearing on the power of RCTs. PMID:24465806
Cairns, David A; Barrett, Jennifer H; Billingham, Lucinda J; Stanley, Anthea J; Xinarianos, George; Field, John K; Johnson, Phillip J; Selby, Peter J; Banks, Rosamonde E
2009-01-01
Mass spectrometric profiling approaches such as MALDI-TOF and SELDI-TOF are increasingly being used in disease marker discovery, particularly in the lower molecular weight proteome. However, little consideration has been given to the issue of sample size in experimental design. The aim of this study was to develop a protocol for the use of sample size calculations in proteomic profiling studies using MS. These sample size calculations can be based on a simple linear mixed model which allows the inclusion of estimates of biological and technical variation inherent in the experiment. The use of a pilot experiment to estimate these components of variance is investigated and is shown to work well when compared with larger studies. Examination of data from a number of studies using different sample types and different chromatographic surfaces shows the need for sample- and preparation-specific sample size calculations.
Nonlinearity of Argon Isotope Measurements for Samples of Different Sizes
NASA Astrophysics Data System (ADS)
Cox, S. E.; Hemming, S. R.; Turrin, B. D.; Swisher, C. C.
2010-12-01
Uncertainty in isotope ratio linearity is not propagated into the final uncertainty of high-precision Ar-Ar analyses. Nonlinearity is assumed to be negligible compared to other sources of error, so mass discrimination is calculated using air pipettes of a single size similar to typical unknowns. The calculated discrimination factor is applied to all measured isotopes regardless of the difference in relative isotope abundance or the difference in gas pressure between the sample and the air pipette. We measured 40Ar/36Ar ratios of different size air samples created using up to twenty pipette shots on two different mass spectrometers with automated air pipette systems (a VG5400 and an MAP 215-50) in order to test the assumption that the measured isotope ratios are consistent at different gas pressures. We typically obtain reproducibility < 0.5% on the 40Ar/36Ar of similar size air standards, but we measured 40Ar/36Ar ratios for aliquots 0.5 to 20 times the typical volume from the same reservoir that varied by as much as 10% (Figure 1). In sets VG1, VG2, and MAP, 40Ar/36Ar ratios increased with gas pressure (expressed as number of air pipette shots; R2 > 0.9). Several months later, we performed the same measurements on the VG5400 with a new filament and different tuning parameters and obtained a different result (Set VG3). In this case, the 40Ar/36Ar ratios still varied with gas pressure, but less drastically (R2 > 0.3), and the slope was reversed--40Ar/36Ar ratios decreased with gas pressure. We conclude that isotope ratio nonlinearity is a common phenomenon that has the potential to affect monitor standard and timescale age calculations at the 0.1% level of significance defined by EARTHTIME. We propose that argon labs incorporate air pipettes of varying size and isotopic compositions to allow for routine calibration of isotope ratio nonlinearity in the course of high-precision analyses. Figure 1: Measured 40Ar/36Ar vs. number of air pipettes. Sets VG1, VG2, and MAP
Sample size determination in medical and surgical research.
Flikkema, Robert M; Toledo-Pereyra, Luis H
2012-02-01
One of the most critical yet frequently misunderstood principles of research is sample size determination. Obtaining an inadequate sample is a serious problem that can invalidate an entire study. Without an extensive background in statistics, the seemingly simple question of selecting a sample size can become quite a daunting task. This article aims to give a researcher with no background in statistics the basic tools needed for sample size determination. After reading this article, the researcher will be aware of all the factors involved in a power analysis and will be able to work more effectively with the statistician when determining sample size. This work also reviews the power of a statistical hypothesis, as well as how to estimate the effect size of a research study. These are the two key components of sample size determination. Several examples will be considered throughout the text.
40 CFR 600.208-77 - Sample calculation.
Code of Federal Regulations, 2010 CFR
2010-07-01
... ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Fuel Economy Regulations for 1977 and Later Model Year Automobiles-Procedures for Calculating Fuel Economy Values § 600.208-77 Sample...
Estimating optimal sampling unit sizes for satellite surveys
NASA Technical Reports Server (NTRS)
Hallum, C. R.; Perry, C. R., Jr.
1984-01-01
This paper reports on an approach for minimizing data loads associated with satellite-acquired data, while improving the efficiency of global crop area estimates using remotely sensed, satellite-based data. Results of a sampling unit size investigation are given that include closed-form models for both nonsampling and sampling error variances. These models provide estimates of the sampling unit sizes that effect minimal costs. Earlier findings from foundational sampling unit size studies conducted by Mahalanobis, Jessen, Cochran, and others are utilized in modeling the sampling error variance as a function of sampling unit size. A conservative nonsampling error variance model is proposed that is realistic in the remote sensing environment where one is faced with numerous unknown nonsampling errors. This approach permits the sampling unit size selection in the global crop inventorying environment to be put on a more quantitative basis while conservatively guarding against expected component error variances.
How Small Is Big: Sample Size and Skewness.
Piovesana, Adina; Senior, Graeme
2016-09-21
Sample sizes of 50 have been cited as sufficient to obtain stable means and standard deviations in normative test data. The influence of skewness on this minimum number, however, has not been evaluated. Normative test data with varying levels of skewness were compiled for 12 measures from 7 tests collected as part of ongoing normative studies in Brisbane, Australia. Means and standard deviations were computed from sample sizes of 10 to 100 drawn with replacement from larger samples of 272 to 973 cases. The minimum sample size was determined by the number at which both mean and standard deviation estimates remained within the 90% confidence intervals surrounding the population estimates. Sample sizes of greater than 85 were found to generate stable means and standard deviations regardless of the level of skewness, with smaller samples required in skewed distributions. A formula was derived to compute recommended sample size at differing levels of skewness.
NASA Astrophysics Data System (ADS)
Campolina, Daniel de A. M.; Lima, Claubia P. B.; Veloso, Maria Auxiliadora F.
2014-06-01
For all the physical components that comprise a nuclear system there is an uncertainty. Assessing the impact of uncertainties in the simulation of fissionable material systems is essential for a best estimate calculation that has been replacing the conservative model calculations as the computational power increases. The propagation of uncertainty in a simulation using a Monte Carlo code by sampling the input parameters is recent because of the huge computational effort required. In this work a sample space of MCNPX calculations was used to propagate the uncertainty. The sample size was optimized using the Wilks formula for a 95th percentile and a two-sided statistical tolerance interval of 95%. Uncertainties in input parameters of the reactor considered included geometry dimensions and densities. It was showed the capacity of the sampling-based method for burnup when the calculations sample size is optimized and many parameter uncertainties are investigated together, in the same input.
Estimation of sample size and testing power (Part 4).
Hu, Liang-ping; Bao, Xiao-lei; Guan, Xue; Zhou, Shi-guo
2012-01-01
Sample size estimation is necessary for any experimental or survey research. An appropriate estimation of sample size based on known information and statistical knowledge is of great significance. This article introduces methods of sample size estimation of difference test for data with the design of one factor with two levels, including sample size estimation formulas and realization based on the formulas and the POWER procedure of SAS software for quantitative data and qualitative data with the design of one factor with two levels. In addition, this article presents examples for analysis, which will play a leading role for researchers to implement the repetition principle during the research design phase.
40 CFR 761.286 - Sample size and procedure for collecting a sample.
Code of Federal Regulations, 2010 CFR
2010-07-01
..., DISTRIBUTION IN COMMERCE, AND USE PROHIBITIONS Sampling To Verify Completion of Self-Implementing Cleanup and...) § 761.286 Sample size and procedure for collecting a sample. At each selected sampling location for...
40 CFR 80.127 - Sample size guidelines.
Code of Federal Regulations, 2010 CFR
2010-07-01
...) REGULATION OF FUELS AND FUEL ADDITIVES Attest Engagements § 80.127 Sample size guidelines. In performing the attest engagement, the auditor shall sample relevant populations to which agreed-upon procedures will...
7 CFR 52.775 - Sample unit size.
Code of Federal Regulations, 2011 CFR
2011-01-01
... United States Standards for Grades of Canned Red Tart Pitted Cherries 1 Sample Unit Size § 52.775 Sample... drained cherries. (b) Defects (other than harmless extraneous material)—100 cherries. (c)...
Sample size reassessment for a two-stage design controlling the false discovery rate
Zehetmayer, Sonja; Graf, Alexandra C.; Posch, Martin
2016-01-01
Sample size calculations for gene expression microarray and NGS-RNA-Seq experiments are challenging because the overall power depends on unknown quantities as the proportion of true null hypotheses and the distribution of the effect sizes under the alternative. We propose a two-stage design with an adaptive interim analysis where these quantities are estimated from the interim data. The second stage sample size is chosen based on these estimates to achieve a specific overall power. The proposed procedure controls the power in all considered scenarios except for very low first stage sample sizes. The false discovery rate (FDR) is controlled despite of the data dependent choice of sample size. The two-stage design can be a useful tool to determine the sample size of high-dimensional studies if in the planning phase there is high uncertainty regarding the expected effect sizes and variability. PMID:26461844
Preliminary Proactive Sample Size Determination for Confirmatory Factor Analysis Models
ERIC Educational Resources Information Center
Koran, Jennifer
2016-01-01
Proactive preliminary minimum sample size determination can be useful for the early planning stages of a latent variable modeling study to set a realistic scope, long before the model and population are finalized. This study examined existing methods and proposed a new method for proactive preliminary minimum sample size determination.
Sample Size Requirements for Estimating Pearson, Spearman and Kendall Correlations.
ERIC Educational Resources Information Center
Bonett, Douglas G.; Wright, Thomas A.
2000-01-01
Reviews interval estimates of the Pearson, Kendall tau-alpha, and Spearman correlates and proposes an improved standard error for the Spearman correlation. Examines the sample size required to yield a confidence interval having the desired width. Findings show accurate results from a two-stage approximation to the sample size. (SLD)
Sample Sizes when Using Multiple Linear Regression for Prediction
ERIC Educational Resources Information Center
Knofczynski, Gregory T.; Mundfrom, Daniel
2008-01-01
When using multiple regression for prediction purposes, the issue of minimum required sample size often needs to be addressed. Using a Monte Carlo simulation, models with varying numbers of independent variables were examined and minimum sample sizes were determined for multiple scenarios at each number of independent variables. The scenarios…
ERIC Educational Resources Information Center
Sahin, Alper; Weiss, David J.
2015-01-01
This study aimed to investigate the effects of calibration sample size and item bank size on examinee ability estimation in computerized adaptive testing (CAT). For this purpose, a 500-item bank pre-calibrated using the three-parameter logistic model with 10,000 examinees was simulated. Calibration samples of varying sizes (150, 250, 350, 500,…
Ultrasonic energy in liposome production: process modelling and size calculation.
Barba, A A; Bochicchio, S; Lamberti, G; Dalmoro, A
2014-04-21
The use of liposomes in several fields of biotechnology, as well as in pharmaceutical and food sciences is continuously increasing. Liposomes can be used as carriers for drugs and other active molecules. Among other characteristics, one of the main features relevant to their target applications is the liposome size. The size of liposomes, which is determined during the production process, decreases due to the addition of energy. The energy is used to break the lipid bilayer into smaller pieces, then these pieces close themselves in spherical structures. In this work, the mechanisms of rupture of the lipid bilayer and the formation of spheres were modelled, accounting for how the energy, supplied by ultrasonic radiation, is stored within the layers, as the elastic energy due to the curvature and as the tension energy due to the edge, and to account for the kinetics of the bending phenomenon. An algorithm to solve the model equations was designed and the relative calculation code was written. A dedicated preparation protocol, which involves active periods during which the energy is supplied and passive periods during which the energy supply is set to zero, was defined and applied. The model predictions compare well with the experimental results, by using the energy supply rate and the time constant as fitting parameters. Working with liposomes of different sizes as the starting point of the experiments, the key parameter is the ratio between the energy supply rate and the initial surface area.
Application of bag sampling technique for particle size distribution measurements.
Mazaheri, M; Johnson, G R; Morawska, L
2009-11-01
Bag sampling techniques can be used to temporarily store the aerosol and therefore provide sufficient time to utilize sensitive but slow instrumental techniques for recording detailed particle size distributions. Laboratory based assessment of the method was conducted to examine size dependant deposition loss coefficients for aerosols held in Velostat bags conforming to a horizontal cylindrical geometry. Deposition losses of NaCl particles in the range of 10 nm to 160 nm were analysed in relation to the bag size, storage time, and sampling flow rate. Results of this study suggest that the bag sampling method is most useful for moderately short sampling periods of about 5 minutes.
SNS Sample Activation Calculator Flux Recommendations and Validation
McClanahan, Tucker C.; Gallmeier, Franz X.; Iverson, Erik B.; Lu, Wei
2015-02-01
The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) uses the Sample Activation Calculator (SAC) to calculate the activation of a sample after the sample has been exposed to the neutron beam in one of the SNS beamlines. The SAC webpage takes user inputs (choice of beamline, the mass, composition and area of the sample, irradiation time, decay time, etc.) and calculates the activation for the sample. In recent years, the SAC has been incorporated into the user proposal and sample handling process, and instrument teams and users have noticed discrepancies in the predicted activation of their samples. The Neutronics Analysis Team validated SAC by performing measurements on select beamlines and confirmed the discrepancies seen by the instrument teams and users. The conclusions were that the discrepancies were a result of a combination of faulty neutron flux spectra for the instruments, improper inputs supplied by SAC (1.12), and a mishandling of cross section data in the Sample Activation Program for Easy Use (SAPEU) (1.1.2). This report focuses on the conclusion that the SAPEU (1.1.2) beamline neutron flux spectra have errors and are a significant contributor to the activation discrepancies. The results of the analysis of the SAPEU (1.1.2) flux spectra for all beamlines will be discussed in detail. The recommendations for the implementation of improved neutron flux spectra in SAPEU (1.1.3) are also discussed.
How to calculate normal curvatures of sampled geological surfaces
NASA Astrophysics Data System (ADS)
Bergbauer, Stephan; Pollard, David D.
2003-02-01
Curvature has been used both to describe geological surfaces and to predict the distribution of deformation in folded or domed strata. Several methods have been proposed in the geoscience literature to approximate the curvature of surfaces; however we advocate a technique for the exact calculation of normal curvature for single-valued gridded surfaces. This technique, based on the First and Second Fundamental Forms of differential geometry, allows for the analytical calculation of the magnitudes and directions of principal curvatures, as well as Gaussian and mean curvature. This approach is an improvement over previous methods to calculate surface curvatures because it avoids common mathematical approximations, which introduce significant errors when calculated over sloped horizons. Moreover, the technique is easily implemented numerically as it calculates curvatures directly from gridded surface data (e.g. seismic or GPS data) without prior surface triangulation. In geological curvature analyses, problems arise because of the sampled nature of geological horizons, which introduces a dependence of calculated curvatures on the sample grid. This dependence makes curvature analysis without prior data manipulation problematic. To ensure a meaningful curvature analysis, surface data should be filtered to extract only those surface wavelengths that scale with the feature under investigation. A curvature analysis of the top-Pennsylvanian horizon at Goose Egg dome, Wyoming shows that sampled surfaces can be smoothed using a moving average low-pass filter to extract curvature information associated with the true morphology of the structure.
Alpha values as a function of sample size, effect size, and power: accuracy over inference.
Bradley, M T; Brand, A
2013-06-01
Tables of alpha values as a function of sample size, effect size, and desired power were presented. The tables indicated expected alphas for small, medium, and large effect sizes given a variety of sample sizes. It was evident that sample sizes for most psychological studies are adequate for large effect sizes defined at .8. The typical alpha level of .05 and desired power of 90% can be achieved with 70 participants in two groups. It was perhaps doubtful if these ideal levels of alpha and power have generally been achieved for medium effect sizes in actual research, since 170 participants would be required. Small effect sizes have rarely been tested with an adequate number of participants or power. Implications were discussed.
40 CFR 91.419 - Raw emission sampling calculations.
Code of Federal Regulations, 2012 CFR
2012-07-01
... (CONTINUED) CONTROL OF EMISSIONS FROM MARINE SPARK-IGNITION ENGINES Gaseous Exhaust Test Procedures § 91.419 Raw emission sampling calculations. (a) Derive the final test results through the steps described in... following equations are used to determine the weighted emission values for the test engine:...
40 CFR 91.419 - Raw emission sampling calculations.
Code of Federal Regulations, 2014 CFR
2014-07-01
... (CONTINUED) CONTROL OF EMISSIONS FROM MARINE SPARK-IGNITION ENGINES Gaseous Exhaust Test Procedures § 91.419 Raw emission sampling calculations. (a) Derive the final test results through the steps described in... following equations are used to determine the weighted emission values for the test engine:...
Hellman-Feynman operator sampling in diffusion Monte Carlo calculations.
Gaudoin, R; Pitarke, J M
2007-09-21
Diffusion Monte Carlo (DMC) calculations typically yield highly accurate results in solid-state and quantum-chemical calculations. However, operators that do not commute with the Hamiltonian are at best sampled correctly up to second order in the error of the underlying trial wave function once simple corrections have been applied. This error is of the same order as that for the energy in variational calculations. Operators that suffer from these problems include potential energies and the density. This Letter presents a new method, based on the Hellman-Feynman theorem, for the correct DMC sampling of all operators diagonal in real space. Our method is easy to implement in any standard DMC code.
Effects of Mesh Size on Sieved Samples of Corophium volutator
NASA Astrophysics Data System (ADS)
Crewe, Tara L.; Hamilton, Diana J.; Diamond, Antony W.
2001-08-01
Corophium volutator (Pallas), gammaridean amphipods found on intertidal mudflats, are frequently collected in mud samples sieved on mesh screens. However, mesh sizes used vary greatly among studies, raising the possibility that sampling methods bias results. The effect of using different mesh sizes on the resulting size-frequency distributions of Corophium was tested by collecting Corophium from mud samples with 0·5 and 0·25 mm sieves. More than 90% of Corophium less than 2 mm long passed through the larger sieve. A significantly smaller, but still substantial, proportion of 2-2·9 mm Corophium (30%) was also lost. Larger size classes were unaffected by mesh size. Mesh size significantly changed the observed size-frequency distribution of Corophium, and effects varied with sampling date. It is concluded that a 0·5 mm sieve is suitable for studies concentrating on adults, but to accurately estimate Corophium density and size-frequency distributions, a 0·25 mm sieve must be used.
The Precision Efficacy Analysis for Regression Sample Size Method.
ERIC Educational Resources Information Center
Brooks, Gordon P.; Barcikowski, Robert S.
The general purpose of this study was to examine the efficiency of the Precision Efficacy Analysis for Regression (PEAR) method for choosing appropriate sample sizes in regression studies used for precision. The PEAR method, which is based on the algebraic manipulation of an accepted cross-validity formula, essentially uses an effect size to…
The Sample Size Needed for the Trimmed "t" Test when One Group Size Is Fixed
ERIC Educational Resources Information Center
Luh, Wei-Ming; Guo, Jiin-Huarng
2009-01-01
The sample size determination is an important issue for planning research. However, limitations in size have seldom been discussed in the literature. Thus, how to allocate participants into different treatment groups to achieve the desired power is a practical issue that still needs to be addressed when one group size is fixed. The authors focused…
NASA Astrophysics Data System (ADS)
Heckmann, T.; Gegg, K.; Gegg, A.; Becht, M.
2014-02-01
Predictive spatial modelling is an important task in natural hazard assessment and regionalisation of geomorphic processes or landforms. Logistic regression is a multivariate statistical approach frequently used in predictive modelling; it can be conducted stepwise in order to select from a number of candidate independent variables those that lead to the best model. In our case study on a debris flow susceptibility model, we investigate the sensitivity of model selection and quality to different sample sizes in light of the following problem: on the one hand, a sample has to be large enough to cover the variability of geofactors within the study area, and to yield stable and reproducible results; on the other hand, the sample must not be too large, because a large sample is likely to violate the assumption of independent observations due to spatial autocorrelation. Using stepwise model selection with 1000 random samples for a number of sample sizes between n = 50 and n = 5000, we investigate the inclusion and exclusion of geofactors and the diversity of the resulting models as a function of sample size; the multiplicity of different models is assessed using numerical indices borrowed from information theory and biodiversity research. Model diversity decreases with increasing sample size and reaches either a local minimum or a plateau; even larger sample sizes do not further reduce it, and they approach the upper limit of sample size given, in this study, by the autocorrelation range of the spatial data sets. In this way, an optimised sample size can be derived from an exploratory analysis. Model uncertainty due to sampling and model selection, and its predictive ability, are explored statistically and spatially through the example of 100 models estimated in one study area and validated in a neighbouring area: depending on the study area and on sample size, the predicted probabilities for debris flow release differed, on average, by 7 to 23 percentage points. In
NASA Astrophysics Data System (ADS)
Heckmann, T.; Gegg, K.; Gegg, A.; Becht, M.
2013-06-01
Predictive spatial modelling is an important task in natural hazard assessment and regionalisation of geomorphic processes or landforms. Logistic regression is a multivariate statistical approach frequently used in predictive modelling; it can be conducted stepwise in order to select from a number of candidate independent variables those that lead to the best model. In our case study on a debris flow susceptibility model, we investigate the sensitivity of model selection and quality to different sample sizes in light of the following problem: on the one hand, a sample has to be large enough to cover the variability of geofactors within the study area, and to yield stable results; on the other hand, the sample must not be too large, because a large sample is likely to violate the assumption of independent observations due to spatial autocorrelation. Using stepwise model selection with 1000 random samples for a number of sample sizes between n = 50 and n = 5000, we investigate the inclusion and exclusion of geofactors and the diversity of the resulting models as a function of sample size; the multiplicity of different models is assessed using numerical indices borrowed from information theory and biodiversity research. Model diversity decreases with increasing sample size and reaches either a local minimum or a plateau; even larger sample sizes do not further reduce it, and approach the upper limit of sample size given, in this study, by the autocorrelation range of the spatial datasets. In this way, an optimised sample size can be derived from an exploratory analysis. Model uncertainty due to sampling and model selection, and its predictive ability, are explored statistically and spatially through the example of 100 models estimated in one study area and validated in a neighbouring area: depending on the study area and on sample size, the predicted probabilities for debris flow release differed, on average, by 7 to 23 percentage points. In view of these results, we
Abstract: Sample Size Planning for Latent Curve Models.
Lai, Keke
2011-11-30
When designing a study that uses structural equation modeling (SEM), an important task is to decide an appropriate sample size. Historically, this task is approached from the power analytic perspective, where the goal is to obtain sufficient power to reject a false null hypothesis. However, hypothesis testing only tells if a population effect is zero and fails to address the question about the population effect size. Moreover, significance tests in the SEM context often reject the null hypothesis too easily, and therefore the problem in practice is having too much power instead of not enough power. An alternative means to infer the population effect is forming confidence intervals (CIs). A CI is more informative than hypothesis testing because a CI provides a range of plausible values for the population effect size of interest. Given the close relationship between CI and sample size, the sample size for an SEM study can be planned with the goal to obtain sufficiently narrow CIs for the population model parameters of interest. Latent curve models (LCMs) is an application of SEM with mean structure to studying change over time. The sample size planning method for LCM from the CI perspective is based on maximum likelihood and expected information matrix. Given a sample, to form a CI for the model parameter of interest in LCM, it requires the sample covariance matrix S, sample mean vector [Formula: see text], and sample size N. Therefore, the width (w) of the resulting CI can be considered a function of S, [Formula: see text], and N. Inverting the CI formation process gives the sample size planning process. The inverted process requires a proxy for the population covariance matrix Σ, population mean vector μ, and the desired width ω as input, and it returns N as output. The specification of the input information for sample size planning needs to be performed based on a systematic literature review. In the context of covariance structure analysis, Lai and Kelley
CSnrc: Correlated sampling Monte Carlo calculations using EGSnrc
Buckley, Lesley A.; Kawrakow, I.; Rogers, D.W.O.
2004-12-01
CSnrc, a new user-code for the EGSnrc Monte Carlo system is described. This user-code improves the efficiency when calculating ratios of doses from similar geometries. It uses a correlated sampling variance reduction technique. CSnrc is developed from an existing EGSnrc user-code CAVRZnrc and improves upon the correlated sampling algorithm used in an earlier version of the code written for the EGS4 Monte Carlo system. Improvements over the EGS4 version of the algorithm avoid repetition of sections of particle tracks. The new code includes a rectangular phantom geometry not available in other EGSnrc cylindrical codes. Comparison to CAVRZnrc shows gains in efficiency of up to a factor of 64 for a variety of test geometries when computing the ratio of doses to the cavity for two geometries. CSnrc is well suited to in-phantom calculations and is used to calculate the central electrode correction factor P{sub cel} in high-energy photon and electron beams. Current dosimetry protocols base the value of P{sub cel} on earlier Monte Carlo calculations. The current CSnrc calculations achieve 0.02% statistical uncertainties on P{sub cel}, much lower than those previously published. The current values of P{sub cel} compare well with the values used in dosimetry protocols for photon beams. For electrons beams, CSnrc calculations are reported at the reference depth used in recent protocols and show up to a 0.2% correction for a graphite electrode, a correction currently ignored by dosimetry protocols. The calculations show that for a 1 mm diameter aluminum central electrode, the correction factor differs somewhat from the values used in both the IAEA TRS-398 code of practice and the AAPM's TG-51 protocol.
Sample size determination for the confidence interval of linear contrast in analysis of covariance.
Liu, Xiaofeng Steven
2013-03-11
This article provides a way to determine sample size for the confidence interval of the linear contrast of treatment means in analysis of covariance (ANCOVA) without prior knowledge of the actual covariate means and covariate sum of squares, which are modeled as a t statistic. Using the t statistic, one can calculate the appropriate sample size to achieve the desired probability of obtaining a specified width in the confidence interval of the covariate-adjusted linear contrast.
Estimating hidden population size using Respondent-Driven Sampling data
Handcock, Mark S.; Gile, Krista J.; Mar, Corinne M.
2015-01-01
Respondent-Driven Sampling (RDS) is n approach to sampling design and inference in hard-to-reach human populations. It is often used in situations where the target population is rare and/or stigmatized in the larger population, so that it is prohibitively expensive to contact them through the available frames. Common examples include injecting drug users, men who have sex with men, and female sex workers. Most analysis of RDS data has focused on estimating aggregate characteristics, such as disease prevalence. However, RDS is often conducted in settings where the population size is unknown and of great independent interest. This paper presents an approach to estimating the size of a target population based on data collected through RDS. The proposed approach uses a successive sampling approximation to RDS to leverage information in the ordered sequence of observed personal network sizes. The inference uses the Bayesian framework, allowing for the incorporation of prior knowledge. A flexible class of priors for the population size is used that aids elicitation. An extensive simulation study provides insight into the performance of the method for estimating population size under a broad range of conditions. A further study shows the approach also improves estimation of aggregate characteristics. Finally, the method demonstrates sensible results when used to estimate the size of known networked populations from the National Longitudinal Study of Adolescent Health, and when used to estimate the size of a hard-to-reach population at high risk for HIV. PMID:26180577
Sample Size Determination for One- and Two-Sample Trimmed Mean Tests
ERIC Educational Resources Information Center
Luh, Wei-Ming; Olejnik, Stephen; Guo, Jiin-Huarng
2008-01-01
Formulas to determine the necessary sample sizes for parametric tests of group comparisons are available from several sources and appropriate when population distributions are normal. However, in the context of nonnormal population distributions, researchers recommend Yuen's trimmed mean test, but formulas to determine sample sizes have not been…
Sample size considerations for historical control studies with survival outcomes.
Zhu, Hong; Zhang, Song; Ahn, Chul
2016-01-01
Historical control trials (HCTs) are frequently conducted to compare an experimental treatment with a control treatment from a previous study, when they are applicable and favored over a randomized clinical trial (RCT) due to feasibility, ethics and cost concerns. Makuch and Simon developed a sample size formula for historical control (HC) studies with binary outcomes, assuming that the observed response rate in the HC group is the true response rate. This method was extended by Dixon and Simon to specify sample size for HC studies comparing survival outcomes. For HC studies with binary and continuous outcomes, many researchers have shown that the popular Makuch and Simon method does not preserve the nominal power and type I error, and suggested alternative approaches. For HC studies with survival outcomes, we reveal through simulation that the conditional power and type I error over all the random realizations of the HC data have highly skewed distributions. Therefore, the sampling variability of the HC data needs to be appropriately accounted for in determining sample size. A flexible sample size formula that controls arbitrary percentiles, instead of means, of the conditional power and type I error, is derived. Although an explicit sample size formula with survival outcomes is not available, the computation is straightforward. Simulations demonstrate that the proposed method preserves the operational characteristics in a more realistic scenario where the true hazard rate of the HC group is unknown. A real data application of an advanced non-small cell lung cancer (NSCLC) clinical trial is presented to illustrate sample size considerations for HC studies in comparison of survival outcomes.
Sample size considerations for historical control studies with survival outcomes
Zhu, Hong; Zhang, Song; Ahn, Chul
2015-01-01
Historical control trials (HCTs) are frequently conducted to compare an experimental treatment with a control treatment from a previous study, when they are applicable and favored over a randomized clinical trial (RCT) due to feasibility, ethics and cost concerns. Makuch and Simon developed a sample size formula for historical control (HC) studies with binary outcomes, assuming that the observed response rate in the HC group is the true response rate. This method was extended by Dixon and Simon to specify sample size for HC studies comparing survival outcomes. For HC studies with binary and continuous outcomes, many researchers have shown that the popular Makuch and Simon method does not preserve the nominal power and type I error, and suggested alternative approaches. For HC studies with survival outcomes, we reveal through simulation that the conditional power and type I error over all the random realizations of the HC data have highly skewed distributions. Therefore, the sampling variability of the HC data needs to be appropriately accounted for in determining sample size. A flexible sample size formula that controls arbitrary percentiles, instead of means, of the conditional power and type I error, is derived. Although an explicit sample size formula with survival outcomes is not available, the computation is straightforward. Simulations demonstrate that the proposed method preserves the operational characteristics in a more realistic scenario where the true hazard rate of the HC group is unknown. A real data application of an advanced non-small cell lung cancer (NSCLC) clinical trial is presented to illustrate sample size considerations for HC studies in comparison of survival outcomes. PMID:26098200
Aircraft studies of size-dependent aerosol sampling through inlets
NASA Technical Reports Server (NTRS)
Porter, J. N.; Clarke, A. D.; Ferry, G.; Pueschel, R. F.
1992-01-01
Representative measurement of aerosol from aircraft-aspirated systems requires special efforts in order to maintain near isokinetic sampling conditions, estimate aerosol losses in the sample system, and obtain a measurement of sufficient duration to be statistically significant for all sizes of interest. This last point is especially critical for aircraft measurements which typically require fast response times while sampling in clean remote regions. This paper presents size-resolved tests, intercomparisons, and analysis of aerosol inlet performance as determined by a custom laser optical particle counter. Measurements discussed here took place during the Global Backscatter Experiment (1988-1989) and the Central Pacific Atmospheric Chemistry Experiment (1988). System configurations are discussed including (1) nozzle design and performance, (2) system transmission efficiency, (3) nonadiabatic effects in the sample line and its effect on the sample-line relative humidity, and (4) the use and calibration of a virtual impactor.
Novikov, I; Fund, N; Freedman, L S
2010-01-15
Different methods for the calculation of sample size for simple logistic regression (LR) with one normally distributed continuous covariate give different results. Sometimes the difference can be large. Furthermore, some methods require the user to specify the prevalence of cases when the covariate equals its population mean, rather than the more natural population prevalence. We focus on two commonly used methods and show through simulations that the power for a given sample size may differ substantially from the nominal value for one method, especially when the covariate effect is large, while the other method performs poorly if the user provides the population prevalence instead of the required parameter. We propose a modification of the method of Hsieh et al. that requires specification of the population prevalence and that employs Schouten's sample size formula for a t-test with unequal variances and group sizes. This approach appears to increase the accuracy of the sample size estimates for LR with one continuous covariate.
Trainable fusion rules. II. Small sample-size effects.
Raudys, Sarunas
2006-12-01
Profound theoretical analysis is performed of small-sample properties of trainable fusion rules to determine in which situations neural network ensembles can improve or degrade classification results. We consider small sample effects, specific only to multiple classifiers system design in the two-category case of two important fusion rules: (1) linear weighted average (weighted voting), realized either by the standard Fisher classifier or by the single-layer perceptron, and (2) the non-linear Behavior-Knowledge-Space method. The small sample effects include: (i) training bias, i.e. learning sample size influence on generalization error of the base experts or of the fusion rule, (ii) optimistic biased outputs of the experts (self-boasting effect) and (iii) sample size impact on determining optimal complexity of the fusion rule. Correction terms developed to reduce the self-boasting effect are studied. It is shown that small learning sets increase classification error of the expert classifiers and damage correlation structure between their outputs. If the sizes of learning sets used to develop the expert classifiers are too small, non-trainable fusion rules can outperform more sophisticated trainable ones. A practical technique to fight sample size problems is a noise injection technique. The noise injection reduces the fusion rule's complexity and diminishes the expert's boasting bias.
Sample size in psychological research over the past 30 years.
Marszalek, Jacob M; Barber, Carolyn; Kohlhart, Julie; Holmes, Cooper B
2011-04-01
The American Psychological Association (APA) Task Force on Statistical Inference was formed in 1996 in response to a growing body of research demonstrating methodological issues that threatened the credibility of psychological research, and made recommendations to address them. One issue was the small, even dramatically inadequate, size of samples used in studies published by leading journals. The present study assessed the progress made since the Task Force's final report in 1999. Sample sizes reported in four leading APA journals in 1955, 1977, 1995, and 2006 were compared using nonparametric statistics, while data from the last two waves were fit to a hierarchical generalized linear growth model for more in-depth analysis. Overall, results indicate that the recommendations for increasing sample sizes have not been integrated in core psychological research, although results slightly vary by field. This and other implications are discussed in the context of current methodological critique and practice.
Sample size bias in the estimation of means.
Smith, Andrew R; Price, Paul C
2010-08-01
The present research concerns the hypothesis that intuitive estimates of the arithmetic mean of a sample of numbers tend to increase as a function of the sample size; that is, they reflect a systematic sample size bias. A similar bias has been observed when people judge the average member of a group of people on an inferred quantity (e.g., a disease risk; see Price, 2001; Price, Smith, & Lench, 2006). Until now, however, it has been unclear whether it would be observed when the stimuli were numbers, in which case the quantity need not be inferred, and "average" can be precisely defined as the arithmetic mean. In two experiments, participants estimated the arithmetic mean of 12 samples of numbers. In the first experiment, samples of from 5 to 20 numbers were presented simultaneously and participants quickly estimated their mean. In the second experiment, the numbers in each sample were presented sequentially. The results of both experiments confirmed the existence of a systematic sample size bias.
Optimization of sample size in controlled experiments: the CLAST rule.
Botella, Juan; Ximénez, Carmen; Revuelta, Javier; Suero, Manuel
2006-02-01
Sequential rules are explored in the context of null hypothesis significance testing. Several studies have demonstrated that the fixed-sample stopping rule, in which the sample size used by researchers is determined in advance, is less practical and less efficient than sequential stopping rules. It is proposed that a sequential stopping rule called CLAST (composite limited adaptive sequential test) is a superior variant of COAST (composite open adaptive sequential test), a sequential rule proposed by Frick (1998). Simulation studies are conducted to test the efficiency of the proposed rule in terms of sample size and power. Two statistical tests are used: the one-tailed t test of mean differences with two matched samples, and the chi-square independence test for twofold contingency tables. The results show that the CLAST rule is more efficient than the COAST rule and reflects more realistically the practice of experimental psychology researchers.
Using electron microscopy to calculate optical properties of biological samples.
Wu, Wenli; Radosevich, Andrew J; Eshein, Adam; Nguyen, The-Quyen; Yi, Ji; Cherkezyan, Lusik; Roy, Hemant K; Szleifer, Igal; Backman, Vadim
2016-11-01
The microscopic structural origins of optical properties in biological media are still not fully understood. Better understanding these origins can serve to improve the utility of existing techniques and facilitate the discovery of other novel techniques. We propose a novel analysis technique using electron microscopy (EM) to calculate optical properties of specific biological structures. This method is demonstrated with images of human epithelial colon cell nuclei. The spectrum of anisotropy factor g, the phase function and the shape factor D of the nuclei are calculated. The results show strong agreement with an independent study. This method provides a new way to extract the true phase function of biological samples and provides an independent validation for optical property measurement techniques.
Using electron microscopy to calculate optical properties of biological samples
Wu, Wenli; Radosevich, Andrew J.; Eshein, Adam; Nguyen, The-Quyen; Yi, Ji; Cherkezyan, Lusik; Roy, Hemant K.; Szleifer, Igal; Backman, Vadim
2016-01-01
The microscopic structural origins of optical properties in biological media are still not fully understood. Better understanding these origins can serve to improve the utility of existing techniques and facilitate the discovery of other novel techniques. We propose a novel analysis technique using electron microscopy (EM) to calculate optical properties of specific biological structures. This method is demonstrated with images of human epithelial colon cell nuclei. The spectrum of anisotropy factor g, the phase function and the shape factor D of the nuclei are calculated. The results show strong agreement with an independent study. This method provides a new way to extract the true phase function of biological samples and provides an independent validation for optical property measurement techniques. PMID:27896013
Lui, Kung-Jong; Chang, Kuang-Chao
2015-05-01
To reduce the lengthy duration of a crossover trial for comparing three treatments, the incomplete block design has been often considered. A sample size calculation procedure for testing nonequality between either of the two experimental treatments and a placebo under such a design is developed. To evaluate the performance of the proposed sample size calculation procedure, Monte Carlo simulation is employed. The accuracy of the sample size calculation procedure developed here is demonstrated in a variety of situations. As compared with the parallel groups design, a substantial proportional reduction in the total minimum required sample size in use of the incomplete block crossover design is found. A crossover trial comparing two different doses of formoterol with a placebo on the forced expiratory volume is applied to illustrate the use of the sample size calculation procedure.
Small Sample Sizes Yield Biased Allometric Equations in Temperate Forests
Duncanson, L.; Rourke, O.; Dubayah, R.
2015-01-01
Accurate quantification of forest carbon stocks is required for constraining the global carbon cycle and its impacts on climate. The accuracies of forest biomass maps are inherently dependent on the accuracy of the field biomass estimates used to calibrate models, which are generated with allometric equations. Here, we provide a quantitative assessment of the sensitivity of allometric parameters to sample size in temperate forests, focusing on the allometric relationship between tree height and crown radius. We use LiDAR remote sensing to isolate between 10,000 to more than 1,000,000 tree height and crown radius measurements per site in six U.S. forests. We find that fitted allometric parameters are highly sensitive to sample size, producing systematic overestimates of height. We extend our analysis to biomass through the application of empirical relationships from the literature, and show that given the small sample sizes used in common allometric equations for biomass, the average site-level biomass bias is ~+70% with a standard deviation of 71%, ranging from −4% to +193%. These findings underscore the importance of increasing the sample sizes used for allometric equation generation. PMID:26598233
7 CFR 52.803 - Sample unit size.
Code of Federal Regulations, 2013 CFR
2013-01-01
... CERTAIN OTHER PROCESSED FOOD PRODUCTS 1 United States Standards for Grades of Frozen Red Tart Pitted... quality factors is based on the following sample unit sizes for the applicable factor: (a) Pits, character... than harmless extraneous material)—100 cherries. Factors of Quality...
7 CFR 52.803 - Sample unit size.
Code of Federal Regulations, 2014 CFR
2014-01-01
... CERTAIN OTHER PROCESSED FOOD PRODUCTS 1 United States Standards for Grades of Frozen Red Tart Pitted... quality factors is based on the following sample unit sizes for the applicable factor: (a) Pits, character... than harmless extraneous material)—100 cherries. Factors of Quality...
Sample Size Tables, "t" Test, and a Prevalent Psychometric Distribution.
ERIC Educational Resources Information Center
Sawilowsky, Shlomo S.; Hillman, Stephen B.
Psychology studies often have low statistical power. Sample size tables, as given by J. Cohen (1988), may be used to increase power, but they are based on Monte Carlo studies of relatively "tame" mathematical distributions, as compared to psychology data sets. In this study, Monte Carlo methods were used to investigate Type I and Type II…
Sample size bias in retrospective estimates of average duration.
Smith, Andrew R; Rule, Shanon; Price, Paul C
2017-03-25
People often estimate the average duration of several events (e.g., on average, how long does it take to drive from one's home to his or her office). While there is a great deal of research investigating estimates of duration for a single event, few studies have examined estimates when people must average across numerous stimuli or events. The current studies were designed to fill this gap by examining how people's estimates of average duration were influenced by the number of stimuli being averaged (i.e., the sample size). Based on research investigating the sample size bias, we predicted that participants' judgments of average duration would increase as the sample size increased. Across four studies, we demonstrated a sample size bias for estimates of average duration with different judgment types (numeric estimates and comparisons), study designs (between and within-subjects), and paradigms (observing images and performing tasks). The results are consistent with the more general notion that psychological representations of magnitudes in one dimension (e.g., quantity) can influence representations of magnitudes in another dimension (e.g., duration).
Small Sample Sizes Yield Biased Allometric Equations in Temperate Forests.
Duncanson, L; Rourke, O; Dubayah, R
2015-11-24
Accurate quantification of forest carbon stocks is required for constraining the global carbon cycle and its impacts on climate. The accuracies of forest biomass maps are inherently dependent on the accuracy of the field biomass estimates used to calibrate models, which are generated with allometric equations. Here, we provide a quantitative assessment of the sensitivity of allometric parameters to sample size in temperate forests, focusing on the allometric relationship between tree height and crown radius. We use LiDAR remote sensing to isolate between 10,000 to more than 1,000,000 tree height and crown radius measurements per site in six U.S. forests. We find that fitted allometric parameters are highly sensitive to sample size, producing systematic overestimates of height. We extend our analysis to biomass through the application of empirical relationships from the literature, and show that given the small sample sizes used in common allometric equations for biomass, the average site-level biomass bias is ~+70% with a standard deviation of 71%, ranging from -4% to +193%. These findings underscore the importance of increasing the sample sizes used for allometric equation generation.
Sample Size Bias in Judgments of Perceptual Averages
ERIC Educational Resources Information Center
Price, Paul C.; Kimura, Nicole M.; Smith, Andrew R.; Marshall, Lindsay D.
2014-01-01
Previous research has shown that people exhibit a sample size bias when judging the average of a set of stimuli on a single dimension. The more stimuli there are in the set, the greater people judge the average to be. This effect has been demonstrated reliably for judgments of the average likelihood that groups of people will experience negative,…
On sample size estimation and re-estimation adjusting for variability in confirmatory trials.
Wu, Pei-Shien; Lin, Min; Chow, Shein-Chung
2016-01-01
Sample size estimation (SSE) is an important issue in the planning of clinical studies. While larger studies are likely to have sufficient power, it may be unethical to expose more patients than necessary to answer a scientific question. Budget considerations may also cause one to limit the study to an adequate size to answer the question at hand. Typically at the planning stage, a statistically based justification for sample size is provided. An effective sample size is usually planned under a pre-specified type I error rate, a desired power under a particular alternative and variability associated with the observations recorded. The nuisance parameter such as the variance is unknown in practice. Thus, information from a preliminary pilot study is often used to estimate the variance. However, calculating the sample size based on the estimated nuisance parameter may not be stable. Sample size re-estimation (SSR) at the interim analysis may provide an opportunity to re-evaluate the uncertainties using accrued data and continue the trial with an updated sample size. This article evaluates a proposed SSR method based on controlling the variability of nuisance parameter. A numerical study is used to assess the performance of proposed method with respect to the control of type I error. The proposed method and concepts could be extended to SSR approaches with respect to other criteria, such as maintaining effect size, achieving conditional power, and reaching a desired reproducibility probability.
Adaptive sample size modification in clinical trials: start small then ask for more?
Jennison, Christopher; Turnbull, Bruce W
2015-12-20
We consider sample size re-estimation in a clinical trial, in particular when there is a significant delay before the measurement of patient response. Mehta and Pocock have proposed methods in which sample size is increased when interim results fall in a 'promising zone' where it is deemed worthwhile to increase conditional power by adding more subjects. Our analysis reveals potential pitfalls in applying this approach. Mehta and Pocock use results of Chen, DeMets and Lan to identify when increasing sample size, but applying a conventional level α significance test at the end of the trial does not inflate the type I error rate: we have found the greatest gains in power per additional observation are liable to lie outside the region defined by this method. Mehta and Pocock increase sample size to achieve a particular conditional power, calculated under the current estimate of treatment effect: this leads to high increases in sample size for a small range of interim outcomes, whereas we have found it more efficient to make moderate increases in sample size over a wider range of cases. If the aforementioned pitfalls are avoided, we believe the broad framework proposed by Mehta and Pocock is valuable for clinical trial design. Working in this framework, we propose sample size rules that apply explicitly the principle of adding observations when they are most beneficial. The resulting trial designs are closely related to efficient group sequential tests for a delayed response proposed by Hampson and Jennison.
Optimal sample size allocation for Welch's test in one-way heteroscedastic ANOVA.
Shieh, Gwowen; Jan, Show-Li
2015-06-01
The determination of an adequate sample size is a vital aspect in the planning stage of research studies. A prudent strategy should incorporate all of the critical factors and cost considerations into sample size calculations. This study concerns the allocation schemes of group sizes for Welch's test in a one-way heteroscedastic ANOVA. Optimal allocation approaches are presented for minimizing the total cost while maintaining adequate power and for maximizing power performance for a fixed cost. The commonly recommended ratio of sample sizes is proportional to the ratio of the population standard deviations or the ratio of the population standard deviations divided by the square root of the ratio of the unit sampling costs. Detailed numerical investigations have shown that these usual allocation methods generally do not give the optimal solution. The suggested procedures are illustrated using an example of the cost-efficiency evaluation in multidisciplinary pain centers.
CALCULATING TIME LAGS FROM UNEVENLY SAMPLED LIGHT CURVES
Zoghbi, A.; Reynolds, C.; Cackett, E. M.
2013-11-01
Timing techniques are powerful tools to study dynamical astrophysical phenomena. In the X-ray band, they offer the potential of probing accretion physics down to the event horizon. Recent work has used frequency- and energy-dependent time lags as tools for studying relativistic reverberation around the black holes in several Seyfert galaxies. This was achieved due to the evenly sampled light curves obtained using XMM-Newton. Continuously sampled data are, however, not always available and standard Fourier techniques are not applicable. Here, building on the work of Miller et al., we discuss and use a maximum likelihood method to obtain frequency-dependent lags that takes into account light curve gaps. Instead of calculating the lag directly, the method estimates the most likely lag values at a particular frequency given two observed light curves. We use Monte Carlo simulations to assess the method's applicability and use it to obtain lag-energy spectra from Suzaku data for two objects, NGC 4151 and MCG-5-23-16, that had previously shown signatures of iron K reverberation. The lags obtained are consistent with those calculated using standard methods using XMM-Newton data.
Detecting Neuroimaging Biomarkers for Psychiatric Disorders: Sample Size Matters
Schnack, Hugo G.; Kahn, René S.
2016-01-01
In a recent review, it was suggested that much larger cohorts are needed to prove the diagnostic value of neuroimaging biomarkers in psychiatry. While within a sample, an increase of diagnostic accuracy of schizophrenia (SZ) with number of subjects (N) has been shown, the relationship between N and accuracy is completely different between studies. Using data from a recent meta-analysis of machine learning (ML) in imaging SZ, we found that while low-N studies can reach 90% and higher accuracy, above N/2 = 50 the maximum accuracy achieved steadily drops to below 70% for N/2 > 150. We investigate the role N plays in the wide variability in accuracy results in SZ studies (63–97%). We hypothesize that the underlying cause of the decrease in accuracy with increasing N is sample heterogeneity. While smaller studies more easily include a homogeneous group of subjects (strict inclusion criteria are easily met; subjects live close to study site), larger studies inevitably need to relax the criteria/recruit from large geographic areas. A SZ prediction model based on a heterogeneous group of patients with presumably a heterogeneous pattern of structural or functional brain changes will not be able to capture the whole variety of changes, thus being limited to patterns shared by most patients. In addition to heterogeneity (sample size), we investigate other factors influencing accuracy and introduce a ML effect size. We derive a simple model of how the different factors, such as sample heterogeneity and study setup determine this ML effect size, and explain the variation in prediction accuracies found from the literature, both in cross-validation and independent sample testing. From this, we argue that smaller-N studies may reach high prediction accuracy at the cost of lower generalizability to other samples. Higher-N studies, on the other hand, will have more generalization power, but at the cost of lower accuracy. In conclusion, when comparing results from different
Effects of sample size on KERNEL home range estimates
Seaman, D.E.; Millspaugh, J.J.; Kernohan, Brian J.; Brundige, Gary C.; Raedeke, Kenneth J.; Gitzen, Robert A.
1999-01-01
Kernel methods for estimating home range are being used increasingly in wildlife research, but the effect of sample size on their accuracy is not known. We used computer simulations of 10-200 points/home range and compared accuracy of home range estimates produced by fixed and adaptive kernels with the reference (REF) and least-squares cross-validation (LSCV) methods for determining the amount of smoothing. Simulated home ranges varied from simple to complex shapes created by mixing bivariate normal distributions. We used the size of the 95% home range area and the relative mean squared error of the surface fit to assess the accuracy of the kernel home range estimates. For both measures, the bias and variance approached an asymptote at about 50 observations/home range. The fixed kernel with smoothing selected by LSCV provided the least-biased estimates of the 95% home range area. All kernel methods produced similar surface fit for most simulations, but the fixed kernel with LSCV had the lowest frequency and magnitude of very poor estimates. We reviewed 101 papers published in The Journal of Wildlife Management (JWM) between 1980 and 1997 that estimated animal home ranges. A minority of these papers used nonparametric utilization distribution (UD) estimators, and most did not adequately report sample sizes. We recommend that home range studies using kernel estimates use LSCV to determine the amount of smoothing, obtain a minimum of 30 observations per animal (but preferably a?Y50), and report sample sizes in published results.
Rock sampling. [method for controlling particle size distribution
NASA Technical Reports Server (NTRS)
Blum, P. (Inventor)
1971-01-01
A method for sampling rock and other brittle materials and for controlling resultant particle sizes is described. The method involves cutting grooves in the rock surface to provide a grouping of parallel ridges and subsequently machining the ridges to provide a powder specimen. The machining step may comprise milling, drilling, lathe cutting or the like; but a planing step is advantageous. Control of the particle size distribution is effected primarily by changing the height and width of these ridges. This control exceeds that obtainable by conventional grinding.
Sample size and power considerations in network meta-analysis
2012-01-01
Background Network meta-analysis is becoming increasingly popular for establishing comparative effectiveness among multiple interventions for the same disease. Network meta-analysis inherits all methodological challenges of standard pairwise meta-analysis, but with increased complexity due to the multitude of intervention comparisons. One issue that is now widely recognized in pairwise meta-analysis is the issue of sample size and statistical power. This issue, however, has so far only received little attention in network meta-analysis. To date, no approaches have been proposed for evaluating the adequacy of the sample size, and thus power, in a treatment network. Findings In this article, we develop easy-to-use flexible methods for estimating the ‘effective sample size’ in indirect comparison meta-analysis and network meta-analysis. The effective sample size for a particular treatment comparison can be interpreted as the number of patients in a pairwise meta-analysis that would provide the same degree and strength of evidence as that which is provided in the indirect comparison or network meta-analysis. We further develop methods for retrospectively estimating the statistical power for each comparison in a network meta-analysis. We illustrate the performance of the proposed methods for estimating effective sample size and statistical power using data from a network meta-analysis on interventions for smoking cessation including over 100 trials. Conclusion The proposed methods are easy to use and will be of high value to regulatory agencies and decision makers who must assess the strength of the evidence supporting comparative effectiveness estimates. PMID:22992327
Calculating Size of the Saturn's "Leopard Skin" Spots
NASA Astrophysics Data System (ADS)
Kochemasov, G. G.
2007-03-01
An IR image of the saturnian south (PIA08333) shows huge storm ~8000 km across containing smaller storms about 300 to 600 km across. Assuming a wave nature of this phenomena calculations with wave modulation give diameters of small forms ~400 km.
Teaching Modelling Concepts: Enter the Pocket-Size Programmable Calculator.
ERIC Educational Resources Information Center
Gaar, Kermit A., Jr.
1980-01-01
Addresses the problem of the failure of students to see a physiological system in an integrated way. Programmable calculators armed with a printer are suggested as useful teaching devices that avoid the expense and the unavailability of computers for modelling in teaching physiology. (Author/SA)
A fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation.
Li, Haisen S; Romeijn, H Edwin; Dempsey, James F
2006-09-01
We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near monoenergetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the
Power and sample size in cost-effectiveness analysis.
Laska, E M; Meisner, M; Siegel, C
1999-01-01
For resource allocation under a constrained budget, optimal decision rules for mutually exclusive programs require that the treatment with the highest incremental cost-effectiveness ratio (ICER) below a willingness-to-pay (WTP) criterion be funded. This is equivalent to determining the treatment with the smallest net health cost. The designer of a cost-effectiveness study needs to select a sample size so that the power to reject the null hypothesis, the equality of the net health costs of two treatments, is high. A recently published formula derived under normal distribution theory overstates sample-size requirements. Using net health costs, the authors present simple methods for power analysis based on conventional normal and on nonparametric statistical theory.
Estimation of sample size and testing power (Part 3).
Hu, Liang-ping; Bao, Xiao-lei; Guan, Xue; Zhou, Shi-guo
2011-12-01
This article introduces the definition and sample size estimation of three special tests (namely, non-inferiority test, equivalence test and superiority test) for qualitative data with the design of one factor with two levels having a binary response variable. Non-inferiority test refers to the research design of which the objective is to verify that the efficacy of the experimental drug is not clinically inferior to that of the positive control drug. Equivalence test refers to the research design of which the objective is to verify that the experimental drug and the control drug have clinically equivalent efficacy. Superiority test refers to the research design of which the objective is to verify that the efficacy of the experimental drug is clinically superior to that of the control drug. By specific examples, this article introduces formulas of sample size estimation for the three special tests, and their SAS realization in detail.
Estimation of sample size and testing power (part 6).
Hu, Liang-ping; Bao, Xiao-lei; Guan, Xue; Zhou, Shi-guo
2012-03-01
The design of one factor with k levels (k ≥ 3) refers to the research that only involves one experimental factor with k levels (k ≥ 3), and there is no arrangement for other important non-experimental factors. This paper introduces the estimation of sample size and testing power for quantitative data and qualitative data having a binary response variable with the design of one factor with k levels (k ≥ 3).
Computer program for the calculation of grain size statistics by the method of moments
Sawyer, Michael B.
1977-01-01
A computer program is presented for a Hewlett-Packard Model 9830A desk-top calculator (1) which calculates statistics using weight or point count data from a grain-size analysis. The program uses the method of moments in contrast to the more commonly used but less inclusive graphic method of Folk and Ward (1957). The merits of the program are: (1) it is rapid; (2) it can accept data in either grouped or ungrouped format; (3) it allows direct comparison with grain-size data in the literature that have been calculated by the method of moments; (4) it utilizes all of the original data rather than percentiles from the cumulative curve as in the approximation technique used by the graphic method; (5) it is written in the computer language BASIC, which is easily modified and adapted to a wide variety of computers; and (6) when used in the HP-9830A, it does not require punching of data cards. The method of moments should be used only if the entire sample has been measured and the worker defines the measured grain-size range. (1) Use of brand names in this paper does not imply endorsement of these products by the U.S. Geological Survey.
Rowley, Christopher N; Woo, Tom K
2009-12-21
Transition path sampling has been established as a powerful tool for studying the dynamics of rare events. The trajectory generation moves of this Monte Carlo procedure, shooting moves and shifting modes, were developed primarily for rate constant calculations, although this method has been more extensively used to study the dynamics of reactive processes. We have devised and implemented three alternative trajectory generation moves for use with transition path sampling. The centering-shooting move incorporates a shifting move into a shooting move, which centers the transition period in the middle of the trajectory, eliminating the need for shifting moves and generating an ensemble where the transition event consistently occurs near the middle of the trajectory. We have also developed varied-perturbation size shooting moves, wherein smaller perturbations are made if the shooting point is far from the transition event. The trajectories generated using these moves decorrelate significantly faster than with conventional, constant sized perturbations. This results in an increase in the statistical efficiency by a factor of 2.5-5 when compared to the conventional shooting algorithm. On the other hand, the new algorithm breaks detailed balance and introduces a small bias in the transition time distribution. We have developed a modification of this varied-perturbation size shooting algorithm that preserves detailed balance, albeit at the cost of decreased sampling efficiency. Both varied-perturbation size shooting algorithms are found to have improved sampling efficiency when compared to the original constant perturbation size shooting algorithm.
Friede, Tim; Kieser, Meinhard
2011-01-01
Baseline adjusted analyses are commonly encountered in practice, and regulatory guidelines endorse this practice. Sample size calculations for this kind of analyses require knowledge of the magnitude of nuisance parameters that are usually not given when the results of clinical trials are reported in the literature. It is therefore quite natural to start with a preliminary calculated sample size based on the sparse information available in the planning phase and to re-estimate the value of the nuisance parameters (and with it the sample size) when a portion of the planned number of patients have completed the study. We investigate the characteristics of this internal pilot study design when an analysis of covariance with normally distributed outcome and one random covariate is applied. For this purpose we first assess the accuracy of four approximate sample size formulae within the fixed sample size design. Then the performance of the recalculation procedure with respect to its actual Type I error rate and power characteristics is examined. The results of simulation studies show that this approach has favorable properties with respect to the Type I error rate and power. Together with its simplicity, these features should make it attractive for practical application.
Effect of Sampling Array Irregularity and Window Size on the Discrimination of Sampled Gratings
Evans, David W.; Wang, Yizhong; Haggerty, Kevin M.; Thibos, Larry N.
2009-01-01
The effect of sampling irregularity and window size on orientation discrimination was investigated using discretely sampled gratings as stimuli. For regular sampling arrays, visual performance could be accounted for by a theoretical analysis of aliasing produced by undersampling. For irregular arrays produced by adding noise to the location of individual samples, the incidence of perceived orientation reversal declined and the spatial frequency range of flawless performance expanded well beyond the nominal Nyquist frequency. These results provide a psychophysical method to estimate the spatial density and the degree of irregularity in the neural sampling arrays that limit human visual resolution. PMID:19815023
Proposed international conventions for particle size-selective sampling.
Soderholm, S C
1989-01-01
Definitions are proposed for the inspirable (also called inhalable), thoracic and respirable fractions of airborne particles. Each definition is expressed as a sampling efficiency (S) which is a function of particle aerodynamic diameter (d) and specifies the fraction of the ambient concentration of airborne particles collected by an ideal sampler. For the inspirable fraction. SI(d) = 0.5 (1 + e-0.06d). For the thoracic fraction, ST(d) = SI(d)[1 - F(x)], where (formula; see text) F(x) is the cumulative probability function of a standardized normal random variable. For the respirable fraction, SR(d) = SI(d)[1 - F(x)], where gamma = 4.25 microns, sigma = 1.5. International harmonization will require resolution of the differences between the firmly established BMRC [Orenstein, A. J. (1960) Proceedings of the Pneumoconiosis Conference, Johannesburg, 1959, pp. 610-621. A.J. Churchill Ltd, London] and ACGIH [(1985) Particle size-selective sampling in the workplace. Report of the ACGIH Technical Committee on Air Sampling Procedures] definitions of the respirable fraction. The proposed definition differs approximately equally from the BMRC and ACGIH definitions and is at least as defensible when compared to available human data. Several standard-setting organizations are in the process of adopting particle size-selective sampling conventions. Much confusion will be avoided if all adopt the same specifications of the collection efficiencies of ideal samplers, such as those proposed here.
Allocating Sample Sizes to Reduce Budget for Fixed-Effect 2×2 Heterogeneous Analysis of Variance
ERIC Educational Resources Information Center
Luh, Wei-Ming; Guo, Jiin-Huarng
2016-01-01
This article discusses the sample size requirements for the interaction, row, and column effects, respectively, by forming a linear contrast for a 2×2 factorial design for fixed-effects heterogeneous analysis of variance. The proposed method uses the Welch t test and its corresponding degrees of freedom to calculate the final sample size in a…
NASA Astrophysics Data System (ADS)
Voss, Sebastian; Zimmermann, Beate; Zimmermann, Alexander
2016-04-01
In the last three decades, an increasing number of studies analyzed spatial patterns in throughfall to investigate the consequences of rainfall redistribution for biogeochemical and hydrological processes in forests. In the majority of cases, variograms were used to characterize the spatial properties of the throughfall data. The estimation of the variogram from sample data requires an appropriate sampling scheme: most importantly, a large sample and an appropriate layout of sampling locations that often has to serve both variogram estimation and geostatistical prediction. While some recommendations on these aspects exist, they focus on Gaussian data and high ratios of the variogram range to the extent of the study area. However, many hydrological data, and throughfall data in particular, do not follow a Gaussian distribution. In this study, we examined the effect of extent, sample size, sampling design, and calculation methods on variogram estimation of throughfall data. For our investigation, we first generated non-Gaussian random fields based on throughfall data with heavy outliers. Subsequently, we sampled the fields with three extents (plots with edge lengths of 25 m, 50 m, and 100 m), four common sampling designs (two grid-based layouts, transect and random sampling), and five sample sizes (50, 100, 150, 200, 400). We then estimated the variogram parameters by method-of-moments and residual maximum likelihood. Our key findings are threefold. First, the choice of the extent has a substantial influence on the estimation of the variogram. A comparatively small ratio of the extent to the correlation length is beneficial for variogram estimation. Second, a combination of a minimum sample size of 150, a design that ensures the sampling of small distances and variogram estimation by residual maximum likelihood offers a good compromise between accuracy and efficiency. Third, studies relying on method-of-moments based variogram estimation may have to employ at least
NASA Astrophysics Data System (ADS)
Voss, Sebastian; Zimmermann, Beate; Zimmermann, Alexander
2016-09-01
In the last decades, an increasing number of studies analyzed spatial patterns in throughfall by means of variograms. The estimation of the variogram from sample data requires an appropriate sampling scheme: most importantly, a large sample and a layout of sampling locations that often has to serve both variogram estimation and geostatistical prediction. While some recommendations on these aspects exist, they focus on Gaussian data and high ratios of the variogram range to the extent of the study area. However, many hydrological data, and throughfall data in particular, do not follow a Gaussian distribution. In this study, we examined the effect of extent, sample size, sampling design, and calculation method on variogram estimation of throughfall data. For our investigation, we first generated non-Gaussian random fields based on throughfall data with large outliers. Subsequently, we sampled the fields with three extents (plots with edge lengths of 25 m, 50 m, and 100 m), four common sampling designs (two grid-based layouts, transect and random sampling) and five sample sizes (50, 100, 150, 200, 400). We then estimated the variogram parameters by method-of-moments (non-robust and robust estimators) and residual maximum likelihood. Our key findings are threefold. First, the choice of the extent has a substantial influence on the estimation of the variogram. A comparatively small ratio of the extent to the correlation length is beneficial for variogram estimation. Second, a combination of a minimum sample size of 150, a design that ensures the sampling of small distances and variogram estimation by residual maximum likelihood offers a good compromise between accuracy and efficiency. Third, studies relying on method-of-moments based variogram estimation may have to employ at least 200 sampling points for reliable variogram estimates. These suggested sample sizes exceed the number recommended by studies dealing with Gaussian data by up to 100 %. Given that most previous
On the repeated measures designs and sample sizes for randomized controlled trials.
Tango, Toshiro
2016-04-01
For the analysis of longitudinal or repeated measures data, generalized linear mixed-effects models provide a flexible and powerful tool to deal with heterogeneity among subject response profiles. However, the typical statistical design adopted in usual randomized controlled trials is an analysis of covariance type analysis using a pre-defined pair of "pre-post" data, in which pre-(baseline) data are used as a covariate for adjustment together with other covariates. Then, the major design issue is to calculate the sample size or the number of subjects allocated to each treatment group. In this paper, we propose a new repeated measures design and sample size calculations combined with generalized linear mixed-effects models that depend not only on the number of subjects but on the number of repeated measures before and after randomization per subject used for the analysis. The main advantages of the proposed design combined with the generalized linear mixed-effects models are (1) it can easily handle missing data by applying the likelihood-based ignorable analyses under the missing at random assumption and (2) it may lead to a reduction in sample size, compared with the simple pre-post design. The proposed designs and the sample size calculations are illustrated with real data arising from randomized controlled trials.
A preliminary model to avoid the overestimation of sample size in bioequivalence studies.
Ramírez, E; Abraira, V; Guerra, P; Borobia, A M; Duque, B; López, J L; Mosquera, B; Lubomirov, R; Carcas, A J; Frías, J
2013-02-01
Often the only available data in literature for sample size estimations in bioequivalence studies is intersubject variability, which tends to result in overestimation of sample size. In this paper, we proposed a preliminary model of intrasubject variability based on intersubject variability for Cmax and AUC data from randomized, crossovers, bioequivalence (BE) studies. From 93 Cmax and 121 AUC data from test-reference comparisons that fulfilled BE criteria, we calculated intersubject variability for the reference formulation and intrasubject variability from ANOVA. Lineal and exponential models (y=a(1-e-bx)) were fitted weighted by the inverse of the variance, to predict the intrasubject variability based on intersubject variability. To validate the model we calculated the coefficient of cross-validation of data from 30 new BE studies. The models fit very well (R2=0.997 and 0.990 for Cmax and AUC respectively) and the cross-validation correlation were 0.847 for Cmax and 0.572 for AUC. A preliminary model analyses allow us to estimate the intrasubject variability based on intersubject variability for sample size calculation purposes in BE studies. This approximation provides an opportunity for sample size reduction avoiding unnecessary exposure of healthy volunteers. Further modelling studies are desirable to confirm these results especially suggestions of the higher intersubject variability range.
NASA Astrophysics Data System (ADS)
Luchko, Tyler; Blinov, Nikolay; Limon, Garrett C.; Joyce, Kevin P.; Kovalenko, Andriy
2016-11-01
Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing (R=0.98 for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining R=0.73 compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to R=0.93. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple pK_{ {a}} correction improved agreement with experiment from R=0.54 to R=0.66, despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.
Luchko, Tyler; Blinov, Nikolay; Limon, Garrett C; Joyce, Kevin P; Kovalenko, Andriy
2016-11-01
Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing ([Formula: see text] for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining [Formula: see text] compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to [Formula: see text]. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple [Formula: see text] correction improved agreement with experiment from [Formula: see text] to [Formula: see text], despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.
GUIDE TO CALCULATING TRANSPORT EFFICIENCY OF AEROSOLS IN OCCUPATIONAL AIR SAMPLING SYSTEMS
Hogue, M.; Hadlock, D.; Thompson, M.; Farfan, E.
2013-11-12
This report will present hand calculations for transport efficiency based on aspiration efficiency and particle deposition losses. Because the hand calculations become long and tedious, especially for lognormal distributions of aerosols, an R script (R 2011) will be provided for each element examined. Calculations are provided for the most common elements in a remote air sampling system, including a thin-walled probe in ambient air, straight tubing, bends and a sample housing. One popular alternative approach would be to put such calculations in a spreadsheet, a thorough version of which is shared by Paul Baron via the Aerocalc spreadsheet (Baron 2012). To provide greater transparency and to avoid common spreadsheet vulnerabilities to errors (Burns 2012), this report uses R. The particle size is based on the concept of activity median aerodynamic diameter (AMAD). The AMAD is a particle size in an aerosol where fifty percent of the activity in the aerosol is associated with particles of aerodynamic diameter greater than the AMAD. This concept allows for the simplification of transport efficiency calculations where all particles are treated as spheres with the density of water (1g cm-3). In reality, particle densities depend on the actual material involved. Particle geometries can be very complicated. Dynamic shape factors are provided by Hinds (Hinds 1999). Some example factors are: 1.00 for a sphere, 1.08 for a cube, 1.68 for a long cylinder (10 times as long as it is wide), 1.05 to 1.11 for bituminous coal, 1.57 for sand and 1.88 for talc. Revision 1 is made to correct an error in the original version of this report. The particle distributions are based on activity weighting of particles rather than based on the number of particles of each size. Therefore, the mass correction made in the original version is removed from the text and the calculations. Results affected by the change are updated.
Efficient Coalescent Simulation and Genealogical Analysis for Large Sample Sizes
Kelleher, Jerome; Etheridge, Alison M; McVean, Gilean
2016-01-01
A central challenge in the analysis of genetic variation is to provide realistic genome simulation across millions of samples. Present day coalescent simulations do not scale well, or use approximations that fail to capture important long-range linkage properties. Analysing the results of simulations also presents a substantial challenge, as current methods to store genealogies consume a great deal of space, are slow to parse and do not take advantage of shared structure in correlated trees. We solve these problems by introducing sparse trees and coalescence records as the key units of genealogical analysis. Using these tools, exact simulation of the coalescent with recombination for chromosome-sized regions over hundreds of thousands of samples is possible, and substantially faster than present-day approximate methods. We can also analyse the results orders of magnitude more quickly than with existing methods. PMID:27145223
Graf, Alexandra C; Bauer, Peter; Glimm, Ekkehard; Koenig, Franz
2014-07-01
Sample size modifications in the interim analyses of an adaptive design can inflate the type 1 error rate, if test statistics and critical boundaries are used in the final analysis as if no modification had been made. While this is already true for designs with an overall change of the sample size in a balanced treatment-control comparison, the inflation can be much larger if in addition a modification of allocation ratios is allowed as well. In this paper, we investigate adaptive designs with several treatment arms compared to a single common control group. Regarding modifications, we consider treatment arm selection as well as modifications of overall sample size and allocation ratios. The inflation is quantified for two approaches: a naive procedure that ignores not only all modifications, but also the multiplicity issue arising from the many-to-one comparison, and a Dunnett procedure that ignores modifications, but adjusts for the initially started multiple treatments. The maximum inflation of the type 1 error rate for such types of design can be calculated by searching for the "worst case" scenarios, that are sample size adaptation rules in the interim analysis that lead to the largest conditional type 1 error rate in any point of the sample space. To show the most extreme inflation, we initially assume unconstrained second stage sample size modifications leading to a large inflation of the type 1 error rate. Furthermore, we investigate the inflation when putting constraints on the second stage sample sizes. It turns out that, for example fixing the sample size of the control group, leads to designs controlling the type 1 error rate.
Piepel, Gregory F.; Matzke, Brett D.; Sego, Landon H.; Amidan, Brett G.
2013-04-27
This report discusses the methodology, formulas, and inputs needed to make characterization and clearance decisions for Bacillus anthracis-contaminated and uncontaminated (or decontaminated) areas using a statistical sampling approach. Specifically, the report includes the methods and formulas for calculating the • number of samples required to achieve a specified confidence in characterization and clearance decisions • confidence in making characterization and clearance decisions for a specified number of samples for two common statistically based environmental sampling approaches. In particular, the report addresses an issue raised by the Government Accountability Office by providing methods and formulas to calculate the confidence that a decision area is uncontaminated (or successfully decontaminated) if all samples collected according to a statistical sampling approach have negative results. Key to addressing this topic is the probability that an individual sample result is a false negative, which is commonly referred to as the false negative rate (FNR). The two statistical sampling approaches currently discussed in this report are 1) hotspot sampling to detect small isolated contaminated locations during the characterization phase, and 2) combined judgment and random (CJR) sampling during the clearance phase. Typically if contamination is widely distributed in a decision area, it will be detectable via judgment sampling during the characterization phrase. Hotspot sampling is appropriate for characterization situations where contamination is not widely distributed and may not be detected by judgment sampling. CJR sampling is appropriate during the clearance phase when it is desired to augment judgment samples with statistical (random) samples. The hotspot and CJR statistical sampling approaches are discussed in the report for four situations: 1. qualitative data (detect and non-detect) when the FNR = 0 or when using statistical sampling methods that account
A Bayesian predictive sample size selection design for single-arm exploratory clinical trials.
Teramukai, Satoshi; Daimon, Takashi; Zohar, Sarah
2012-12-30
The aim of an exploratory clinical trial is to determine whether a new intervention is promising for further testing in confirmatory clinical trials. Most exploratory clinical trials are designed as single-arm trials using a binary outcome with or without interim monitoring for early stopping. In this context, we propose a Bayesian adaptive design denoted as predictive sample size selection design (PSSD). The design allows for sample size selection following any planned interim analyses for early stopping of a trial, together with sample size determination before starting the trial. In the PSSD, we determine the sample size using the method proposed by Sambucini (Statistics in Medicine 2008; 27:1199-1224), which adopts a predictive probability criterion with two kinds of prior distributions, that is, an 'analysis prior' used to compute posterior probabilities and a 'design prior' used to obtain prior predictive distributions. In the sample size determination of the PSSD, we provide two sample sizes, that is, N and N(max) , using two types of design priors. At each interim analysis, we calculate the predictive probabilities of achieving a successful result at the end of the trial using the analysis prior in order to stop the trial in case of low or high efficacy (Lee et al., Clinical Trials 2008; 5:93-106), and we select an optimal sample size, that is, either N or N(max) as needed, on the basis of the predictive probabilities. We investigate the operating characteristics through simulation studies, and the PSSD retrospectively applies to a lung cancer clinical trial. (243)
Sample Size for Assessing Agreement between Two Methods of Measurement by Bland-Altman Method.
Lu, Meng-Jie; Zhong, Wei-Hua; Liu, Yu-Xiu; Miao, Hua-Zhang; Li, Yong-Chang; Ji, Mu-Huo
2016-11-01
The Bland-Altman method has been widely used for assessing agreement between two methods of measurement. However, it remains unsolved about sample size estimation. We propose a new method of sample size estimation for Bland-Altman agreement assessment. According to the Bland-Altman method, the conclusion on agreement is made based on the width of the confidence interval for LOAs (limits of agreement) in comparison to predefined clinical agreement limit. Under the theory of statistical inference, the formulae of sample size estimation are derived, which depended on the pre-determined level of α, β, the mean and the standard deviation of differences between two measurements, and the predefined limits. With this new method, the sample sizes are calculated under different parameter settings which occur frequently in method comparison studies, and Monte-Carlo simulation is used to obtain the corresponding powers. The results of Monte-Carlo simulation showed that the achieved powers could coincide with the pre-determined level of powers, thus validating the correctness of the method. The method of sample size estimation can be applied in the Bland-Altman method to assess agreement between two methods of measurement.
Reduced sample sizes for atrophy outcomes in Alzheimer's disease trials: baseline adjustment
Schott, J.M.; Bartlett, J.W.; Barnes, J.; Leung, K.K.; Ourselin, S.; Fox, N.C.
2010-01-01
Cerebral atrophy rate is increasingly used as an outcome measure for Alzheimer's disease (AD) trials. We used the Alzheimer's disease Neuroimaging initiative (ADNI) dataset to assess if adjusting for baseline characteristics can reduce sample sizes. Controls (n = 199), patients with mild cognitive impairment (MCI) (n = 334) and AD (n = 144) had two MRI scans, 1-year apart; ~ 55% had baseline CSF tau, p-tau, and Aβ1-42. Whole brain (KN–BSI) and hippocampal (HMAPS-HBSI) atrophy rate, and ventricular expansion (VBSI) were calculated for each group; numbers required to power a placebo-controlled trial were estimated. Sample sizes per arm (80% power, 25% absolute rate reduction) for AD were (95% CI): brain atrophy = 81 (64,109), hippocampal atrophy = 88 (68,119), ventricular expansion = 118 (92,157); and for MCI: brain atrophy = 149 (122,188), hippocampal atrophy = 201 (160,262), ventricular expansion = 234 (191,295). To detect a 25% reduction relative to normal aging required increased sample sizes ~ 3-fold (AD), and ~ 5-fold (MCI). Disease severity and Aβ1-42 contributed significantly to atrophy rate variability. Adjusting for 11 predefined covariates reduced sample sizes by up to 30%. Treatment trials in AD should consider the effects of normal aging; adjusting for baseline characteristics can significantly reduce required sample sizes. PMID:20620665
Tsai, Chen-An; Huang, Chih-Yang; Liu, Jen-Pei
2014-08-30
The approval of generic drugs requires the evidence of average bioequivalence (ABE) on both the area under the concentration-time curve and the peak concentration Cmax . The bioequivalence (BE) hypothesis can be decomposed into the non-inferiority (NI) and non-superiority (NS) hypothesis. Most of regulatory agencies employ the two one-sided tests (TOST) procedure to test ABE between two formulations. As it is based on the intersection-union principle, the TOST procedure is conservative in terms of the type I error rate. However, the type II error rate is the sum of the type II error rates with respect to each null hypothesis of NI and NS hypotheses. When the difference in population means between two treatments is not 0, no close-form solution for the sample size for the BE hypothesis is available. Current methods provide the sample sizes with either insufficient power or unnecessarily excessive power. We suggest an approximate method for sample size determination, which can also provide the type II rate for each of NI and NS hypotheses. In addition, the proposed method is flexible to allow extension from one pharmacokinetic (PK) response to determination of the sample size required for multiple PK responses. We report the results of a numerical study. An R code is provided to calculate the sample size for BE testing based on the proposed methods.
How do respiratory state and measurement method affect bra size calculations?
McGhee, D E; Steele, J R
2006-01-01
Objectives To investigate the effects of respiratory state and measurement method on bra size calculation. Methods The bra sizes of 16 large‐breasted women were measured during two respiratory states, end voluntary inspiration and relaxed voluntary expiration, and using two sizing methods, which were compared against subject‐reported bra sizes. Results Both respiratory state and measurement method significantly affected bra size estimations, whereby measuring chest circumference during inspiration increased both band and decreased cup size. However, whereas bra size calculated using the standard method differed significantly from subject‐reported bra size, cup size calculated using the breast hemi‐circumference method did not differ significantly from subject‐reported cup size. Conclusions As respiratory state significantly affects bra sizes, it should be standardised during bra size measurements. A more valid and reliable bra sizing method should be developed, possibly using the breast hemi‐circumference method for cup size estimations and raw under‐bust chest circumference values for band size. PMID:17021004
Enhanced Ligand Sampling for Relative Protein–Ligand Binding Free Energy Calculations
2016-01-01
Free energy calculations are used to study how strongly potential drug molecules interact with their target receptors. The accuracy of these calculations depends on the accuracy of the molecular dynamics (MD) force field as well as proper sampling of the major conformations of each molecule. However, proper sampling of ligand conformations can be difficult when there are large barriers separating the major ligand conformations. An example of this is for ligands with an asymmetrically substituted phenyl ring, where the presence of protein loops hinders the proper sampling of the different ring conformations. These ring conformations become more difficult to sample when the size of the functional groups attached to the ring increases. The Adaptive Integration Method (AIM) has been developed, which adaptively changes the alchemical coupling parameter λ during the MD simulation so that conformations sampled at one λ can aid sampling at the other λ values. The Accelerated Adaptive Integration Method (AcclAIM) builds on AIM by lowering potential barriers for specific degrees of freedom at intermediate λ values. However, these methods may not work when there are very large barriers separating the major ligand conformations. In this work, we describe a modification to AIM that improves sampling of the different ring conformations, even when there is a very large barrier between them. This method combines AIM with conformational Monte Carlo sampling, giving improved convergence of ring populations and the resulting free energy. This method, called AIM/MC, is applied to study the relative binding free energy for a pair of ligands that bind to thrombin and a different pair of ligands that bind to aspartyl protease β-APP cleaving enzyme 1 (BACE1). These protein–ligand binding free energy calculations illustrate the improvements in conformational sampling and the convergence of the free energy compared to both AIM and AcclAIM. PMID:25906170
Enhancing sampling design in mist-net bat surveys by accounting for sample size optimization.
Trevelin, Leonardo Carreira; Novaes, Roberto Leonan Morim; Colas-Rosas, Paul François; Benathar, Thayse Cristhina Melo; Peres, Carlos A
2017-01-01
The advantages of mist-netting, the main technique used in Neotropical bat community studies to date, include logistical implementation, standardization and sampling representativeness. Nonetheless, study designs still have to deal with issues of detectability related to how different species behave and use the environment. Yet there is considerable sampling heterogeneity across available studies in the literature. Here, we approach the problem of sample size optimization. We evaluated the common sense hypothesis that the first six hours comprise the period of peak night activity for several species, thereby resulting in a representative sample for the whole night. To this end, we combined re-sampling techniques, species accumulation curves, threshold analysis, and community concordance of species compositional data, and applied them to datasets of three different Neotropical biomes (Amazonia, Atlantic Forest and Cerrado). We show that the strategy of restricting sampling to only six hours of the night frequently results in incomplete sampling representation of the entire bat community investigated. From a quantitative standpoint, results corroborated the existence of a major Sample Area effect in all datasets, although for the Amazonia dataset the six-hour strategy was significantly less species-rich after extrapolation, and for the Cerrado dataset it was more efficient. From the qualitative standpoint, however, results demonstrated that, for all three datasets, the identity of species that are effectively sampled will be inherently impacted by choices of sub-sampling schedule. We also propose an alternative six-hour sampling strategy (at the beginning and the end of a sample night) which performed better when resampling Amazonian and Atlantic Forest datasets on bat assemblages. Given the observed magnitude of our results, we propose that sample representativeness has to be carefully weighed against study objectives, and recommend that the trade-off between
Enhancing sampling design in mist-net bat surveys by accounting for sample size optimization
Trevelin, Leonardo Carreira; Novaes, Roberto Leonan Morim; Colas-Rosas, Paul François; Benathar, Thayse Cristhina Melo; Peres, Carlos A.
2017-01-01
The advantages of mist-netting, the main technique used in Neotropical bat community studies to date, include logistical implementation, standardization and sampling representativeness. Nonetheless, study designs still have to deal with issues of detectability related to how different species behave and use the environment. Yet there is considerable sampling heterogeneity across available studies in the literature. Here, we approach the problem of sample size optimization. We evaluated the common sense hypothesis that the first six hours comprise the period of peak night activity for several species, thereby resulting in a representative sample for the whole night. To this end, we combined re-sampling techniques, species accumulation curves, threshold analysis, and community concordance of species compositional data, and applied them to datasets of three different Neotropical biomes (Amazonia, Atlantic Forest and Cerrado). We show that the strategy of restricting sampling to only six hours of the night frequently results in incomplete sampling representation of the entire bat community investigated. From a quantitative standpoint, results corroborated the existence of a major Sample Area effect in all datasets, although for the Amazonia dataset the six-hour strategy was significantly less species-rich after extrapolation, and for the Cerrado dataset it was more efficient. From the qualitative standpoint, however, results demonstrated that, for all three datasets, the identity of species that are effectively sampled will be inherently impacted by choices of sub-sampling schedule. We also propose an alternative six-hour sampling strategy (at the beginning and the end of a sample night) which performed better when resampling Amazonian and Atlantic Forest datasets on bat assemblages. Given the observed magnitude of our results, we propose that sample representativeness has to be carefully weighed against study objectives, and recommend that the trade-off between
Optimization of finite-size errors in finite-temperature calculations of unordered phases
NASA Astrophysics Data System (ADS)
Iyer, Deepak; Srednicki, Mark; Rigol, Marcos
It is common knowledge that the microcanonical, canonical, and grand canonical ensembles are equivalent in thermodynamically large systems. Here, we study finite-size effects in the latter two ensembles. We show that contrary to naive expectations, finite-size errors are exponentially small in grand canonical ensemble calculations of translationally invariant systems in unordered phases at finite temperature. Open boundary conditions and canonical ensemble calculations suffer from finite-size errors that are only polynomially small in the system size. We further show that finite-size effects are generally smallest in numerical linked cluster expansions. Our conclusions are supported by analytical and numerical analyses of classical and quantum systems.
Optimization of finite-size errors in finite-temperature calculations of unordered phases
NASA Astrophysics Data System (ADS)
Iyer, Deepak; Srednicki, Mark; Rigol, Marcos
2015-06-01
It is common knowledge that the microcanonical, canonical, and grand-canonical ensembles are equivalent in thermodynamically large systems. Here, we study finite-size effects in the latter two ensembles. We show that contrary to naive expectations, finite-size errors are exponentially small in grand canonical ensemble calculations of translationally invariant systems in unordered phases at finite temperature. Open boundary conditions and canonical ensemble calculations suffer from finite-size errors that are only polynomially small in the system size. We further show that finite-size effects are generally smallest in numerical linked cluster expansions. Our conclusions are supported by analytical and numerical analyses of classical and quantum systems.
General Conformity Training Modules: Appendix A Sample Emissions Calculations
Appendix A of the training modules gives example calculations for external and internal combustion sources, construction, fuel storage and transfer, on-road vehicles, aircraft operations, storage piles, and paved roads.
40 CFR 89.418 - Raw emission sampling calculations.
Code of Federal Regulations, 2012 CFR
2012-07-01
... EXHW Gas mass = v × Gas conc. × V EXHD Gas mass = w × Gas conc. × V EXHW The coefficients u (wet), v... percent. Note: The given coefficients u, v, and w are calculated for 273.15 °K (0 °C) and 101.3 kPa. In...) The following equations may be used to calculate the coefficients u, v, and w in paragraph (e) of...
40 CFR 89.418 - Raw emission sampling calculations.
Code of Federal Regulations, 2014 CFR
2014-07-01
... EXHW Gas mass = v × Gas conc. × V EXHD Gas mass = w × Gas conc. × V EXHW The coefficients u (wet), v... percent. Note: The given coefficients u, v, and w are calculated for 273.15 °K (0 °C) and 101.3 kPa. In...) The following equations may be used to calculate the coefficients u, v, and w in paragraph (e) of...
Ozay, Guner; Seyhan, Ferda; Yilmaz, Aysun; Whitaker, Thomas B; Slate, Andrew B; Giesbrecht, Francis G
2007-01-01
About 100 countries have established regulatory limits for aflatoxin in food and feeds. Because these limits vary widely among regulating countries, the Codex Committee on Food Additives and Contaminants began work in 2004 to harmonize aflatoxin limits and sampling plans for aflatoxin in almonds, pistachios, hazelnuts, and Brazil nuts. Studies were developed to measure the uncertainty and distribution among replicated sample aflatoxin test results taken from aflatoxin-contaminated treenut lots. The uncertainty and distribution information is used to develop a model that can evaluate the performance (risk of misclassifying lots) of aflatoxin sampling plan designs for treenuts. Once the performance of aflatoxin sampling plans can be predicted, they can be designed to reduce the risks of misclassifying lots traded in either the domestic or export markets. A method was developed to evaluate the performance of sampling plans designed to detect aflatoxin in hazelnuts lots. Twenty hazelnut lots with varying levels of contamination were sampled according to an experimental protocol where 16 test samples were taken from each lot. The observed aflatoxin distribution among the 16 aflatoxin sample test results was compared to lognormal, compound gamma, and negative binomial distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits to observed distributions among sample test results taken from a wide range of lot concentrations. Using the negative binomial distribution, computer models were developed to calculate operating characteristic curves for specific aflatoxin sampling plan designs. The effect of sample size and accept/reject limits on the chances of rejecting good lots (sellers' risk) and accepting bad lots (buyers' risk) was demonstrated for various sampling plan designs.
MEPAG Recommendations for a 2018 Mars Sample Return Caching Lander - Sample Types, Number, and Sizes
NASA Technical Reports Server (NTRS)
Allen, Carlton C.
2011-01-01
The return to Earth of geological and atmospheric samples from the surface of Mars is among the highest priority objectives of planetary science. The MEPAG Mars Sample Return (MSR) End-to-End International Science Analysis Group (MEPAG E2E-iSAG) was chartered to propose scientific objectives and priorities for returned sample science, and to map out the implications of these priorities, including for the proposed joint ESA-NASA 2018 mission that would be tasked with the crucial job of collecting and caching the samples. The E2E-iSAG identified four overarching scientific aims that relate to understanding: (A) the potential for life and its pre-biotic context, (B) the geologic processes that have affected the martian surface, (C) planetary evolution of Mars and its atmosphere, (D) potential for future human exploration. The types of samples deemed most likely to achieve the science objectives are, in priority order: (1A). Subaqueous or hydrothermal sediments (1B). Hydrothermally altered rocks or low temperature fluid-altered rocks (equal priority) (2). Unaltered igneous rocks (3). Regolith, including airfall dust (4). Present-day atmosphere and samples of sedimentary-igneous rocks containing ancient trapped atmosphere Collection of geologically well-characterized sample suites would add considerable value to interpretations of all collected rocks. To achieve this, the total number of rock samples should be about 30-40. In order to evaluate the size of individual samples required to meet the science objectives, the E2E-iSAG reviewed the analytical methods that would likely be applied to the returned samples by preliminary examination teams, for planetary protection (i.e., life detection, biohazard assessment) and, after distribution, by individual investigators. It was concluded that sample size should be sufficient to perform all high-priority analyses in triplicate. In keeping with long-established curatorial practice of extraterrestrial material, at least 40% by
40 CFR 89.424 - Dilute emission sampling calculations.
Code of Federal Regulations, 2011 CFR
2011-07-01
... mode for bag measurements and diesel heat exchanger system measurements is determined from the..., for diesel heat exchanger systems, average hydrocarbon concentration of the dilute exhaust sample...
Blinded sample size recalculation in multicentre trials with normally distributed outcome.
Jensen, Katrin; Kieser, Meinhard
2010-06-01
The internal pilot study design enables to estimate nuisance parameters required for sample size calculation on the basis of data accumulated in an ongoing trial. By this, misspecifications made when determining the sample size in the planning phase can be corrected employing updated knowledge. According to regulatory guidelines, blindness of all personnel involved in the trial has to be preserved and the specified type I error rate has to be controlled when the internal pilot study design is applied. Especially in the late phase of drug development, most clinical studies are run in more than one centre. In these multicentre trials, one may have to deal with an unequal distribution of the patient numbers among the centres. Depending on the type of the analysis (weighted or unweighted), unequal centre sample sizes may lead to a substantial loss of power. Like the variance, the magnitude of imbalance is difficult to predict in the planning phase. We propose a blinded sample size recalculation procedure for the internal pilot study design in multicentre trials with normally distributed outcome and two balanced treatment groups that are analysed applying the weighted or the unweighted approach. The method addresses both uncertainty with respect to the variance of the endpoint and the extent of disparity of the centre sample sizes. The actual type I error rate as well as the expected power and sample size of the procedure is investigated in simulation studies. For the weighted analysis as well as for the unweighted analysis, the maximal type I error rate was not or only minimally exceeded. Furthermore, application of the proposed procedure led to an expected power that achieves the specified value in many cases and is throughout very close to it.
Implications of sampling design and sample size for national carbon accounting systems
2011-01-01
Background Countries willing to adopt a REDD regime need to establish a national Measurement, Reporting and Verification (MRV) system that provides information on forest carbon stocks and carbon stock changes. Due to the extensive areas covered by forests the information is generally obtained by sample based surveys. Most operational sampling approaches utilize a combination of earth-observation data and in-situ field assessments as data sources. Results We compared the cost-efficiency of four different sampling design alternatives (simple random sampling, regression estimators, stratified sampling, 2-phase sampling with regression estimators) that have been proposed in the scope of REDD. Three of the design alternatives provide for a combination of in-situ and earth-observation data. Under different settings of remote sensing coverage, cost per field plot, cost of remote sensing imagery, correlation between attributes quantified in remote sensing and field data, as well as population variability and the percent standard error over total survey cost was calculated. The cost-efficiency of forest carbon stock assessments is driven by the sampling design chosen. Our results indicate that the cost of remote sensing imagery is decisive for the cost-efficiency of a sampling design. The variability of the sample population impairs cost-efficiency, but does not reverse the pattern of cost-efficiency of the individual design alternatives. Conclusions, brief summary and potential implications Our results clearly indicate that it is important to consider cost-efficiency in the development of forest carbon stock assessments and the selection of remote sensing techniques. The development of MRV-systems for REDD need to be based on a sound optimization process that compares different data sources and sampling designs with respect to their cost-efficiency. This helps to reduce the uncertainties related with the quantification of carbon stocks and to increase the financial
Threshold-dependent sample sizes for selenium assessment with stream fish tissue
Hitt, Nathaniel P.; Smith, David R.
2015-01-01
Natural resource managers are developing assessments of selenium (Se) contamination in freshwater ecosystems based on fish tissue concentrations. We evaluated the effects of sample size (i.e., number of fish per site) on the probability of correctly detecting mean whole-body Se values above a range of potential management thresholds. We modeled Se concentrations as gamma distributions with shape and scale parameters fitting an empirical mean-to-variance relationship in data from southwestern West Virginia, USA (63 collections, 382 individuals). We used parametric bootstrapping techniques to calculate statistical power as the probability of detecting true mean concentrations up to 3 mg Se/kg above management thresholds ranging from 4 to 8 mg Se/kg. Sample sizes required to achieve 80% power varied as a function of management thresholds and Type I error tolerance (α). Higher thresholds required more samples than lower thresholds because populations were more heterogeneous at higher mean Se levels. For instance, to assess a management threshold of 4 mg Se/kg, a sample of eight fish could detect an increase of approximately 1 mg Se/kg with 80% power (given α = 0.05), but this sample size would be unable to detect such an increase from a management threshold of 8 mg Se/kg with more than a coin-flip probability. Increasing α decreased sample size requirements to detect above-threshold mean Se concentrations with 80% power. For instance, at an α-level of 0.05, an 8-fish sample could detect an increase of approximately 2 units above a threshold of 8 mg Se/kg with 80% power, but when α was relaxed to 0.2, this sample size was more sensitive to increasing mean Se concentrations, allowing detection of an increase of approximately 1.2 units with equivalent power. Combining individuals into 2- and 4-fish composite samples for laboratory analysis did not decrease power because the reduced number of laboratory samples was compensated for by increased
40 CFR Appendix II to Part 600 - Sample Fuel Economy Calculations
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 31 2013-07-01 2013-07-01 false Sample Fuel Economy Calculations II... FUEL ECONOMY AND GREENHOUSE GAS EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App. II Appendix II to Part 600—Sample Fuel Economy Calculations (a) This sample fuel economy calculation is applicable...
40 CFR Appendix II to Part 600 - Sample Fuel Economy Calculations
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 30 2011-07-01 2011-07-01 false Sample Fuel Economy Calculations II... FUEL ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App. II Appendix II to Part 600—Sample Fuel Economy Calculations (a) This sample fuel economy calculation is applicable...
40 CFR Appendix II to Part 600 - Sample Fuel Economy Calculations
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 29 2010-07-01 2010-07-01 false Sample Fuel Economy Calculations II... FUEL ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App. II Appendix II to Part 600—Sample Fuel Economy Calculations (a) This sample fuel economy calculation is applicable...
7 CFR 51.1406 - Sample for grade or size determination.
Code of Federal Regulations, 2010 CFR
2010-01-01
..., AND STANDARDS) United States Standards for Grades of Pecans in the Shell 1 Sample for Grade Or Size Determination § 51.1406 Sample for grade or size determination. Each sample shall consist of 100 pecans....
7 CFR 51.1406 - Sample for grade or size determination.
Code of Federal Regulations, 2012 CFR
2012-01-01
..., AND STANDARDS) United States Standards for Grades of Pecans in the Shell 1 Sample for Grade Or Size Determination § 51.1406 Sample for grade or size determination. Each sample shall consist of 100 pecans....
7 CFR 51.1406 - Sample for grade or size determination.
Code of Federal Regulations, 2011 CFR
2011-01-01
..., AND STANDARDS) United States Standards for Grades of Pecans in the Shell 1 Sample for Grade Or Size Determination § 51.1406 Sample for grade or size determination. Each sample shall consist of 100 pecans....
Chang, Yu-Wei; Tsong, Yi; Zhao, Zhigen
2016-12-09
Assessing equivalence or similarity has drawn much attention recently as many drug products have lost or will lose their patents in the next few years, especially certain best-selling biologics. To claim equivalence between the test treatment and the reference treatment when assay sensitivity is well-established from historical data, one has to demonstrate both superiority of the test treatment over placebo and equivalence between the test treatment and the reference treatment. Thus, there is urgency for practitioners to derive a practical way to calculate sample size for a three-arm equivalence trial. The primary endpoints of a clinical trial may not always be continuous, but may be discrete. In this paper, the authors derive power function and discuss sample size requirement for a three-arm equivalence trial with Poisson and negative binomial clinical endpoints. In addition, the authors examine the effect of the dispersion parameter on the power and the sample size by varying its coefficient from small to large. In extensive numerical studies, the authors demonstrate that required sample size heavily depends on the dispersion parameter. Therefore, misusing a Poisson model for negative binomial data may easily lose power up to 20%, depending on the value of the dispersion parameter.
Whitehead, John; Cleary, Faye; Turner, Amanda
2015-05-30
In this paper, a Bayesian approach is developed for simultaneously comparing multiple experimental treatments with a common control treatment in an exploratory clinical trial. The sample size is set to ensure that, at the end of the study, there will be at least one treatment for which the investigators have a strong belief that it is better than control, or else they have a strong belief that none of the experimental treatments are substantially better than control. This criterion bears a direct relationship with conventional frequentist power requirements, while allowing prior opinion to feature in the analysis with a consequent reduction in sample size. If it is concluded that at least one of the experimental treatments shows promise, then it is envisaged that one or more of these promising treatments will be developed further in a definitive phase III trial. The approach is developed in the context of normally distributed responses sharing a common standard deviation regardless of treatment. To begin with, the standard deviation will be assumed known when the sample size is calculated. The final analysis will not rely upon this assumption, although the intended properties of the design may not be achieved if the anticipated standard deviation turns out to be inappropriate. Methods that formally allow for uncertainty about the standard deviation, expressed in the form of a Bayesian prior, are then explored. Illustrations of the sample sizes computed from the new method are presented, and comparisons are made with frequentist methods devised for the same situation.
Sample size and allocation of effort in point count sampling of birds in bottomland hardwood forests
Smith, W.P.; Twedt, D.J.; Cooper, R.J.; Wiedenfeld, D.A.; Hamel, P.B.; Ford, R.P.; Ralph, C. John; Sauer, John R.; Droege, Sam
1995-01-01
To examine sample size requirements and optimum allocation of effort in point count sampling of bottomland hardwood forests, we computed minimum sample sizes from variation recorded during 82 point counts (May 7-May 16, 1992) from three localities containing three habitat types across three regions of the Mississippi Alluvial Valley (MAV). Also, we estimated the effect of increasing the number of points or visits by comparing results of 150 four-minute point counts obtained from each of four stands on Delta Experimental Forest (DEF) during May 8-May 21, 1991 and May 30-June 12, 1992. For each stand, we obtained bootstrap estimates of mean cumulative number of species each year from all possible combinations of six points and six visits. ANOVA was used to model cumulative species as a function of number of points visited, number of visits to each point, and interaction of points and visits. There was significant variation in numbers of birds and species between regions and localities (nested within region); neither habitat, nor the interaction between region and habitat, was significant. For a = 0.05 and a = 0.10, minimum sample size estimates (per factor level) varied by orders of magnitude depending upon the observed or specified range of desired detectable difference. For observed regional variation, 20 and 40 point counts were required to accommodate variability in total individuals (MSE = 9.28) and species (MSE = 3.79), respectively, whereas ? 25 percent of the mean could be achieved with five counts per factor level. Sample size sufficient to detect actual differences of Wood Thrush (Hylocichla mustelina) was >200, whereas the Prothonotary Warbler (Protonotaria citrea) required <10 counts. Differences in mean cumulative species were detected among number of points visited and among number of visits to a point. In the lower MAV, mean cumulative species increased with each added point through five points and with each additional visit through four visits
Treatment Trials for Neonatal Seizures: The Effect of Design on Sample Size.
Stevenson, Nathan J; Boylan, Geraldine B; Hellström-Westas, Lena; Vanhatalo, Sampsa
2016-01-01
Neonatal seizures are common in the neonatal intensive care unit. Clinicians treat these seizures with several anti-epileptic drugs (AEDs) to reduce seizures in a neonate. Current AEDs exhibit sub-optimal efficacy and several randomized control trials (RCT) of novel AEDs are planned. The aim of this study was to measure the influence of trial design on the required sample size of a RCT. We used seizure time courses from 41 term neonates with hypoxic ischaemic encephalopathy to build seizure treatment trial simulations. We used five outcome measures, three AED protocols, eight treatment delays from seizure onset (Td) and four levels of trial AED efficacy to simulate different RCTs. We performed power calculations for each RCT design and analysed the resultant sample size. We also assessed the rate of false positives, or placebo effect, in typical uncontrolled studies. We found that the false positive rate ranged from 5 to 85% of patients depending on RCT design. For controlled trials, the choice of outcome measure had the largest effect on sample size with median differences of 30.7 fold (IQR: 13.7-40.0) across a range of AED protocols, Td and trial AED efficacy (p<0.001). RCTs that compared the trial AED with positive controls required sample sizes with a median fold increase of 3.2 (IQR: 1.9-11.9; p<0.001). Delays in AED administration from seizure onset also increased the required sample size 2.1 fold (IQR: 1.7-2.9; p<0.001). Subgroup analysis showed that RCTs in neonates treated with hypothermia required a median fold increase in sample size of 2.6 (IQR: 2.4-3.0) compared to trials in normothermic neonates (p<0.001). These results show that RCT design has a profound influence on the required sample size. Trials that use a control group, appropriate outcome measure, and control for differences in Td between groups in analysis will be valid and minimise sample size.
Treatment Trials for Neonatal Seizures: The Effect of Design on Sample Size
Stevenson, Nathan J.; Boylan, Geraldine B.; Hellström-Westas, Lena; Vanhatalo, Sampsa
2016-01-01
Neonatal seizures are common in the neonatal intensive care unit. Clinicians treat these seizures with several anti-epileptic drugs (AEDs) to reduce seizures in a neonate. Current AEDs exhibit sub-optimal efficacy and several randomized control trials (RCT) of novel AEDs are planned. The aim of this study was to measure the influence of trial design on the required sample size of a RCT. We used seizure time courses from 41 term neonates with hypoxic ischaemic encephalopathy to build seizure treatment trial simulations. We used five outcome measures, three AED protocols, eight treatment delays from seizure onset (Td) and four levels of trial AED efficacy to simulate different RCTs. We performed power calculations for each RCT design and analysed the resultant sample size. We also assessed the rate of false positives, or placebo effect, in typical uncontrolled studies. We found that the false positive rate ranged from 5 to 85% of patients depending on RCT design. For controlled trials, the choice of outcome measure had the largest effect on sample size with median differences of 30.7 fold (IQR: 13.7–40.0) across a range of AED protocols, Td and trial AED efficacy (p<0.001). RCTs that compared the trial AED with positive controls required sample sizes with a median fold increase of 3.2 (IQR: 1.9–11.9; p<0.001). Delays in AED administration from seizure onset also increased the required sample size 2.1 fold (IQR: 1.7–2.9; p<0.001). Subgroup analysis showed that RCTs in neonates treated with hypothermia required a median fold increase in sample size of 2.6 (IQR: 2.4–3.0) compared to trials in normothermic neonates (p<0.001). These results show that RCT design has a profound influence on the required sample size. Trials that use a control group, appropriate outcome measure, and control for differences in Td between groups in analysis will be valid and minimise sample size. PMID:27824913
Axelrod, M
2005-08-18
Discovery sampling is a tool used in a discovery auditing. The purpose of such an audit is to provide evidence that some (usually large) inventory of items complies with a defined set of criteria by inspecting (or measuring) a representative sample drawn from the inventory. If any of the items in the sample fail compliance (defective items), then the audit has discovered an impropriety, which often triggers some action. However finding defective items in a sample is an unusual event--auditors expect the inventory to be in compliance because they come to the audit with an ''innocent until proven guilty attitude''. As part of their work product, the auditors must provide a confidence statement about compliance level of the inventory. Clearly the more items they inspect, the greater their confidence, but more inspection means more cost. Audit costs can be purely economic, but in some cases, the cost is political because more inspection means more intrusion, which communicates an attitude of distrust. Thus, auditors have every incentive to minimize the number of items in the sample. Indeed, in some cases the sample size can be specifically limited by a prior agreement or an ongoing policy. Statements of confidence about the results of a discovery sample generally use the method of confidence intervals. After finding no defectives in the sample, the auditors provide a range of values that bracket the number of defective items that could credibly be in the inventory. They also state a level of confidence for the interval, usually 90% or 95%. For example, the auditors might say: ''We believe that this inventory of 1,000 items contains no more than 10 defectives with a confidence of 95%''. Frequently clients ask their auditors questions such as: How many items do you need to measure to be 95% confident that there are no more than 10 defectives in the entire inventory? Sometimes when the auditors answer with big numbers like ''300'', their clients balk. They balk because a
Lee, Eun Gyung; Lee, Taekhee; Kim, Seung Won; Lee, Larry; Flemmer, Michael M.; Harper, Martin
2015-01-01
This second, and concluding, part of this study evaluated changes in sampling efficiency of respirable size-selective samplers due to air pulsations generated by the selected personal sampling pumps characterized in Part I (Lee E, Lee L, Möhlmann C et al. Evaluation of pump pulsation in respirable size-selective sampling: Part I. Pulsation measurements. Ann Occup Hyg 2013). Nine particle sizes of monodisperse ammonium fluorescein (from 1 to 9 μm mass median aerodynamic diameter) were generated individually by a vibrating orifice aerosol generator from dilute solutions of fluorescein in aqueous ammonia and then injected into an environmental chamber. To collect these particles, 10-mm nylon cyclones, also known as Dorr-Oliver (DO) cyclones, were used with five medium volumetric flow rate pumps. Those were the Apex IS, HFS513, GilAir5, Elite5, and Basic5 pumps, which were found in Part I to generate pulsations of 5% (the lowest), 25%, 30%, 56%, and 70% (the highest), respectively. GK2.69 cyclones were used with the Legacy [pump pulsation (PP) = 15%] and Elite12 (PP = 41%) pumps for collection at high flows. The DO cyclone was also used to evaluate changes in sampling efficiency due to pulse shape. The HFS513 pump, which generates a more complex pulse shape, was compared to a single sine wave fluctuation generated by a piston. The luminescent intensity of the fluorescein extracted from each sample was measured with a luminescence spectrometer. Sampling efficiencies were obtained by dividing the intensity of the fluorescein extracted from the filter placed in a cyclone with the intensity obtained from the filter used with a sharp-edged reference sampler. Then, sampling efficiency curves were generated using a sigmoid function with three parameters and each sampling efficiency curve was compared to that of the reference cyclone by constructing bias maps. In general, no change in sampling efficiency (bias under ±10%) was observed until pulsations exceeded 25% for the
Lee, Eun Gyung; Lee, Taekhee; Kim, Seung Won; Lee, Larry; Flemmer, Michael M; Harper, Martin
2014-01-01
This second, and concluding, part of this study evaluated changes in sampling efficiency of respirable size-selective samplers due to air pulsations generated by the selected personal sampling pumps characterized in Part I (Lee E, Lee L, Möhlmann C et al. Evaluation of pump pulsation in respirable size-selective sampling: Part I. Pulsation measurements. Ann Occup Hyg 2013). Nine particle sizes of monodisperse ammonium fluorescein (from 1 to 9 μm mass median aerodynamic diameter) were generated individually by a vibrating orifice aerosol generator from dilute solutions of fluorescein in aqueous ammonia and then injected into an environmental chamber. To collect these particles, 10-mm nylon cyclones, also known as Dorr-Oliver (DO) cyclones, were used with five medium volumetric flow rate pumps. Those were the Apex IS, HFS513, GilAir5, Elite5, and Basic5 pumps, which were found in Part I to generate pulsations of 5% (the lowest), 25%, 30%, 56%, and 70% (the highest), respectively. GK2.69 cyclones were used with the Legacy [pump pulsation (PP) = 15%] and Elite12 (PP = 41%) pumps for collection at high flows. The DO cyclone was also used to evaluate changes in sampling efficiency due to pulse shape. The HFS513 pump, which generates a more complex pulse shape, was compared to a single sine wave fluctuation generated by a piston. The luminescent intensity of the fluorescein extracted from each sample was measured with a luminescence spectrometer. Sampling efficiencies were obtained by dividing the intensity of the fluorescein extracted from the filter placed in a cyclone with the intensity obtained from the filter used with a sharp-edged reference sampler. Then, sampling efficiency curves were generated using a sigmoid function with three parameters and each sampling efficiency curve was compared to that of the reference cyclone by constructing bias maps. In general, no change in sampling efficiency (bias under ±10%) was observed until pulsations exceeded 25% for the
CaSPA - an algorithm for calculation of the size of percolating aggregates
NASA Astrophysics Data System (ADS)
Magee, James E.; Dutton, Helen; Siperstein, Flor R.
2009-09-01
We present an algorithm (CaSPA) which accounts for the effects of periodic boundary conditions in the calculation of size of percolating aggregated clusters. The algorithm calculates the gyration tensor, allowing for a mixture of infinite (macroscale) and finite (microscale) principle moments. Equilibration of a triblock copolymer system from a disordered initial configuration to a hexagonal phase is examined using the algorithm.
Dependence of thermal and epithermal neutron self-shielding on sample size and irradiation site
NASA Astrophysics Data System (ADS)
Chilian, C.; St-Pierre, J.; Kennedy, G.
2006-08-01
Analytical expressions recently developed for calculating thermal and epithermal neutron self-shielding for cylindrical samples used in neutron activation analysis were verified using three different irradiation sites of a SLOWPOKE reactor. The amount of self-shielding varied by less than 10% from one site to another. The self-shielding parameters varied with the size of the cylinder as r(r+h), for h/r ratios from 0.02 to 6.0, even in slightly non-isotropic neutron fields. A practical expression, based on the parameters of the neutron spectrum and the well-known thermal neutron absorption cross-section and the newly defined epithermal neutron absorption cross-section, is proposed for calculating the self-shielding in cylindrical samples.
Guo, Jiin-Huarng; Luh, Wei-Ming
2009-05-01
When planning a study, sample size determination is one of the most important tasks facing the researcher. The size will depend on the purpose of the study, the cost limitations, and the nature of the data. By specifying the standard deviation ratio and/or the sample size ratio, the present study considers the problem of heterogeneous variances and non-normality for Yuen's two-group test and develops sample size formulas to minimize the total cost or maximize the power of the test. For a given power, the sample size allocation ratio can be manipulated so that the proposed formulas can minimize the total cost, the total sample size, or the sum of total sample size and total cost. On the other hand, for a given total cost, the optimum sample size allocation ratio can maximize the statistical power of the test. After the sample size is determined, the present simulation applies Yuen's test to the sample generated, and then the procedure is validated in terms of Type I errors and power. Simulation results show that the proposed formulas can control Type I errors and achieve the desired power under the various conditions specified. Finally, the implications for determining sample sizes in experimental studies and future research are discussed.
Free energy calculation from umbrella sampling using Bayesian inference
NASA Astrophysics Data System (ADS)
Bernstein, Noam; Stecher, Thomas; Csányi, Gábor
2013-03-01
Using simulations to obtain information about the free energy of a system far from its free energy minima requires biased sampling, for example using a series of harmonic umbrella confining potentials to scan over a range of collective variable values. One fundamental distinction between existing methods that use this approach is in what quantities are measured and how they are used: histograms of the system's probability distribution in WHAM, or gradients of the potential of mean force for umbrella integration (UI) and the single-sweep radial basis function (RBF) approach. Here we present a method that reconstructs the free energy from umbrella sampling data using Bayesian inference that effectively uses all available information from multiple umbrella windows. We show that for a single collective variable, our method can use histograms, gradients, or both, to match or outperform WHAM and UI in the accuracy of free energy for a given amount of total simulation time. In higher dimensions, our method can effectively use gradient information to reconstruct the multidimensional free energy surface. We test our method for the alanine polypeptide model system, and show that it is more accurate than a RBF reconstruction for sparse data, and more stable for abundant data.
Effects of sample size and sampling frequency on studies of brown bear home ranges and habitat use
Arthur, Steve M.; Schwartz, Charles C.
1999-01-01
We equipped 9 brown bears (Ursus arctos) on the Kenai Peninsula, Alaska, with collars containing both conventional very-high-frequency (VHF) transmitters and global positioning system (GPS) receivers programmed to determine an animal's position at 5.75-hr intervals. We calculated minimum convex polygon (MCP) and fixed and adaptive kernel home ranges for randomly-selected subsets of the GPS data to examine the effects of sample size on accuracy and precision of home range estimates. We also compared results obtained by weekly aerial radiotracking versus more frequent GPS locations to test for biases in conventional radiotracking data. Home ranges based on the MCP were 20-606 km2 (x = 201) for aerial radiotracking data (n = 12-16 locations/bear) and 116-1,505 km2 (x = 522) for the complete GPS data sets (n = 245-466 locations/bear). Fixed kernel home ranges were 34-955 km2 (x = 224) for radiotracking data and 16-130 km2 (x = 60) for the GPS data. Differences between means for radiotracking and GPS data were due primarily to the larger samples provided by the GPS data. Means did not differ between radiotracking data and equivalent-sized subsets of GPS data (P > 0.10). For the MCP, home range area increased and variability decreased asymptotically with number of locations. For the kernel models, both area and variability decreased with increasing sample size. Simulations suggested that the MCP and kernel models required >60 and >80 locations, respectively, for estimates to be both accurate (change in area <1%/additional location) and precise (CV < 50%). Although the radiotracking data appeared unbiased, except for the relationship between area and sample size, these data failed to indicate some areas that likely were important to bears. Our results suggest that the usefulness of conventional radiotracking data may be limited by potential biases and variability due to small samples. Investigators that use home range estimates in statistical tests should consider the
ERIC Educational Resources Information Center
Shieh, Gwowen
2013-01-01
The a priori determination of a proper sample size necessary to achieve some specified power is an important problem encountered frequently in practical studies. To establish the needed sample size for a two-sample "t" test, researchers may conduct the power analysis by specifying scientifically important values as the underlying population means…
Linden, Ariel
2008-04-01
Prior to implementing a disease management (DM) strategy, a needs assessment should be conducted to determine whether sufficient opportunity exists for an intervention to be successful in the given population. A central component of this assessment is a sample size analysis to determine whether the population is of sufficient size to allow the expected program effect to achieve statistical significance. This paper discusses the parameters that comprise the generic sample size formula for independent samples and their interrelationships, followed by modifications for the DM setting. In addition, a table is provided with sample size estimates for various effect sizes. Examples are described in detail along with strategies for overcoming common barriers. Ultimately, conducting these calculations up front will help set appropriate expectations about the ability to demonstrate the success of the intervention.
Sample size allocation for food item radiation monitoring and safety inspection.
Seto, Mayumi; Uriu, Koichiro
2015-03-01
The objective of this study is to identify a procedure for determining sample size allocation for food radiation inspections of more than one food item to minimize the potential risk to consumers of internal radiation exposure. We consider a simplified case of food radiation monitoring and safety inspection in which a risk manager is required to monitor two food items, milk and spinach, in a contaminated area. Three protocols for food radiation monitoring with different sample size allocations were assessed by simulating random sampling and inspections of milk and spinach in a conceptual monitoring site. Distributions of (131)I and radiocesium concentrations were determined in reference to (131)I and radiocesium concentrations detected in Fukushima prefecture, Japan, for March and April 2011. The results of the simulations suggested that a protocol that allocates sample size to milk and spinach based on the estimation of (131)I and radiocesium concentrations using the apparent decay rate constants sequentially calculated from past monitoring data can most effectively minimize the potential risks of internal radiation exposure.
10 CFR Appendix to Part 474 - Sample Petroleum-Equivalent Fuel Economy Calculations
Code of Federal Regulations, 2011 CFR
2011-01-01
... 10 Energy 3 2011-01-01 2011-01-01 false Sample Petroleum-Equivalent Fuel Economy Calculations..., DEVELOPMENT, AND DEMONSTRATION PROGRAM; PETROLEUM-EQUIVALENT FUEL ECONOMY CALCULATION Pt. 474, App. Appendix to Part 474—Sample Petroleum-Equivalent Fuel Economy Calculations Example 1: An electric vehicle...
10 CFR Appendix to Part 474 - Sample Petroleum-Equivalent Fuel Economy Calculations
Code of Federal Regulations, 2014 CFR
2014-01-01
... 10 Energy 3 2014-01-01 2014-01-01 false Sample Petroleum-Equivalent Fuel Economy Calculations..., DEVELOPMENT, AND DEMONSTRATION PROGRAM; PETROLEUM-EQUIVALENT FUEL ECONOMY CALCULATION Pt. 474, App. Appendix to Part 474—Sample Petroleum-Equivalent Fuel Economy Calculations Example 1: An electric vehicle...
10 CFR Appendix to Part 474 - Sample Petroleum-Equivalent Fuel Economy Calculations
Code of Federal Regulations, 2013 CFR
2013-01-01
... 10 Energy 3 2013-01-01 2013-01-01 false Sample Petroleum-Equivalent Fuel Economy Calculations..., DEVELOPMENT, AND DEMONSTRATION PROGRAM; PETROLEUM-EQUIVALENT FUEL ECONOMY CALCULATION Pt. 474, App. Appendix to Part 474—Sample Petroleum-Equivalent Fuel Economy Calculations Example 1: An electric vehicle...
10 CFR Appendix to Part 474 - Sample Petroleum-Equivalent Fuel Economy Calculations
Code of Federal Regulations, 2010 CFR
2010-01-01
... 10 Energy 3 2010-01-01 2010-01-01 false Sample Petroleum-Equivalent Fuel Economy Calculations..., DEVELOPMENT, AND DEMONSTRATION PROGRAM; PETROLEUM-EQUIVALENT FUEL ECONOMY CALCULATION Pt. 474, App. Appendix to Part 474—Sample Petroleum-Equivalent Fuel Economy Calculations Example 1: An electric vehicle...
10 CFR Appendix to Part 474 - Sample Petroleum-Equivalent Fuel Economy Calculations
Code of Federal Regulations, 2012 CFR
2012-01-01
... 10 Energy 3 2012-01-01 2012-01-01 false Sample Petroleum-Equivalent Fuel Economy Calculations..., DEVELOPMENT, AND DEMONSTRATION PROGRAM; PETROLEUM-EQUIVALENT FUEL ECONOMY CALCULATION Pt. 474, App. Appendix to Part 474—Sample Petroleum-Equivalent Fuel Economy Calculations Example 1: An electric vehicle...
Comparing Server Energy Use and Efficiency Using Small Sample Sizes
Coles, Henry C.; Qin, Yong; Price, Phillip N.
2014-11-01
This report documents a demonstration that compared the energy consumption and efficiency of a limited sample size of server-type IT equipment from different manufacturers by measuring power at the server power supply power cords. The results are specific to the equipment and methods used. However, it is hoped that those responsible for IT equipment selection can used the methods described to choose models that optimize energy use efficiency. The demonstration was conducted in a data center at Lawrence Berkeley National Laboratory in Berkeley, California. It was performed with five servers of similar mechanical and electronic specifications; three from Intel and one each from Dell and Supermicro. Server IT equipment is constructed using commodity components, server manufacturer-designed assemblies, and control systems. Server compute efficiency is constrained by the commodity component specifications and integration requirements. The design freedom, outside of the commodity component constraints, provides room for the manufacturer to offer a product with competitive efficiency that meets market needs at a compelling price. A goal of the demonstration was to compare and quantify the server efficiency for three different brands. The efficiency is defined as the average compute rate (computations per unit of time) divided by the average energy consumption rate. The research team used an industry standard benchmark software package to provide a repeatable software load to obtain the compute rate and provide a variety of power consumption levels. Energy use when the servers were in an idle state (not providing computing work) were also measured. At high server compute loads, all brands, using the same key components (processors and memory), had similar results; therefore, from these results, it could not be concluded that one brand is more efficient than the other brands. The test results show that the power consumption variability caused by the key components as a
Pang, Herbert; Jung, Sin-Ho
2013-04-01
A variety of prediction methods are used to relate high-dimensional genome data with a clinical outcome using a prediction model. Once a prediction model is developed from a data set, it should be validated using a resampling method or an independent data set. Although the existing prediction methods have been intensively evaluated by many investigators, there has not been a comprehensive study investigating the performance of the validation methods, especially with a survival clinical outcome. Understanding the properties of the various validation methods can allow researchers to perform more powerful validations while controlling for type I error. In addition, sample size calculation strategy based on these validation methods is lacking. We conduct extensive simulations to examine the statistical properties of these validation strategies. In both simulations and a real data example, we have found that 10-fold cross-validation with permutation gave the best power while controlling type I error close to the nominal level. Based on this, we have also developed a sample size calculation method that will be used to design a validation study with a user-chosen combination of prediction. Microarray and genome-wide association studies data are used as illustrations. The power calculation method in this presentation can be used for the design of any biomedical studies involving high-dimensional data and survival outcomes.
A Novel Size-Selective Airborne Particle Sampling Instrument (Wras) for Health Risk Evaluation
NASA Astrophysics Data System (ADS)
Gnewuch, H.; Muir, R.; Gorbunov, B.; Priest, N. D.; Jackson, P. R.
Health risks associated with inhalation of airborne particles are known to be influenced by particle sizes. A reliable, size resolving sampler, classifying particles in size ranges from 2 nm—30 μm and suitable for use in the field would be beneficial in investigating health risks associated with inhalation of airborne particles. A review of current aerosol samplers highlighted a number of limitations. These could be overcome by combining an inertial deposition impactor with a diffusion collector in a single device. The instrument was designed for analysing mass size distributions. Calibration was carried out using a number of recognised techniques. The instrument was tested in the field by collecting size resolved samples of lead containing aerosols present at workplaces in factories producing crystal glass. The mass deposited on each substrate proved sufficient to be detected and measured using atomic absorption spectroscopy. Mass size distributions of lead were produced and the proportion of lead present in the aerosol nanofraction calculated and varied from 10% to 70% by weight.
ERIC Educational Resources Information Center
Algina, James; Moulder, Bradley C.
2001-01-01
Studied sample sizes for confidence intervals on the increase in the squared multiple correlation coefficient using simulation. Discusses predictors and actual coverage probability and provides sample-size guidelines for probability coverage to be near the nominal confidence interval. (SLD)
NASA Technical Reports Server (NTRS)
Sandlin, Doral R.; Swanson, Stephen Mark
1990-01-01
The creation of a computer module used to calculate the size of the horizontal control surfaces of a conceptual aircraft design is discussed. The control surface size is determined by first calculating the size needed to rotate the aircraft during takeoff, and, second, by determining if the calculated size is large enough to maintain stability of the aircraft throughout any specified mission. The tail size needed to rotate during takeoff is calculated from a summation of forces about the main landing gear of the aircraft. The stability of the aircraft is determined from a summation of forces about the center of gravity during different phases of the aircraft's flight. Included in the horizontal control surface analysis are: downwash effects on an aft tail, upwash effects on a forward canard, and effects due to flight in close proximity to the ground. Comparisons of production aircraft with numerical models show good accuracy for control surface sizing. A modified canard design verified the accuracy of the module for canard configurations. Added to this stability and control module is a subroutine that determines one of the three design variables, for a stable vectored thrust aircraft. These include forward thrust nozzle position, aft thrust nozzle angle, and forward thrust split.
Exploring the Dependence of QM/MM Calculations of Enzyme Catalysis on the Size of the QM Region
2016-01-01
Although QM/MM calculations are the primary current tool for modeling enzymatic reactions, the reliability of such calculations can be limited by the size of the QM region. Thus, we examine in this work the dependence of QM/MM calculations on the size of the QM region, using the reaction of catechol-O-methyl transferase (COMT) as a test case. Our study focuses on the effect of adding residues to the QM region on the activation free energy, obtained with extensive QM/MM sampling. It is found that the sensitivity of the activation barrier to the size of the QM is rather limited, while the dependence of the reaction free energy is somewhat larger. Of course, the results depend on the inclusion of the first solvation shell in the QM regions. For example, the inclusion of the Mg2+ ion can change the activation barrier due to charge transfer effects. However, such effects can easily be included in semiempirical approaches by proper parametrization. Overall, we establish that QM/MM calculations of activation barriers of enzymatic reactions are not highly sensitive to the size of the QM region, beyond the immediate region that describes the reacting atoms. PMID:27552257
A contemporary decennial global sample of changing agricultural field sizes
NASA Astrophysics Data System (ADS)
White, E.; Roy, D. P.
2011-12-01
In the last several hundred years agriculture has caused significant human induced Land Cover Land Use Change (LCLUC) with dramatic cropland expansion and a marked increase in agricultural productivity. The size of agricultural fields is a fundamental description of rural landscapes and provides an insight into the drivers of rural LCLUC. Increasing field sizes cause a subsequent decrease in the number of fields and therefore decreased landscape spatial complexity with impacts on biodiversity, habitat, soil erosion, plant-pollinator interactions, diffusion of disease pathogens and pests, and loss or degradation in buffers to nutrient, herbicide and pesticide flows. In this study, globally distributed locations with significant contemporary field size change were selected guided by a global map of agricultural yield and literature review and were selected to be representative of different driving forces of field size change (associated with technological innovation, socio-economic conditions, government policy, historic patterns of land cover land use, and environmental setting). Seasonal Landsat data acquired on a decadal basis (for 1980, 1990, 2000 and 2010) were used to extract field boundaries and the temporal changes in field size quantified and their causes discussed.
Increasing the sample size at interim for a two-sample experiment without Type I error inflation.
Dunnigan, Keith; King, Dennis W
2010-01-01
For the case of a one-sample experiment with known variance σ² =1, it has been shown that at interim analysis the sample size (SS) may be increased by any arbitrary amount provided: (1) The conditional power (CP) at interim is ≥ 50% and (2) there can be no decision to decrease the SS (stop the trial early). In this paper we verify this result for the case of a two-sample experiment with proportional SS in the treatment groups and an arbitrary common variance. Numerous authors have presented the formula for the CP at interim for a two-sample test with equal SS in the treatment groups and an arbitrary common variance, for both the one- and two-sided hypothesis tests. In this paper we derive the corresponding formula for the case of unequal, but proportional SS in the treatment groups for both one-sided superiority and two-sided hypothesis tests. Finally, we present an SAS macro for doing this calculation and provide a worked out hypothetical example. In discussion we note that this type of trial design trades the ability to stop early (for lack of efficacy) for the elimination of the Type I error penalty. The loss of early stopping requires that such a design employs a data monitoring committee, blinding of the sponsor to the interim calculations, and pre-planning of how much and under what conditions to increase the SS and that this all be formally written into an interim analysis plan before the start of the study.
Sample Size Determination for Regression Models Using Monte Carlo Methods in R
ERIC Educational Resources Information Center
Beaujean, A. Alexander
2014-01-01
A common question asked by researchers using regression models is, What sample size is needed for my study? While there are formulae to estimate sample sizes, their assumptions are often not met in the collected data. A more realistic approach to sample size determination requires more information such as the model of interest, strength of the…
M. Gross
2004-09-01
The purpose of this scientific analysis is to define the sampled values of stochastic (random) input parameters for (1) rockfall calculations in the lithophysal and nonlithophysal zones under vibratory ground motions, and (2) structural response calculations for the drip shield and waste package under vibratory ground motions. This analysis supplies: (1) Sampled values of ground motion time history and synthetic fracture pattern for analysis of rockfall in emplacement drifts in nonlithophysal rock (Section 6.3 of ''Drift Degradation Analysis'', BSC 2004 [DIRS 166107]); (2) Sampled values of ground motion time history and rock mechanical properties category for analysis of rockfall in emplacement drifts in lithophysal rock (Section 6.4 of ''Drift Degradation Analysis'', BSC 2004 [DIRS 166107]); (3) Sampled values of ground motion time history and metal to metal and metal to rock friction coefficient for analysis of waste package and drip shield damage to vibratory motion in ''Structural Calculations of Waste Package Exposed to Vibratory Ground Motion'' (BSC 2004 [DIRS 167083]) and in ''Structural Calculations of Drip Shield Exposed to Vibratory Ground Motion'' (BSC 2003 [DIRS 163425]). The sampled values are indices representing the number of ground motion time histories, number of fracture patterns and rock mass properties categories. These indices are translated into actual values within the respective analysis and model reports or calculations. This report identifies the uncertain parameters and documents the sampled values for these parameters. The sampled values are determined by GoldSim V6.04.007 [DIRS 151202] calculations using appropriate distribution types and parameter ranges. No software development or model development was required for these calculations. The calculation of the sampled values allows parameter uncertainty to be incorporated into the rockfall and structural response calculations that support development of the seismic scenario for the
7 CFR 201.43 - Size of sample.
Code of Federal Regulations, 2013 CFR
2013-01-01
... Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE (CONTINUED) FEDERAL SEED ACT FEDERAL SEED ACT... seeds of similar or larger size. (e) Two quarts (2.2 liters) of screenings. (f) Vegetable seed...
Efficiency of whole-body counter for various body size calculated by MCNP5 software.
Krstic, D; Nikezic, D
2012-11-01
The efficiency of a whole-body counter for (137)Cs and (40)K was calculated using the MCNP5 code. The ORNL phantoms of a human body of different body sizes were applied in a sitting position in front of a detector. The aim was to investigate the dependence of efficiency on the body size (age) and the detector position with respect to the body and to estimate the accuracy of real measurements. The calculation work presented here is related to the NaI detector, which is available in the Serbian Whole-body Counter facility in Vinca Institute.
Determination of the size of a radiation source by the method of calculation of diffraction patterns
NASA Astrophysics Data System (ADS)
Tilikin, I. N.; Shelkovenko, T. A.; Pikuz, S. A.; Hammer, D. A.
2013-07-01
In traditional X-ray radiography, which has been used for various purposes since the discovery of X-ray radiation, the shadow image of an object under study is constructed based on the difference in the absorption of the X-ray radiation by different parts of the object. The main method that ensures a high spatial resolution is the method of point projection X-ray radiography, i.e., radiography from a point and bright radiation source. For projection radiography, the small size of the source is the most important characteristic of the source, which mainly determines the spatial resolution of the method. In this work, as a point source of soft X-ray radiation for radiography with a high spatial and temporal resolution, radiation from a hot spot of X-pinches is used. The size of the radiation source in different setups and configurations can be different. For four different high-current generators, we have calculated the sizes of sources of soft X-ray radiation from X-ray patterns of corresponding objects using Fresnel-Kirchhoff integrals. Our calculations show that the size of the source is in the range 0.7-2.8 μm. The method of the determination of the size of a radiation source from calculations of Fresnel-Kirchhoff integrals makes it possible to determine the size with an accuracy that exceeds the diffraction limit, which frequently restricts the resolution of standard methods.
ERIC Educational Resources Information Center
Bill, Anthony; Henderson, Sally; Penman, John
2010-01-01
Two test items that examined high school students' beliefs of sample size for large populations using the context of opinion polls conducted prior to national and state elections were developed. A trial of the two items with 21 male and 33 female Year 9 students examined their naive understanding of sample size: over half of students chose a…
Cavern/Vault Disposal Concepts and Thermal Calculations for Direct Disposal of 37-PWR Size DPCs
Hardin, Ernest; Hadgu, Teklu; Clayton, Daniel James
2015-03-01
This report provides two sets of calculations not presented in previous reports on the technical feasibility of spent nuclear fuel (SNF) disposal directly in dual-purpose canisters (DPCs): 1) thermal calculations for reference disposal concepts using larger 37-PWR size DPC-based waste packages, and 2) analysis and thermal calculations for underground vault-type storage and eventual disposal of DPCs. The reader is referred to the earlier reports (Hardin et al. 2011, 2012, 2013; Hardin and Voegele 2013) for contextual information on DPC direct disposal alternatives.
Naimi, Ladan J.; Collard, Flavien; Bi, Xiaotao; ...
2016-01-05
Size reduction is an unavoidable operation for preparing biomass for biofuels and bioproduct conversion. Yet, there is considerable uncertainty in power input requirement and the uniformity of ground biomass. Considerable gains are possible if the required power input for a size reduction ratio is estimated accurately. In this research three well-known mechanistic equations attributed to Rittinger, Kick, and Bond available for predicting energy input for grinding pine wood chips were tested against experimental grinding data. Prior to testing, samples of pine wood chips were conditioned to 11.7% wb, moisture content. The wood chips were successively ground in a hammer millmore » using screen sizes of 25.4 mm, 10 mm, 6.4 mm, and 3.2 mm. The input power and the flow of material into the grinder were recorded continuously. The recorded power input vs. mean particle size showed that the Rittinger equation had the best fit to the experimental data. The ground particle sizes were 4 to 7 times smaller than the size of installed screen. Geometric mean size of particles were calculated using two methods (1) Tyler sieves and using particle size analysis and (2) Sauter mean diameter calculated from the ratio of volume to surface that were estimated from measured length and width. The two mean diameters agreed well, pointing to the fact that either mechanical sieving or particle imaging can be used to characterize particle size. In conclusion, specific energy input to the hammer mill increased from 1.4 kWh t–1 (5.2 J g–1) for large 25.1-mm screen to 25 kWh t–1 (90.4 J g–1) for small 3.2-mm screen.« less
Naimi, Ladan J.; Collard, Flavien; Bi, Xiaotao; Lim, C. Jim; Sokhansanj, Shahab
2016-01-05
Size reduction is an unavoidable operation for preparing biomass for biofuels and bioproduct conversion. Yet, there is considerable uncertainty in power input requirement and the uniformity of ground biomass. Considerable gains are possible if the required power input for a size reduction ratio is estimated accurately. In this research three well-known mechanistic equations attributed to Rittinger, Kick, and Bond available for predicting energy input for grinding pine wood chips were tested against experimental grinding data. Prior to testing, samples of pine wood chips were conditioned to 11.7% wb, moisture content. The wood chips were successively ground in a hammer mill using screen sizes of 25.4 mm, 10 mm, 6.4 mm, and 3.2 mm. The input power and the flow of material into the grinder were recorded continuously. The recorded power input vs. mean particle size showed that the Rittinger equation had the best fit to the experimental data. The ground particle sizes were 4 to 7 times smaller than the size of installed screen. Geometric mean size of particles were calculated using two methods (1) Tyler sieves and using particle size analysis and (2) Sauter mean diameter calculated from the ratio of volume to surface that were estimated from measured length and width. The two mean diameters agreed well, pointing to the fact that either mechanical sieving or particle imaging can be used to characterize particle size. In conclusion, specific energy input to the hammer mill increased from 1.4 kWh t^{–1} (5.2 J g^{–1}) for large 25.1-mm screen to 25 kWh t^{–1} (90.4 J g^{–1}) for small 3.2-mm screen.
Utility of Inferential Norming with Smaller Sample Sizes
ERIC Educational Resources Information Center
Zhu, Jianjun; Chen, Hsin-Yi
2011-01-01
We examined the utility of inferential norming using small samples drawn from the larger "Wechsler Intelligence Scales for Children-Fourth Edition" (WISC-IV) standardization data set. The quality of the norms was estimated with multiple indexes such as polynomial curve fit, percentage of cases receiving the same score, average absolute…
7 CFR 52.775 - Sample unit size.
Code of Federal Regulations, 2010 CFR
2010-01-01
... Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE REGULATIONS AND STANDARDS UNDER THE AGRICULTURAL MARKETING ACT OF 1946... extraneous material—The total contents of each container in the sample. Factors of Quality...
Precision of Student Growth Percentiles with Small Sample Sizes
ERIC Educational Resources Information Center
Culbertson, Michael J.
2016-01-01
States in the Regional Educational Laboratory (REL) Central region serve a largely rural population with many states enrolling fewer than 350,000 students. A common challenge identified among REL Central educators is identifying appropriate methods for analyzing data with small samples of students. In particular, members of the REL Central…
40 CFR Appendix III to Part 600 - Sample Fuel Economy Label Calculation
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 29 2010-07-01 2010-07-01 false Sample Fuel Economy Label Calculation...) ENERGY POLICY FUEL ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App. III Appendix III to Part 600—Sample Fuel Economy Label Calculation Suppose that a manufacturer called...
Zeestraten, Eva; Lambert, Christian; Chis Ster, Irina; Williams, Owen A; Lawrence, Andrew J; Patel, Bhavini; MacKinnon, Andrew D; Barrick, Thomas R; Markus, Hugh S
2016-01-01
Detecting treatment efficacy using cognitive change in trials of cerebral small vessel disease (SVD) has been challenging, making the use of surrogate markers such as magnetic resonance imaging (MRI) attractive. We determined the sensitivity of MRI to change in SVD and used this information to calculate sample size estimates for a clinical trial. Data from the prospective SCANS (St George’s Cognition and Neuroimaging in Stroke) study of patients with symptomatic lacunar stroke and confluent leukoaraiosis was used (n = 121). Ninety-nine subjects returned at one or more time points. Multimodal MRI and neuropsychologic testing was performed annually over 3 years. We evaluated the change in brain volume, T2 white matter hyperintensity (WMH) volume, lacunes, and white matter damage on diffusion tensor imaging (DTI). Over 3 years, change was detectable in all MRI markers but not in cognitive measures. WMH volume and DTI parameters were most sensitive to change and therefore had the smallest sample size estimates. MRI markers, particularly WMH volume and DTI parameters, are more sensitive to SVD progression over short time periods than cognition. These markers could significantly reduce the size of trials to screen treatments for efficacy in SVD, although further validation from longitudinal and intervention studies is required. PMID:26036939
Sample size needs for characterizing pollutant concentrations in highway runoff
Thomson, N.R.; Mostrenko, I.; McBean, E.A.; Snodgrass, W.
1997-10-01
The identification of environmentally acceptable and cost-effective technologies for the control of highway storm-water runoff is of significant concern throughout North America. The environmental impact of storm-water runoff, in particular at highway crossings over small surface waterbodies is of sufficient concern to require examination of the detrimental impacts of highway runoff on the flora and fauna. The number of samples necessary for characterization of highway storm-water runoff concentrations is examined. Using extensive field monitoring results available from Minnesota, the statistical modeling results demonstrate that approximately 15 to 20 samples are required to provide reasonable estimates of the mean concentrations of runoff events for total suspended solids, total dissolved solids, total organic carbon, and zinc.
ANOVA with random sample sizes: An application to a Brazilian database on cancer registries
NASA Astrophysics Data System (ADS)
Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.
2013-10-01
We apply our results on random sample size ANOVA to a Brazilian database on cancer registries. The samples sizes will be considered as realizations of random variables. The interest of this approach lies in avoiding false rejections obtained when using the classical fixed size F-tests.
Sample-size considerations and strategies for linkage analysis in autosomal recessive disorders.
Wong, F L; Cantor, R M; Rotter, J I
1986-01-01
The opportunity raised by recombinant DNA technology to develop a linkage marker panel that spans the human genome requires cost-efficient strategies for its optimal utilization. Questions arise as to whether it is more cost-effective to convert a dimorphic restriction enzyme marker system into a highly polymorphic system or, instead, to increase the number of families studied, simply using the available marker alleles. The choice is highly dependent on the population available for study, and, therefore, an examination of the informational content of the various family structures is important to obtain the most informative data. To guide such decisions, we have developed tables of the average sample number of families required to detect linkage for autosomal recessive disorders under single backcross and under "fully informative" matings. The latter cross consists of a marker locus with highly polymorphic codominant alleles such that the parental marker genotypes can be uniquely distinguished. The sampling scheme considers families with unaffected parents of known mating types ascertained via affected offspring, for sibship sizes ranging from two to four and various numbers of affected individuals. The sample-size tables, calculated for various values of the recombination fractions and lod scores, may serve as a guide to a more efficient application of the restriction fragment length polymorphism technology to sequential linkage analysis. PMID:3019130
Presentation of coefficient of variation for bioequivalence sample-size calculation .
Lee, Yi Lin; Mak, Wen Yao; Looi, Irene; Wong, Jia Woei; Yuen, Kah Hay
2017-03-03
The current study aimed to further contribute information on intrasubject coefficient of variation (CV) from 43 bioequivalence studies conducted by our center. Consistent with Yuen et al. (2001), current work also attempted to evaluate the effect of different parameters (AUC0-t, AUC0-∞, and Cmax) used in the estimation of the study power. Furthermore, we have estimated the number of subjects required for each study by looking at the values of intrasubject CV of AUC0-∞ and have also taken into consideration the minimum sample-size requirement set by the US FDA. A total of 37 immediate-release and 6 extended-release formulations from 28 different active pharmaceutical ingredients (APIs) were evaluated. Out of the total number of studies conducted, 10 studies did not achieve satisfactory statistical power on two or more parameters; 4 studies consistently scored poorly across all three parameters. In general, intrasubject CV values calculated from Cmax were more variable compared to either AUC0-t and AUC0-∞. 20 out of 43 studies did not achieve more than 80% power when the value was calculated from Cmax value, compared to only 11 (AUC0-∞) and 8 (AUC0-t) studies. This finding is consistent with Steinijans et al. (1995) [2] and Yuen et al. (2001) [3]. In conclusion, the CV values obtained from AUC0-t and AUC0-∞ were similar, while those derived from Cmax were consistently more variable. Hence, CV derived from AUC instead of Cmax should be used in sample-size calculation to achieve a sufficient, yet practical, test power. .
Structured estimation - Sample size reduction for adaptive pattern classification
NASA Technical Reports Server (NTRS)
Morgera, S.; Cooper, D. B.
1977-01-01
The Gaussian two-category classification problem with known category mean value vectors and identical but unknown category covariance matrices is considered. The weight vector depends on the unknown common covariance matrix, so the procedure is to estimate the covariance matrix in order to obtain an estimate of the optimum weight vector. The measure of performance for the adapted classifier is the output signal-to-interference noise ratio (SIR). A simple approximation for the expected SIR is gained by using the general sample covariance matrix estimator; this performance is both signal and true covariance matrix independent. An approximation is also found for the expected SIR obtained by using a Toeplitz form covariance matrix estimator; this performance is found to be dependent on both the signal and the true covariance matrix.
A Note on Sample Size and Solution Propriety for Confirmatory Factor Analytic Models
ERIC Educational Resources Information Center
Jackson, Dennis L.; Voth, Jennifer; Frey, Marc P.
2013-01-01
Determining an appropriate sample size for use in latent variable modeling techniques has presented ongoing challenges to researchers. In particular, small sample sizes are known to present concerns over sampling error for the variances and covariances on which model estimation is based, as well as for fit indexes and convergence failures. The…
Sample Size in Differential Item Functioning: An Application of Hierarchical Linear Modeling
ERIC Educational Resources Information Center
Acar, Tulin
2011-01-01
The purpose of this study is to examine the number of DIF items detected by HGLM at different sample sizes. Eight different sized data files have been composed. The population of the study is 798307 students who had taken the 2006 OKS Examination. 10727 students of 798307 are chosen by random sampling method as the sample of the study. Turkish,…
Distance software: design and analysis of distance sampling surveys for estimating population size.
Thomas, Len; Buckland, Stephen T; Rexstad, Eric A; Laake, Jeff L; Strindberg, Samantha; Hedley, Sharon L; Bishop, Jon Rb; Marques, Tiago A; Burnham, Kenneth P
2010-02-01
1.Distance sampling is a widely used technique for estimating the size or density of biological populations. Many distance sampling designs and most analyses use the software Distance.2.We briefly review distance sampling and its assumptions, outline the history, structure and capabilities of Distance, and provide hints on its use.3.Good survey design is a crucial prerequisite for obtaining reliable results. Distance has a survey design engine, with a built-in geographic information system, that allows properties of different proposed designs to be examined via simulation, and survey plans to be generated.4.A first step in analysis of distance sampling data is modelling the probability of detection. Distance contains three increasingly sophisticated analysis engines for this: conventional distance sampling, which models detection probability as a function of distance from the transect and assumes all objects at zero distance are detected; multiple-covariate distance sampling, which allows covariates in addition to distance; and mark-recapture distance sampling, which relaxes the assumption of certain detection at zero distance.5.All three engines allow estimation of density or abundance, stratified if required, with associated measures of precision calculated either analytically or via the bootstrap.6.Advanced analysis topics covered include the use of multipliers to allow analysis of indirect surveys (such as dung or nest surveys), the density surface modelling analysis engine for spatial and habitat modelling, and information about accessing the analysis engines directly from other software.7.Synthesis and applications. Distance sampling is a key method for producing abundance and density estimates in challenging field conditions. The theory underlying the methods continues to expand to cope with realistic estimation situations. In step with theoretical developments, state-of-the-art software that implements these methods is described that makes the methods
NASA Astrophysics Data System (ADS)
Bormann, H.
2006-09-01
This paper analyses the effect of spatial input data resolution on the simulated effects of regional scale landuse scenarios using the TOPLATS model. A data set of 25 m resolution of the central German Dill catchment (693 km2) and three different landuse scenarios are used for the investigation. Landuse scenarios in this study are field size scenarios, and depending on a specific target field size (0.5 ha, 1.5 ha and 5.0 ha) landuse is determined by optimising economic outcome of agricultural used areas and forest. After an aggregation of digital elevation model, soil map, current landuse and landuse scenarios to 50 m, 75 m, 100 m, 150 m, 200 m, 300 m, 500 m, 1 km and 2 km, water balances and water flow components for a 20 years time period are calculated for the entire Dill catchment as well as for 3 subcatchments without any recalibration. Additionally water balances based on the three landuse scenarios as well as changes between current conditions and scenarios are calculated. The study reveals that both model performance measures (for current landuse) as well as water balances (for current landuse and landuse scenarios) almost remain constant for most of the aggregation steps for all investigated catchments. Small deviations are detected at the resolution of 50 m to 500 m, while significant differences occur at the resolution of 1 km and 2 km which can be explained by changes in the statistics of the input data. Calculating the scenario effects based on increasing grid sizes yields similar results. However, the change effects react more sensitive to data aggregation than simple water balance calculations. Increasing deviations between simulations based on small grid sizes and simulations using grid sizes of 300 m and more are observed. Summarizing, this study indicates that an aggregation of input data for the calculation of regional water balances using TOPLATS type models does not lead to significant errors up to a resolution of 500 m. Focusing on scenario
40 CFR 761.243 - Standard wipe sample method and size.
Code of Federal Regulations, 2012 CFR
2012-07-01
..., AND USE PROHIBITIONS Determining a PCB Concentration for Purposes of Abandonment or Disposal of Natural Gas Pipeline: Selecting Sample Sites, Collecting Surface Samples, and Analyzing Standard PCB Wipe Samples § 761.243 Standard wipe sample method and size. (a) Collect a surface sample from a natural...
40 CFR 761.243 - Standard wipe sample method and size.
Code of Federal Regulations, 2013 CFR
2013-07-01
..., AND USE PROHIBITIONS Determining a PCB Concentration for Purposes of Abandonment or Disposal of Natural Gas Pipeline: Selecting Sample Sites, Collecting Surface Samples, and Analyzing Standard PCB Wipe Samples § 761.243 Standard wipe sample method and size. (a) Collect a surface sample from a natural...
40 CFR 761.243 - Standard wipe sample method and size.
Code of Federal Regulations, 2014 CFR
2014-07-01
..., AND USE PROHIBITIONS Determining a PCB Concentration for Purposes of Abandonment or Disposal of Natural Gas Pipeline: Selecting Sample Sites, Collecting Surface Samples, and Analyzing Standard PCB Wipe Samples § 761.243 Standard wipe sample method and size. (a) Collect a surface sample from a natural...
Evaluation of design flood estimates with respect to sample size
NASA Astrophysics Data System (ADS)
Kobierska, Florian; Engeland, Kolbjorn
2016-04-01
Estimation of design floods forms the basis for hazard management related to flood risk and is a legal obligation when building infrastructure such as dams, bridges and roads close to water bodies. Flood inundation maps used for land use planning are also produced based on design flood estimates. In Norway, the current guidelines for design flood estimates give recommendations on which data, probability distribution, and method to use dependent on length of the local record. If less than 30 years of local data is available, an index flood approach is recommended where the local observations are used for estimating the index flood and regional data are used for estimating the growth curve. For 30-50 years of data, a 2 parameter distribution is recommended, and for more than 50 years of data, a 3 parameter distribution should be used. Many countries have national guidelines for flood frequency estimation, and recommended distributions include the log Pearson II, generalized logistic and generalized extreme value distributions. For estimating distribution parameters, ordinary and linear moments, maximum likelihood and Bayesian methods are used. The aim of this study is to r-evaluate the guidelines for local flood frequency estimation. In particular, we wanted to answer the following questions: (i) Which distribution gives the best fit to the data? (ii) Which estimation method provides the best fit to the data? (iii) Does the answer to (i) and (ii) depend on local data availability? To answer these questions we set up a test bench for local flood frequency analysis using data based cross-validation methods. The criteria were based on indices describing stability and reliability of design flood estimates. Stability is used as a criterion since design flood estimates should not excessively depend on the data sample. The reliability indices describe to which degree design flood predictions can be trusted.
Got power? A systematic review of sample size adequacy in health professions education research.
Cook, David A; Hatala, Rose
2015-03-01
Many education research studies employ small samples, which in turn lowers statistical power. We re-analyzed the results of a meta-analysis of simulation-based education to determine study power across a range of effect sizes, and the smallest effect that could be plausibly excluded. We systematically searched multiple databases through May 2011, and included all studies evaluating simulation-based education for health professionals in comparison with no intervention or another simulation intervention. Reviewers working in duplicate abstracted information to calculate standardized mean differences (SMD's). We included 897 original research studies. Among the 627 no-intervention-comparison studies the median sample size was 25. Only two studies (0.3%) had ≥80% power to detect a small difference (SMD > 0.2 standard deviations) and 136 (22%) had power to detect a large difference (SMD > 0.8). 110 no-intervention-comparison studies failed to find a statistically significant difference, but none excluded a small difference and only 47 (43%) excluded a large difference. Among 297 studies comparing alternate simulation approaches the median sample size was 30. Only one study (0.3%) had ≥80% power to detect a small difference and 79 (27%) had power to detect a large difference. Of the 128 studies that did not detect a statistically significant effect, 4 (3%) excluded a small difference and 91 (71%) excluded a large difference. In conclusion, most education research studies are powered only to detect effects of large magnitude. For most studies that do not reach statistical significance, the possibility of large and important differences still exists.
Issues of sample size in sensitivity and specificity analysis with special reference to oncology.
Juneja, Atul; Sharma, Shashi
2015-01-01
Sample size is one of the basics issues, which medical researcher including oncologist faces with any research program. The current communication attempts to discuss the computation of sample size when sensitivity and specificity are being evaluated. The article intends to present the situation that the researcher could easily visualize for appropriate use of sample size techniques for sensitivity and specificity when any screening method for early detection of cancer is in question. Moreover, the researcher would be in a position to efficiently communicate with a statistician for sample size computation and most importantly applicability of the results under the conditions of the negotiated precision.
NASA Astrophysics Data System (ADS)
Nitschke, Naomi; Atkovska, Kalina; Hub, Jochen S.
2016-09-01
Molecular dynamics simulations are capable of predicting the permeability of lipid membranes for drug-like solutes, but the calculations have remained prohibitively expensive for high-throughput studies. Here, we analyze simple measures for accelerating potential of mean force (PMF) calculations of membrane permeation, namely, (i) using smaller simulation systems, (ii) simulating multiple solutes per system, and (iii) using shorter cutoffs for the Lennard-Jones interactions. We find that PMFs for membrane permeation are remarkably robust against alterations of such parameters, suggesting that accurate PMF calculations are possible at strongly reduced computational cost. In addition, we evaluated the influence of the definition of the membrane center of mass (COM), used to define the transmembrane reaction coordinate. Membrane-COM definitions based on all lipid atoms lead to artifacts due to undulations and, consequently, to PMFs dependent on membrane size. In contrast, COM definitions based on a cylinder around the solute lead to size-independent PMFs, down to systems of only 16 lipids per monolayer. In summary, compared to popular setups that simulate a single solute in a membrane of 128 lipids with a Lennard-Jones cutoff of 1.2 nm, the measures applied here yield a speedup in sampling by factor of ˜40, without reducing the accuracy of the calculated PMF.
Sampling bee communities using pan traps: alternative methods increase sample size
Technology Transfer Automated Retrieval System (TEKTRAN)
Monitoring of the status of bee populations and inventories of bee faunas require systematic sampling. Efficiency and ease of implementation has encouraged the use of pan traps to sample bees. Efforts to find an optimal standardized sampling method for pan traps have focused on pan trap color. Th...
ERIC Educational Resources Information Center
Eisenberg, Sarita L.; Guo, Ling-Yu
2015-01-01
Purpose: The purpose of this study was to investigate whether a shorter language sample elicited with fewer pictures (i.e., 7) would yield a percent grammatical utterances (PGU) score similar to that computed from a longer language sample elicited with 15 pictures for 3-year-old children. Method: Language samples were elicited by asking forty…
Assessing and improving the stability of chemometric models in small sample size situations.
Beleites, Claudia; Salzer, Reiner
2008-03-01
Small sample sizes are very common in multivariate analysis. Sample sizes of 10-100 statistically independent objects (rejects from processes or loading dock analysis, or patients with a rare disease), each with hundreds of data points, cause unstable models with poor predictive quality. Model stability is assessed by comparing models that were built using slightly varying training data. Iterated k-fold cross-validation is used for this purpose. Aggregation stabilizes models. It is possible to assess the quality of the aggregated model without calculating further models. The validation and aggregation methods investigated in this study apply to regression as well as to classification. These techniques are useful for analyzing data with large numbers of variates, e.g., any spectral data like FT-IR, Raman, UV/VIS, fluorescence, AAS, and MS. FT-IR images of tumor tissue were used in this study. Some tissue types occur frequently, while some are very rare. They are classified using LDA. Initial models were severely unstable. Aggregation stabilizes the predictions. The hit rate increased from 67% to 82%.
Distribution of the two-sample t-test statistic following blinded sample size re-estimation.
Lu, Kaifeng
2016-05-01
We consider the blinded sample size re-estimation based on the simple one-sample variance estimator at an interim analysis. We characterize the exact distribution of the standard two-sample t-test statistic at the final analysis. We describe a simulation algorithm for the evaluation of the probability of rejecting the null hypothesis at given treatment effect. We compare the blinded sample size re-estimation method with two unblinded methods with respect to the empirical type I error, the empirical power, and the empirical distribution of the standard deviation estimator and final sample size. We characterize the type I error inflation across the range of standardized non-inferiority margin for non-inferiority trials, and derive the adjusted significance level to ensure type I error control for given sample size of the internal pilot study. We show that the adjusted significance level increases as the sample size of the internal pilot study increases. Copyright © 2016 John Wiley & Sons, Ltd.
Dziak, John J; Lanza, Stephanie T; Tan, Xianming
2014-01-01
Selecting the number of different classes which will be assumed to exist in the population is an important step in latent class analysis (LCA). The bootstrap likelihood ratio test (BLRT) provides a data-driven way to evaluate the relative adequacy of a (K -1)-class model compared to a K-class model. However, very little is known about how to predict the power or the required sample size for the BLRT in LCA. Based on extensive Monte Carlo simulations, we provide practical effect size measures and power curves which can be used to predict power for the BLRT in LCA given a proposed sample size and a set of hypothesized population parameters. Estimated power curves and tables provide guidance for researchers wishing to size a study to have sufficient power to detect hypothesized underlying latent classes.
Dziak, John J.; Lanza, Stephanie T.; Tan, Xianming
2014-01-01
Selecting the number of different classes which will be assumed to exist in the population is an important step in latent class analysis (LCA). The bootstrap likelihood ratio test (BLRT) provides a data-driven way to evaluate the relative adequacy of a (K −1)-class model compared to a K-class model. However, very little is known about how to predict the power or the required sample size for the BLRT in LCA. Based on extensive Monte Carlo simulations, we provide practical effect size measures and power curves which can be used to predict power for the BLRT in LCA given a proposed sample size and a set of hypothesized population parameters. Estimated power curves and tables provide guidance for researchers wishing to size a study to have sufficient power to detect hypothesized underlying latent classes. PMID:25328371
XAFSmass: a program for calculating the optimal mass of XAFS samples
NASA Astrophysics Data System (ADS)
Klementiev, K.; Chernikov, R.
2016-05-01
We present a new implementation of the XAFSmass program that calculates the optimal mass of XAFS samples. It has several improvements as compared to the old Windows based program XAFSmass: 1) it is truly platform independent, as provided by Python language, 2) it has an improved parser of chemical formulas that enables parentheses and nested inclusion-to-matrix weight percentages. The program calculates the absorption edge height given the total optical thickness, operates with differently determined sample amounts (mass, pressure, density or sample area) depending on the aggregate state of the sample and solves the inverse problem of finding the elemental composition given the experimental absorption edge jump and the chemical formula.
NASA Astrophysics Data System (ADS)
Lai, B. W.; Wu, Z. X.; Dong, X. P.; Lu, D.; Tao, S. C.
2016-07-01
We proposed a novel method to calculate the similarity between samples with only small differences at unknown and specific positions in their Raman spectra, using a moving interval window scanning across the whole Raman spectra. Two ABS plastic samples, one with and the other without flame retardant, were tested in the experiment. Unlike the traditional method in which the similarity is calculated based on the whole spectrum, we do the calculation by using a window to cut out a certain segment from Raman spectra, each at a time as the window moves across the entire spectrum range. By our method, a curve of similarity versus wave number is obtained. And the curve shows a large change where the partial spectra of the two samples is different. Thus, the new similarity calculation method identifies samples with tiny difference in their Raman spectra better.
40 CFR 761.286 - Sample size and procedure for collecting a sample.
Code of Federal Regulations, 2011 CFR
2011-07-01
... (CONTINUED) TOXIC SUBSTANCES CONTROL ACT POLYCHLORINATED BIPHENYLS (PCBs) MANUFACTURING, PROCESSING, DISTRIBUTION IN COMMERCE, AND USE PROHIBITIONS Sampling To Verify Completion of Self-Implementing Cleanup...
7 CFR 51.308 - Methods of sampling and calculation of percentages.
Code of Federal Regulations, 2011 CFR
2011-01-01
..., CERTIFICATION, AND STANDARDS) United States Standards for Grades of Apples Methods of Sampling and Calculation... where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be calculated on the basis of count. (b) In all...
7 CFR 51.308 - Methods of sampling and calculation of percentages.
Code of Federal Regulations, 2010 CFR
2010-01-01
..., CERTIFICATION, AND STANDARDS) United States Standards for Grades of Apples Methods of Sampling and Calculation... where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be calculated on the basis of count. (b) In all...
7 CFR 51.308 - Methods of sampling and calculation of percentages.
Code of Federal Regulations, 2012 CFR
2012-01-01
..., CERTIFICATION, AND STANDARDS) United States Standards for Grades of Apples Methods of Sampling and Calculation... where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be calculated on the basis of count. (b) In all...
Air and smear sample calculational tool for Fluor Hanford Radiological control
BAUMANN, B.L.
2003-07-11
A spreadsheet calculation tool was developed to automate the calculations performed for determining the concentration of airborne radioactivity and smear counting as outlined in HNF-13536, Section 5.2.7, ''Analyzing Air and Smear Samples''. This document reports on the design and testing of the calculation tool. Radiological Control Technicians (RCTs) will save time and reduce hand written and calculation errors by using an electronic form for documenting and calculating work place air samples. Current expectations are RCTs will perform an air sample and collect the filter or perform a smear for surface contamination. RCTs will then survey the filter for gross alpha and beta/gamma radioactivity and with the gross counts utilize either hand calculation method or a calculator to determine activity on the filter. The electronic form will allow the RCT with a few key strokes to document the individual's name, payroll, gross counts, instrument identifiers; produce an error free record. This productivity gain is realized by the enhanced ability to perform mathematical calculations electronically (reducing errors) and at the same time, documenting the air sample.
40 CFR 600.211-08 - Sample calculation of fuel economy values for labeling.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 30 2011-07-01 2011-07-01 false Sample calculation of fuel economy... AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Procedures for Calculating Fuel Economy and Carbon-Related Exhaust Emission Values for 1977 and Later...
40 CFR 600.211-08 - Sample calculation of fuel economy values for labeling.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 29 2010-07-01 2010-07-01 false Sample calculation of fuel economy... AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Fuel Economy Regulations for 1977 and Later Model Year Automobiles-Procedures for Calculating Fuel...
Weighting by Inverse Variance or by Sample Size in Random-Effects Meta-Analysis
ERIC Educational Resources Information Center
Marin-Martinez, Fulgencio; Sanchez-Meca, Julio
2010-01-01
Most of the statistical procedures in meta-analysis are based on the estimation of average effect sizes from a set of primary studies. The optimal weight for averaging a set of independent effect sizes is the inverse variance of each effect size, but in practice these weights have to be estimated, being affected by sampling error. When assuming a…
ERIC Educational Resources Information Center
Wolf, Erika J.; Harrington, Kelly M.; Clark, Shaunna L.; Miller, Mark W.
2013-01-01
Determining sample size requirements for structural equation modeling (SEM) is a challenge often faced by investigators, peer reviewers, and grant writers. Recent years have seen a large increase in SEMs in the behavioral science literature, but consideration of sample size requirements for applied SEMs often relies on outdated rules-of-thumb.…
ERIC Educational Resources Information Center
Algina, James; Olejnik, Stephen
2003-01-01
Tables for selecting sample size in correlation studies are presented. Some of the tables allow selection of sample size so that r (or r[squared], depending on the statistic the researcher plans to interpret) will be within a target interval around the population parameter with probability 0.95. The intervals are [plus or minus] 0.05, [plus or…
Sample Size for Confidence Interval of Covariate-Adjusted Mean Difference
ERIC Educational Resources Information Center
Liu, Xiaofeng Steven
2010-01-01
This article provides a way to determine adequate sample size for the confidence interval of covariate-adjusted mean difference in randomized experiments. The standard error of adjusted mean difference depends on covariate variance and balance, which are two unknown quantities at the stage of planning sample size. If covariate observations are…
Sample Size Requirements for Accurate Estimation of Squared Semi-Partial Correlation Coefficients.
ERIC Educational Resources Information Center
Algina, James; Moulder, Bradley C.; Moser, Barry K.
2002-01-01
Studied the sample size requirements for accurate estimation of squared semi-partial correlation coefficients through simulation studies. Results show that the sample size necessary for adequate accuracy depends on: (1) the population squared multiple correlation coefficient (p squared); (2) the population increase in p squared; and (3) the…
Sample Size and Item Parameter Estimation Precision When Utilizing the One-Parameter "Rasch" Model
ERIC Educational Resources Information Center
Custer, Michael
2015-01-01
This study examines the relationship between sample size and item parameter estimation precision when utilizing the one-parameter model. Item parameter estimates are examined relative to "true" values by evaluating the decline in root mean squared deviation (RMSD) and the number of outliers as sample size increases. This occurs across…
Using the Student's "t"-Test with Extremely Small Sample Sizes
ERIC Educational Resources Information Center
de Winter, J. C .F.
2013-01-01
Researchers occasionally have to work with an extremely small sample size, defined herein as "N" less than or equal to 5. Some methodologists have cautioned against using the "t"-test when the sample size is extremely small, whereas others have suggested that using the "t"-test is feasible in such a case. The present…
Thermomagnetic behavior of magnetic susceptibility - heating rate and sample size effects
NASA Astrophysics Data System (ADS)
Jordanova, Diana; Jordanova, Neli
2015-12-01
Thermomagnetic analysis of magnetic susceptibility k(T) was carried out for a number of natural powder materials from soils, baked clay and anthropogenic dust samples using fast (11oC/min) and slow (6.5oC/min) heating rates available in the furnace of Kappabridge KLY2 (Agico). Based on the additional data for mineralogy, grain size and magnetic properties of the studied samples, behaviour of k(T) cycles and the observed differences in the curves for fast and slow heating rate are interpreted in terms of mineralogical transformations and Curie temperatures (Tc). The effect of different sample size is also explored, using large volume and small volume of powder material. It is found that soil samples show enhanced information on mineralogical transformations and appearance of new strongly magnetic phases when using fast heating rate and large sample size. This approach moves the transformation at higher temperature, but enhances the amplitude of the signal of newly created phase. Large sample size gives prevalence of the local micro- environment, created by evolving gases, released during transformations. The example from archeological brick reveals the effect of different sample sizes on the observed Curie temperatures on heating and cooling curves, when the magnetic carrier is substituted magnetite (Mn0.2Fe2.70O4). Large sample size leads to bigger differences in Tcs on heating and cooling, while small sample size results in similar Tcs for both heating rates.
Sample size determination in group-sequential clinical trials with two co-primary endpoints.
Asakura, Koko; Hamasaki, Toshimitsu; Sugimoto, Tomoyuki; Hayashi, Kenichi; Evans, Scott R; Sozu, Takashi
2014-07-30
We discuss sample size determination in group-sequential designs with two endpoints as co-primary. We derive the power and sample size within two decision-making frameworks. One is to claim the test intervention's benefit relative to control when superiority is achieved for the two endpoints at the same interim timepoint of the trial. The other is when superiority is achieved for the two endpoints at any interim timepoint, not necessarily simultaneously. We evaluate the behaviors of sample size and power with varying design elements and provide a real example to illustrate the proposed sample size methods. In addition, we discuss sample size recalculation based on observed data and evaluate the impact on the power and Type I error rate.
7 CFR 51.308 - Methods of sampling and calculation of percentages.
Code of Federal Regulations, 2013 CFR
2013-01-01
... Grades of Apples Methods of Sampling and Calculation of Percentages § 51.308 Methods of sampling and... weigh ten pounds or less, or in any container where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be...
7 CFR 51.308 - Methods of sampling and calculation of percentages.
Code of Federal Regulations, 2014 CFR
2014-01-01
... Grades of Apples Methods of Sampling and Calculation of Percentages § 51.308 Methods of sampling and... weigh ten pounds or less, or in any container where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be...
NASA Technical Reports Server (NTRS)
Johnson, Kenneth L.; White, K. Preston, Jr.
2012-01-01
The NASA Engineering and Safety Center was requested to improve on the Best Practices document produced for the NESC assessment, Verification of Probabilistic Requirements for the Constellation Program, by giving a recommended procedure for using acceptance sampling by variables techniques as an alternative to the potentially resource-intensive acceptance sampling by attributes method given in the document. In this paper, the results of empirical tests intended to assess the accuracy of acceptance sampling plan calculators implemented for six variable distributions are presented.
Hartman, Joshua D.; Neubauer, Thomas J.; Caulkins, Bethany G.; Mueller, Leonard J.; Beran, Gregory J. O.
2015-01-01
Ab initio chemical shielding calculations greatly facilitate the interpretation of nuclear magnetic resonance (NMR) chemical shifts in biological systems, but the large sizes of these systems requires approximations in the chemical models used to represent them. Achieving good convergence in the predicted chemical shieldings is necessary before one can unravel how other complex structural and dynamical factors affect the NMR measurements. Here, we investigate how to balance trade-offs between using a better basis set or a larger cluster model for predicting the chemical shieldings of the substrates in two representative examples of protein-substrate systems involving different domains in tryptophan synthase: the N-(4′-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F9) ligand which binds in the α active site, and the 2-aminophenol (2AP) quinonoid intermediate formed in the β active site. We first demonstrate that a chemically intuitive three-layer, locally dense basis model that uses a large basis on the substrate, a medium triple-zeta basis to describe its hydrogen-bonding partners and/or surrounding van derWaals cavity, and a crude basis set for more distant atoms provides chemical shieldings in good agreement with much more expensive large basis calculations. Second, long-range quantum mechanical interactions are important, and one can accurately estimate them as a small-basis correction to larger-basis calculations on a smaller cluster. The combination of these approaches enables one to perform density functional theory NMR chemical shift calculations in protein systems that are well-converged with respect to both basis set and cluster size. PMID:25993979
Guo, Ling-Yu
2015-01-01
Purpose The purpose of this study was to investigate whether a shorter language sample elicited with fewer pictures (i.e., 7) would yield a percent grammatical utterances (PGU) score similar to that computed from a longer language sample elicited with 15 pictures for 3-year-old children. Method Language samples were elicited by asking forty 3-year-old children with varying language skills to talk about pictures in response to prompts. PGU scores were computed for each of two 7-picture sets and for the full set of 15 pictures. Results PGU scores for the two 7-picture sets did not differ significantly from, and were highly correlated with, PGU scores for the full set and with each other. Agreement for making pass–fail decisions between each 7-picture set and the full set and between the two 7-picture sets ranged from 80% to 100%. Conclusion The current study suggests that the PGU measure is robust enough that it can be computed on the basis of 7, at least in 3-year-old children whose language samples were elicited using similar procedures. PMID:25615691
Kohigashi, Tsuyoshi; Otsuka, Yoichi; Shimazu, Ryo; Matsumoto, Takuya; Iwata, Futoshi; Kawasaki, Hideya; Arakawa, Ryuichi
2016-01-01
Mass spectrometry imaging (MSI) with ambient sampling and ionization can rapidly and easily capture the distribution of chemical components in a solid sample. Because the spatial resolution of MSI is limited by the size of the sampling area, reducing sampling size is an important goal for high resolution MSI. Here, we report the first use of a nanopipette for sampling and ionization by tapping-mode scanning probe electrospray ionization (t-SPESI). The spot size of the sampling area of a dye molecular film on a glass substrate was decreased to 6 μm on average by using a nanopipette. On the other hand, ionization efficiency increased with decreasing solvent flow rate. Our results indicate the compatibility between a reduced sampling area and the ionization efficiency using a nanopipette. MSI of micropatterns of ink on a glass and a polymer substrate were also demonstrated. PMID:28101441
Calculation of the radionuclides in PWR spent fuel samples for SFR experiment planning.
Naegeli, Robert Earl
2004-06-01
This report documents the calculation of radionuclide content in the pressurized water reactor (PWR) spent fuel samples planned for use in the Spent Fuel Ratio (SPR) Experiments at Sandia National Laboratories, Albuquerque, New Mexico (SNL) to aid in experiment planning. The calculation methods using the ORIGEN2 and ORIGEN-ARP computer codes and the input modeling of the planned PWR spent fuel from the H. B. Robinson and the Surry nuclear power plants are discussed. The safety hazards for the calculated nuclide inventories in the spent fuel samples are characterized by the potential airborne dose and by the portion of the nuclear facility hazard category 2 and 3 thresholds that the experiment samples would present. In addition, the gamma ray photon energy source for the nuclide inventories is tabulated to facilitate subsequent calculation of the direct and shielded dose rates expected from the samples. The relative hazards of the high burnup 72 gigawatt-day per metric ton of uranium (GWd/MTU) spent fuel from H. B. Robinson and the medium burnup 36 GWd/MTU spent fuel from Surry are compared against a parametric calculation of various fuel burnups to assess the potential for higher hazard PWR fuel samples.
The importance of a priori sample size estimation in strength and conditioning research.
Beck, Travis W
2013-08-01
The statistical power, or sensitivity of an experiment, is defined as the probability of rejecting a false null hypothesis. Only 3 factors can affect statistical power: (a) the significance level (α), (b) the magnitude or size of the treatment effect (effect size), and (c) the sample size (n). Of these 3 factors, only the sample size can be manipulated by the investigator because the significance level is usually selected before the study, and the effect size is determined by the effectiveness of the treatment. Thus, selection of an appropriate sample size is one of the most important components of research design but is often misunderstood by beginning researchers. The purpose of this tutorial is to describe procedures for estimating sample size for a variety of different experimental designs that are common in strength and conditioning research. Emphasis is placed on selecting an appropriate effect size because this step fully determines sample size when power and the significance level are fixed. There are many different software packages that can be used for sample size estimation. However, I chose to describe the procedures for the G*Power software package (version 3.1.4) because this software is freely downloadable and capable of estimating sample size for many of the different statistical tests used in strength and conditioning research. Furthermore, G*Power provides a number of different auxiliary features that can be useful for researchers when designing studies. It is my hope that the procedures described in this article will be beneficial for researchers in the field of strength and conditioning.
Wolf, Erika J; Harrington, Kelly M; Clark, Shaunna L; Miller, Mark W
2013-12-01
Determining sample size requirements for structural equation modeling (SEM) is a challenge often faced by investigators, peer reviewers, and grant writers. Recent years have seen a large increase in SEMs in the behavioral science literature, but consideration of sample size requirements for applied SEMs often relies on outdated rules-of-thumb. This study used Monte Carlo data simulation techniques to evaluate sample size requirements for common applied SEMs. Across a series of simulations, we systematically varied key model properties, including number of indicators and factors, magnitude of factor loadings and path coefficients, and amount of missing data. We investigated how changes in these parameters affected sample size requirements with respect to statistical power, bias in the parameter estimates, and overall solution propriety. Results revealed a range of sample size requirements (i.e., from 30 to 460 cases), meaningful patterns of association between parameters and sample size, and highlight the limitations of commonly cited rules-of-thumb. The broad "lessons learned" for determining SEM sample size requirements are discussed.
Parameter Estimation with Small Sample Size: A Higher-Order IRT Model Approach
ERIC Educational Resources Information Center
de la Torre, Jimmy; Hong, Yuan
2010-01-01
Sample size ranks as one of the most important factors that affect the item calibration task. However, due to practical concerns (e.g., item exposure) items are typically calibrated with much smaller samples than what is desired. To address the need for a more flexible framework that can be used in small sample item calibration, this article…
Personnel Selection Procedures as a Function of Sample Size, Cut Scores, and Quartile Ranking.
ERIC Educational Resources Information Center
Ferrara, F. Felicia
Cut scores, quartile ranking, sample size, and overall classification scheme were studied as personnel selection procedures in two samples. The first was 120 simulated observations of employee scores based on actual selection procedures for applicants for administrative assistant positions. The other sample was composed of test results for 73…
PIXE-PIGE analysis of size-segregated aerosol samples from remote areas
NASA Astrophysics Data System (ADS)
Calzolai, G.; Chiari, M.; Lucarelli, F.; Nava, S.; Taccetti, F.; Becagli, S.; Frosini, D.; Traversi, R.; Udisti, R.
2014-01-01
The chemical characterization of size-segregated samples is helpful to study the aerosol effects on both human health and environment. The sampling with multi-stage cascade impactors (e.g., Small Deposit area Impactor, SDI) produces inhomogeneous samples, with a multi-spot geometry and a non-negligible particle stratification.
Nam, Jun-Mo
2011-10-01
Consider clustered matched-pair studies for non-inferiority where clusters are independent but units in a cluster are correlated. An inexpensive new procedure and the expensive standard one are applied to each unit and outcomes are binary responses. Appropriate statistics testing non-inferiority of a new procedure have been developed recently by several investigators. In this note, we investigate power and sample size requirement of the clustered matched pair study for non-inferiority. Power of a test is related primarily to the number of clusters. The effect of a cluster size on power is secondary. The efficiency of a clustered matched-pair design is inversely related to the intra-class correlation coefficient within a cluster. We present an explicit formula for obtaining the number of clusters for given a cluster size and the cluster size for a given number of clusters for a specific power. We also provide alternative sample size calculations when available information regarding parameters are limited. The formulae can be useful in designing a clustered matched-pair study for non-inferiority. An example for determining sample size to establish non-inferiority for a clustered matched-pair study is illustrated.
Light propagation in tissues: effect of finite size of tissue sample
NASA Astrophysics Data System (ADS)
Melnik, Ivan S.; Dets, Sergiy M.; Rusina, Tatyana V.
1995-12-01
Laser beam propagation inside tissues with different lateral dimensions has been considered. Scattering and anisotropic properties of tissue critically determine spatial fluence distribution and predict sizes of tissue specimens when deviations of this distribution can be neglected. Along the axis of incident beam the fluence rate weakly depends on sample size whereas its relative increase (more than 20%) towards the lateral boundaries. The finite sizes were considered to be substantial only for samples with sizes comparable with the diameter of the laser beam. Interstitial irradiance patterns simulated by Monte Carlo method were compared with direct measurements in human brain specimens.
König, Gerhard; Miller, Benjamin T; Boresch, Stefan; Wu, Xiongwu; Brooks, Bernard R
2012-10-09
One of the key requirements for the accurate calculation of free energy differences is proper sampling of conformational space. Especially in biological applications, molecular dynamics simulations are often confronted with rugged energy surfaces and high energy barriers, leading to insufficient sampling and, in turn, poor convergence of the free energy results. In this work, we address this problem by employing enhanced sampling methods. We explore the possibility of using self-guided Langevin dynamics (SGLD) to speed up the exploration process in free energy simulations. To obtain improved free energy differences from such simulations, it is necessary to account for the effects of the bias due to the guiding forces. We demonstrate how this can be accomplished for the Bennett's acceptance ratio (BAR) and the enveloping distribution sampling (EDS) methods. While BAR is considered among the most efficient methods available for free energy calculations, the EDS method developed by Christ and van Gunsteren is a promising development that reduces the computational costs of free energy calculations by simulating a single reference state. To evaluate the accuracy of both approaches in connection with enhanced sampling, EDS was implemented in CHARMM. For testing, we employ benchmark systems with analytical reference results and the mutation of alanine to serine. We find that SGLD with reweighting can provide accurate results for BAR and EDS where conventional molecular dynamics simulations fail. In addition, we compare the performance of EDS with other free energy methods. We briefly discuss the implications of our results and provide practical guidelines for conducting free energy simulations with SGLD.
Zhang, Yong; Voth, Gregory A.
2011-01-01
Free energy calculations are one of the most useful methods for the study of ion transport mechanisms through confined spaces such as protein ion channels. Their reliability depends on a correctly defined reaction coordinate (RC). A straight line is usually not a proper RC for such complicated processes so in this work a combined metadynamics/umbrella sampling (MTD/US) method is proposed. In the combined method, the ion transport pathway is first identified by the MTD method and then the free energy profile or potential of mean force (PMF) along the path is calculated using umbrella sampling. This combined method avoids the discontinuity problem often associated with normal umbrella sampling calculations that assume a straight line RC and it provides a more physically accurate PMF for such processes. The method is demonstrated for the proton transport process through the protein channel of aquaporin-1. PMID:25100923
NASA Technical Reports Server (NTRS)
Bice, K.; Clement, S. C.
1981-01-01
X-ray diffraction and spectroscopy were used to investigate the mineralogical and chemical properties of the Calvert, Ball Old Mine, Ball Martin, and Jordan Sediments. The particle size distribution and index of refraction of each sample were determined. The samples are composed primarily of quartz, kaolinite, and illite. The clay minerals are most abundant in the finer particle size fractions. The chemical properties of the four samples are similar. The Calvert sample is most notably different in that it contains a relatively high amount of iron. The dominant particle size fraction in each sample is silt, with lesser amounts of clay and sand. The indices of refraction of the sediments are the same with the exception of the Calvert sample which has a slightly higher value.
John L. Bowen; Rowena Gonzalez; David S. Shafer
2001-05-01
As part of the preliminary site characterization conducted for Project 57, soils samples were collected for separation into several size-fractions using the Suspended Soil Particle Sizing System (SSPSS). Soil samples were collected specifically for separation by the SSPSS at three general locations in the deposited Project 57 plume, the projected radioactivity of which ranged from 100 to 600 pCi/g. The primary purpose in focusing on samples with this level of activity is that it would represent anticipated residual soil contamination levels at the site after corrective actions are completed. Consequently, the results of the SSPSS analysis can contribute to dose calculation and corrective action-level determinations for future land-use scenarios at the site.
SAMPLE AOR CALCULATION USING ANSYS FULL PARAMETRIC MODEL FOR TANK SST-SX
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS parametric 360-degree model for single-shell tank SX and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric full model for the single shell tank (SST) SX to deal with asymmetry loading conditions and provide a sample analysis of the SST-SX tank based on analysis of record (AOR) loads. The SST-SX model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS SLICE PARAMETRIC MODEL FOR TANK SST-SX
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS slice parametric model for single-shell tank SX and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for the single shell tank (SST) SX, and provide a sample analysis of the SST-SX tank based on analysis of record (AOR) loads. The SST-SX model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS AXISYMMETRIC PARAMETRIC MODEL FOR TANK SST-S
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS axisymmetric parametric model for single-shell tank S and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for single shell tank (SST) S, and provide a sample analysis of SST-S tank based on analysis of record (AOR) loads. The SST-S model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS SLICE PARAMETRIC MODEL FOR TANK SST-BX
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS slice parametric model for single-shell tank BX and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for the single shell tank (SST) BX, and provide a sample analysis of the SST-BX tank based on analysis of record (AOR) loads. The SST-BX model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS SLICE PARAMETRIC MODEL FOR TANK SST-A
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS slice parametric model for single-shell tank A and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for the single shell tank (S) A, and provide a sample analysis of the SST-S tank based on analysis of record (AOR) loads. The SST-A model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS AXISYMMETRIC PARAMETRIC MODEL FOR TANK SST-AX
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS axisymmetric parametric model for single-shell tank AX and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for single shell tank (SST) AX, and provide a sample analysis of SST-AX tank based on analysis of record (AOR) loads. The SST-AX model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS SLICE PARAMETRIC MODEL FOR TANK SST-S
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS slice parametric model for single-shell tank S and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for the single shell tank (SST) S, and provide a sample analysis of the SST-S tank based on analysis of record (AOR) loads. The SST-S model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS SLICE PARAMETRIC MODEL FOR TANK SST-AX
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS slice parametric model for single-shell tank AX and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for the single shell tank (SST) AX, and provide a sample analysis of the SST-AX tank based on analysis of record (AOR) loads. The SST-AX model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS AXISYMMETRIC PARAMETRIC MODEL FOR TANK SST-SX
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS axisymmetric parametric model for single-shell tank SX and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for single shell tank (SST) SX, and provide a sample analysis of the SST-SX tank based on analysis of record (AOR) loads. The SST-SX model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
SAMPLE AOR CALCULATION USING ANSYS AXISYMMETRIC PARAMETRIC MODEL FOR TANK SST-A
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS axisymmetric parametric model for single-shell tank A and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to develop a parametric model for single shell tank (SST) A, and provide a sample analysis of SST-A tank based on analysis of record (AOR) loads. The SST-A model is based on buyer-supplied as-built drawings and information for the AOR for SSTs, encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
Small sample sizes in the study of ontogenetic allometry; implications for palaeobiology
Vavrek, Matthew J.
2015-01-01
Quantitative morphometric analyses, particularly ontogenetic allometry, are common methods used in quantifying shape, and changes therein, in both extinct and extant organisms. Due to incompleteness and the potential for restricted sample sizes in the fossil record, palaeobiological analyses of allometry may encounter higher rates of error. Differences in sample size between fossil and extant studies and any resulting effects on allometric analyses have not been thoroughly investigated, and a logical lower threshold to sample size is not clear. Here we show that studies based on fossil datasets have smaller sample sizes than those based on extant taxa. A similar pattern between vertebrates and invertebrates indicates this is not a problem unique to either group, but common to both. We investigate the relationship between sample size, ontogenetic allometric relationship and statistical power using an empirical dataset of skull measurements of modern Alligator mississippiensis. Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the null hypothesis). This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms. These limitations are not restricted to fossil data and are equally applicable to allometric analyses of rare extant taxa. No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes. PMID:25780770
Frictional behaviour of sandstone: A sample-size dependent triaxial investigation
NASA Astrophysics Data System (ADS)
Roshan, Hamid; Masoumi, Hossein; Regenauer-Lieb, Klaus
2017-01-01
Frictional behaviour of rocks from the initial stage of loading to final shear displacement along the formed shear plane has been widely investigated in the past. However the effect of sample size on such frictional behaviour has not attracted much attention. This is mainly related to the limitations in rock testing facilities as well as the complex mechanisms involved in sample-size dependent frictional behaviour of rocks. In this study, a suite of advanced triaxial experiments was performed on Gosford sandstone samples at different sizes and confining pressures. The post-peak response of the rock along the formed shear plane has been captured for the analysis with particular interest in sample-size dependency. Several important phenomena have been observed from the results of this study: a) the rate of transition from brittleness to ductility in rock is sample-size dependent where the relatively smaller samples showed faster transition toward ductility at any confining pressure; b) the sample size influences the angle of formed shear band and c) the friction coefficient of the formed shear plane is sample-size dependent where the relatively smaller sample exhibits lower friction coefficient compared to larger samples. We interpret our results in terms of a thermodynamics approach in which the frictional properties for finite deformation are viewed as encompassing a multitude of ephemeral slipping surfaces prior to the formation of the through going fracture. The final fracture itself is seen as a result of the self-organisation of a sufficiently large ensemble of micro-slip surfaces and therefore consistent in terms of the theory of thermodynamics. This assumption vindicates the use of classical rock mechanics experiments to constrain failure of pressure sensitive rocks and the future imaging of these micro-slips opens an exciting path for research in rock failure mechanisms.
ERIC Educational Resources Information Center
Kelley, Ken; Rausch, Joseph R.
2011-01-01
Longitudinal studies are necessary to examine individual change over time, with group status often being an important variable in explaining some individual differences in change. Although sample size planning for longitudinal studies has focused on statistical power, recent calls for effect sizes and their corresponding confidence intervals…
The Impact of Sample Size and Other Factors When Estimating Multilevel Logistic Models
ERIC Educational Resources Information Center
Schoeneberger, Jason A.
2016-01-01
The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying…
Size and modal analyses of fines and ultrafines from some Apollo 17 samples
NASA Technical Reports Server (NTRS)
Greene, G. M.; King, D. T., Jr.; Banholzer, G. S., Jr.; King, E. A.
1975-01-01
Scanning electron and optical microscopy techniques have been used to determine the grain-size frequency distributions and morphology-based modal analyses of fine and ultrafine fractions of some Apollo 17 regolith samples. There are significant and large differences between the grain-size frequency distributions of the less than 10-micron size fraction of Apollo 17 samples, but there are no clear relations to the local geologic setting from which individual samples have been collected. This may be due to effective lateral mixing of regolith particles in this size range by micrometeoroid impacts. None of the properties of the frequency distributions support the idea of selective transport of any fine grain-size fraction, as has been proposed by other workers. All of the particle types found in the coarser size fractions also occur in the less than 10-micron particles. In the size range from 105 to 10 microns there is a strong tendency for the percentage of regularly shaped glass to increase as the graphic mean grain size of the less than 1-mm size fraction decreases, both probably being controlled by exposure age.
A margin based approach to determining sample sizes via tolerance bounds.
Newcomer, Justin T.; Freeland, Katherine Elizabeth
2013-09-01
This paper proposes a tolerance bound approach for determining sample sizes. With this new methodology we begin to think of sample size in the context of uncertainty exceeding margin. As the sample size decreases the uncertainty in the estimate of margin increases. This can be problematic when the margin is small and only a few units are available for testing. In this case there may be a true underlying positive margin to requirements but the uncertainty may be too large to conclude we have sufficient margin to those requirements with a high level of statistical confidence. Therefore, we provide a methodology for choosing a sample size large enough such that an estimated QMU uncertainty based on the tolerance bound approach will be smaller than the estimated margin (assuming there is positive margin). This ensures that the estimated tolerance bound will be within performance requirements and the tolerance ratio will be greater than one, supporting a conclusion that we have sufficient margin to the performance requirements. In addition, this paper explores the relationship between margin, uncertainty, and sample size and provides an approach and recommendations for quantifying risk when sample sizes are limited.
Guo, Jiin-Huarng; Chen, Hubert J; Luh, Wei-Ming
2011-11-01
The allocation of sufficient participants into different experimental groups for various research purposes under given constraints is an important practical problem faced by researchers. We address the problem of sample size determination between two independent groups for unequal and/or unknown variances when both the power and the differential cost are taken into consideration. We apply the well-known Welch approximate test to derive various sample size allocation ratios by minimizing the total cost or, equivalently, maximizing the statistical power. Two types of hypotheses including superiority/non-inferiority and equivalence of two means are each considered in the process of sample size planning. A simulation study is carried out and the proposed method is validated in terms of Type I error rate and statistical power. As a result, the simulation study reveals that the proposed sample size formulas are very satisfactory under various variances and sample size allocation ratios. Finally, a flowchart, tables, and figures of several sample size allocations are presented for practical reference.
Phonological process analysis from spontaneous speech: the influence of sample size.
Crary, M A
1983-03-01
Phonological process analysis is becoming a popular technique for the evaluation of unintelligible children and adults. Spontaneous speech sampling procedures have been advocated as a representative sampling base for phonological process analysis; however, little research has been reported detailing the parameters of spontaneous samples in reference to this assessment technique. The purpose of the present study was to evaluate the influence of increasing sample size on phonological process analyses from spontaneous speech. Results clearly indicated that samples of 50 words provided descriptive information similar to samples of 100 words. Additional studies are called for to investigate other variables that might influence the results of spontaneous speech analysis.
NASA Astrophysics Data System (ADS)
Odbadrakh, Khorgolkhuu; Nicholson, Don; Eisenbach, Markus; Brown, Gregory; Rusanu, Aurelian; Materials Theory Group Team
2014-03-01
Magnetic entropy change in Magneto-caloric Effect materials is one of the key parameters in choosing materials appropriate for magnetic cooling and offers insight into the coupling between the materials' thermodynamic and magnetic degrees of freedoms. We present computational workflow to calculate the change of magnetic entropy due to a magnetic field using the DFT based statistical sampling of the energy landscape of Ni2MnGa. The statistical density of magnetic states is calculated with Wang-Landau sampling, and energies are calculated with the Locally Self-consistent Multiple Scattering technique. The high computational cost of calculating energies of each state from first principles is tempered by exploiting a model Hamiltonian fitted to the DFT based sampling. The workflow is described and justified. The magnetic adiabatic temperature change calculated from the statistical density of states agrees with the experimentally obtained value in the absence of structural transformation. The study also reveals that the magnetic subsystem alone cannot explain the large MCE observed in Ni2MnGa alloys. This work was performed at the ORNL, which is managed by UT-Batelle for the U.S. DOE. It was sponsored by the Division of Material Sciences and Engineering, OBES. This research used resources of the OLCF at ORNL, which is supported by the Office of Science of the U.S. DOE under Contract DE-AC05-00OR22725.
Shih, Weichung Joe; Li, Gang; Wang, Yining
2016-03-01
Sample size plays a crucial role in clinical trials. Flexible sample-size designs, as part of the more general category of adaptive designs that utilize interim data, have been a popular topic in recent years. In this paper, we give a comparative review of four related methods for such a design. The likelihood method uses the likelihood ratio test with an adjusted critical value. The weighted method adjusts the test statistic with given weights rather than the critical value. The dual test method requires both the likelihood ratio statistic and the weighted statistic to be greater than the unadjusted critical value. The promising zone approach uses the likelihood ratio statistic with the unadjusted value and other constraints. All four methods preserve the type-I error rate. In this paper we explore their properties and compare their relationships and merits. We show that the sample size rules for the dual test are in conflict with the rules of the promising zone approach. We delineate what is necessary to specify in the study protocol to ensure the validity of the statistical procedure and what can be kept implicit in the protocol so that more flexibility can be attained for confirmatory phase III trials in meeting regulatory requirements. We also prove that under mild conditions, the likelihood ratio test still preserves the type-I error rate when the actual sample size is larger than the re-calculated one.
González-Vacarezza, N; Abad-Santos, F; Carcas-Sansuan, A; Dorado, P; Peñas-Lledó, E; Estévez-Carrizo, F; Llerena, A
2013-10-01
In bioequivalence studies, intra-individual variability (CV(w)) is critical in determining sample size. In particular, highly variable drugs may require enrollment of a greater number of subjects. We hypothesize that a strategy to reduce pharmacokinetic CV(w), and hence sample size and costs, would be to include subjects with decreased metabolic enzyme capacity for the drug under study. Therefore, two mirtazapine studies, two-way, two-period crossover design (n=68) were re-analysed to calculate the total CV(w) and the CV(w)s in three different CYP2D6 genotype groups (0, 1 and ≥ 2 active genes). The results showed that a 29.2 or 15.3% sample size reduction would have been possible if the recruitment had been of individuals carrying just 0 or 0 plus 1 CYP2D6 active genes, due to the lower CV(w). This suggests that there may be a role for pharmacogenetics in the design of bioequivalence studies to reduce sample size and costs, thus introducing a new paradigm for the biopharmaceutical evaluation of drug products.
A normative inference approach for optimal sample sizes in decisions from experience.
Ostwald, Dirk; Starke, Ludger; Hertwig, Ralph
2015-01-01
"Decisions from experience" (DFE) refers to a body of work that emerged in research on behavioral decision making over the last decade. One of the major experimental paradigms employed to study experience-based choice is the "sampling paradigm," which serves as a model of decision making under limited knowledge about the statistical structure of the world. In this paradigm respondents are presented with two payoff distributions, which, in contrast to standard approaches in behavioral economics, are specified not in terms of explicit outcome-probability information, but by the opportunity to sample outcomes from each distribution without economic consequences. Participants are encouraged to explore the distributions until they feel confident enough to decide from which they would prefer to draw from in a final trial involving real monetary payoffs. One commonly employed measure to characterize the behavior of participants in the sampling paradigm is the sample size, that is, the number of outcome draws which participants choose to obtain from each distribution prior to terminating sampling. A natural question that arises in this context concerns the "optimal" sample size, which could be used as a normative benchmark to evaluate human sampling behavior in DFE. In this theoretical study, we relate the DFE sampling paradigm to the classical statistical decision theoretic literature and, under a probabilistic inference assumption, evaluate optimal sample sizes for DFE. In our treatment we go beyond analytically established results by showing how the classical statistical decision theoretic framework can be used to derive optimal sample sizes under arbitrary, but numerically evaluable, constraints. Finally, we critically evaluate the value of deriving optimal sample sizes under this framework as testable predictions for the experimental study of sampling behavior in DFE.
40 CFR Appendix II to Part 600 - Sample Fuel Economy Calculations
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 31 2012-07-01 2012-07-01 false Sample Fuel Economy Calculations II Appendix II to Part 600 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND GREENHOUSE GAS EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App. II Appendix II...
40 CFR Appendix III to Part 600 - Sample Fuel Economy Label Calculation
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 30 2014-07-01 2014-07-01 false Sample Fuel Economy Label Calculation III Appendix III to Part 600 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND GREENHOUSE GAS EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App....
40 CFR Appendix II to Part 600 - Sample Fuel Economy Calculations
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 30 2014-07-01 2014-07-01 false Sample Fuel Economy Calculations II Appendix II to Part 600 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND GREENHOUSE GAS EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App. II Appendix II...
40 CFR Appendix III to Part 600 - Sample Fuel Economy Label Calculation
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 31 2012-07-01 2012-07-01 false Sample Fuel Economy Label Calculation III Appendix III to Part 600 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND GREENHOUSE GAS EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App....
SAMPLE AOR CALCULATION USING ANSYS PARAMETRIC MODEL FOR TANK SST-AY
JULYK, L.J.; MACKEY, T.C.
2003-06-19
This document documents the ANSYS parametric model for double-shell tank AY and provides sample calculation for analysis-of-record mechanical load conditions. The purpose of this calculation is to provide a sample analysis of the DST-AY tanks based on AOR loads, plus loads identified in the Statement of Work (SOW) for CHG contract 92879. This is not an analysis. Instead, the present calculation utilizes the parametric model generated for the double shell tank DST-AY, which is based on Buyer-supplied as-built drawings and information for the analyses of record (AOR) for Double-Shell Tanks (DSTs), encompassing the existing tank load conditions, and evaluates stresses and deformations throughout the tank and surrounding soil mass.
NASA Astrophysics Data System (ADS)
Malm, William C.; Pitchford, Marc L.
Size distributions and resulting optical properties of sulfur aerosols were investigated at three national parks by a Davis Rotating-drum Universal-size-cut Monitoring (DRUM) impactor. Sulfur size distribution measurements for 88, 177, and 315 consecutive time periods were made at Grand Canyon National Park during January and February 1988, Meadview, AZ during July, August, and September 1992, and at Shenandoah National Park during summer, 1990, respectively. The DRUM impactor is designed to collect aerosols with an aerodynamic diameter between 0.07 and 15.0 μm in eight size ranges. Focused beam particle-induced X-ray emission (PIXE) analysis of the aerosol deposits produces a time history of size-resolved elemental composition of varied temporal resolution. As part of the quality assurance protocol, an interagency monitoring of protected visual environments (IMPROVE) channel A sampler collecting 0-2.5 μm diameter particles was operated simultaneously alongside the DRUM sampler. During these sampling periods, the average sulfur mass, interpreted as ammonium sulfate, is 0.49, 2.30, and 10.36 μg m -3 at Grand Canyon, Meadview, and Shenandoah, respectively. The five drum stages were "inverted" using the Twomey (1975) scheme to give 486 size distributions, each made up of 72 discreet pairs of d C/dlog( D) and diameter ( D). From these distributions mass mean diameters ( Dg), geometric standard deviations ( σg), and mass scattering efficiencies ( em)) were calculated. The geometric mass mean diameters in ascending order were 0.21 μm at Meadview, 0.32 μm at Grand Canyon, and 0.42 μm at Shenandoah corresponding σg were 2.1, 2.3, and 1.9. Mie theory mass scattering efficiencies calculated from d C/dlog( D) distributions for the three locations were 2.05, 2.59, and 3.81 m 2 g -1, respectively. At Shenandoah, mass scattering efficiencies approached five but only when the mass median diameters were approximately 0.4 μm and σg were about 1.5. σg near 1.5 were
Marubashi, Shigeru; Nagano, Hiroaki; Eguchi, Hidetoshi; Wada, Hiroshi; Asaoka, Tadafumi; Tomimaru, Yoshito; Tomokuni, Akira; Umeshita, Koji; Doki, Yuichiro; Mori, Masaki
2016-05-01
Small-for-size graft syndrome is an inevitable complication in living donor liver transplantation (LDLT). We hypothesized that graft weight (GW) measured after graft procurement is one of the variables predicting postoperative graft function. A total of 138 consecutive recipients of adult-to-adult LDLT between March 1999 and October 2014 were included in this study. We investigated the factors associated with small-for-size-associated graft loss (SAGL) to determine the GW required for each patient. Both preoperatively assessed and postoperatively obtained risk factors for SAGL were analyzed in univariate and multivariate logistic regression analysis. Twelve (8.8%) of the transplant recipients had SAGL. In multivariate logistic regression analyses using preoperatively assessed variables, the preoperative Model for End-Stage Liver Disease (MELD) score (P < 0.001) and actual GW/recipient standard liver volume (SLV) ratio (P = 0.008) were independent predictors of SAGL. The recommended graft volume by preoperative computed tomography volumetry was calculated as SLV × (1.616 × MELD + 0.344)/100/0.85 (mL) [MELD ≥ 18.2], or SLV × 0.35 (mL) [MELD < 18.2]. The required allograft volume in LDLT can be determined by the preoperative MELD score of the recipient, and patients with higher MELD scores require larger grafts or deceased donor whole liver transplant to avoid SAGL. Liver Transplantation 22 599-606 2016 AASLD.
Influence of sampling rate on the calculated fidelity of an aircraft simulation
NASA Technical Reports Server (NTRS)
Howard, J. C.
1983-01-01
One of the factors that influences the fidelity of an aircraft digital simulation is the sampling rate. As the sampling rate is increased, the calculated response of the discrete representation tends to coincide with the response of the corresponding continuous system. Because of computer limitations, however, the sampling rate cannot be increased indefinitely. Moreover, real-time simulation requirements demand that a finite sampling rate be adopted. In view of these restrictions, a study was undertaken to determine the influence of sampling rate on the response characteristics of a simulated aircraft describing short-period oscillations. Changes in the calculated response characteristics of the simulated aircraft degrade the fidelity of the simulation. In the present context, fidelity degradation is defined as the percentage change in those characteristics that have the greatest influence on pilot opinion: short period frequency omega, short period damping ratio zeta, and the product omega zeta. To determine the influence of the sampling period on these characteristics, the equations describing the response of a DC-8 aircraft to elevator control inputs were used. The results indicate that if the sampling period is too large, the fidelity of the simulation can be degraded.
Experimental and calculational analyses of actinide samples irradiated in EBR-II
Gilai, D.; Williams, M.L.; Cooper, J.H.; Laing, W.R.; Walker, R.L.; Raman, S.; Stelson, P.H.
1982-10-01
Higher actinides influence the characteristics of spent and recycled fuel and dominate the long-term hazards of the reactor waste. Reactor irradiation experiments provide useful benchmarks for testing the evaluated nuclear data for these actinides. During 1967 to 1970, several actinide samples were irradiated in the Idaho EBR-II fast reactor. These samples have now been analyzed, employing mass and alpha spectrometry, to determine the heavy element products. A simple spherical model for the EBR-II core and a recent version of the ORIGEN code with ENDF/B-V data were employed to calculate the exposure products. A detailed comparison between the experimental and calculated results has been made. For samples irradiated at locations near the core center, agreement within 10% was obtained for the major isotopes and their first daughters, and within 20% for the nuclides up the chain. A sensitivity analysis showed that the assumed flux should be increased by 10%.
ERIC Educational Resources Information Center
Du, Yunfei
This paper discusses the impact of sampling error on the construction of confidence intervals around effect sizes. Sampling error affects the location and precision of confidence intervals. Meta-analytic resampling demonstrates that confidence intervals can haphazardly bounce around the true population parameter. Special software with graphical…
Goodness of Fit Confirmatory Factor Analysis: The Effects of Sample Size and Model Parsimony.
ERIC Educational Resources Information Center
Marsh, Herbert W.; Balla, John
The influence of sample size (N) and model parsimony on a set of 22 goodness of fit indices was investigated, including those typically used in confirmatory factor analysis and some recently developed indices. For sample data simulated from 2 known population data structures, values for 6 of 22 fit indices were reasonably independent of N and were…
Computer program for sample sizes required to determine disease incidence in fish populations
Ossiander, Frank J.; Wedemeyer, Gary
1973-01-01
A computer program is described for generating the sample size tables required in fish hatchery disease inspection and certification. The program was designed to aid in detection of infectious pancreatic necrosis (IPN) in salmonids, but it is applicable to any fish disease inspection when the sampling plan follows the hypergeometric distribution.
ERIC Educational Resources Information Center
Finch, W. Holmes; Finch, Maria E. Hernandez
2016-01-01
Researchers and data analysts are sometimes faced with the problem of very small samples, where the number of variables approaches or exceeds the overall sample size; i.e. high dimensional data. In such cases, standard statistical models such as regression or analysis of variance cannot be used, either because the resulting parameter estimates…
Minimum Sample Size for Cronbach's Coefficient Alpha: A Monte-Carlo Study
ERIC Educational Resources Information Center
Yurdugul, Halil
2008-01-01
The coefficient alpha is the most widely used measure of internal consistency for composite scores in the educational and psychological studies. However, due to the difficulties of data gathering in psychometric studies, the minimum sample size for the sample coefficient alpha has been frequently debated. There are various suggested minimum sample…
Norm Block Sample Sizes: A Review of 17 Individually Administered Intelligence Tests
ERIC Educational Resources Information Center
Norfolk, Philip A.; Farmer, Ryan L.; Floyd, Randy G.; Woods, Isaac L.; Hawkins, Haley K.; Irby, Sarah M.
2015-01-01
The representativeness, recency, and size of norm samples strongly influence the accuracy of inferences drawn from their scores. Inadequate norm samples may lead to inflated or deflated scores for individuals and poorer prediction of developmental and academic outcomes. The purpose of this study was to apply Kranzler and Floyd's method for…
Optimal sample sizes for Welch's test under various allocation and cost considerations.
Jan, Show-Li; Shieh, Gwowen
2011-12-01
The issue of the sample size necessary to ensure adequate statistical power has been the focus of considerableattention in scientific research. Conventional presentations of sample size determination do not consider budgetary and participant allocation scheme constraints, although there is some discussion in the literature. The introduction of additional allocation and cost concerns complicates study design, although the resulting procedure permits a practical treatment of sample size planning. This article presents exact techniques for optimizing sample size determinations in the context of Welch (Biometrika, 29, 350-362, 1938) test of the difference between two means under various design and cost considerations. The allocation schemes include cases in which (1) the ratio of group sizes is given and (2) one sample size is specified. The cost implications suggest optimally assigning subjects (1) to attain maximum power performance for a fixed cost and (2) to meet adesignated power level for the least cost. The proposed methods provide useful alternatives to the conventional procedures and can be readily implemented with the developed R and SAS programs that are available as supplemental materials from brm.psychonomic-journals.org/content/supplemental.
Fienen, Michael N.; Selbig, William R.
2012-01-01
A new sample collection system was developed to improve the representation of sediment entrained in urban storm water by integrating water quality samples from the entire water column. The depth-integrated sampler arm (DISA) was able to mitigate sediment stratification bias in storm water, thereby improving the characterization of suspended-sediment concentration and particle size distribution at three independent study locations. Use of the DISA decreased variability, which improved statistical regression to predict particle size distribution using surrogate environmental parameters, such as precipitation depth and intensity. The performance of this statistical modeling technique was compared to results using traditional fixed-point sampling methods and was found to perform better. When environmental parameters can be used to predict particle size distributions, environmental managers have more options when characterizing concentrations, loads, and particle size distributions in urban runoff.
Ifoulis, A A; Savopoulou-Soultani, M
2006-10-01
The purpose of this research was to quantify the spatial pattern and develop a sampling program for larvae of Lobesia botrana Denis and Schiffermüller (Lepidoptera: Tortricidae), an important vineyard pest in northern Greece. Taylor's power law and Iwao's patchiness regression were used to model the relationship between the mean and the variance of larval counts. Analysis of covariance was carried out, separately for infestation and injury, with combined second and third generation data, for vine and half-vine sample units. Common regression coefficients were estimated to permit use of the sampling plan over a wide range of conditions. Optimum sample sizes for infestation and injury, at three levels of precision, were developed. An investigation of a multistage sampling plan with a nested analysis of variance showed that if the goal of sampling is focusing on larval infestation, three grape clusters should be sampled in a half-vine; if the goal of sampling is focusing on injury, then two grape clusters per half-vine are recommended.
A determination of sampling intensity to characterize a Landsat MSS scene using two block sizes
NASA Technical Reports Server (NTRS)
Horning, N.; Case, D.; Nelson, R.
1986-01-01
Three Landsat MSS scenes were processed to empirically determine the sampling intensity needed to characterize various land cover types including water, conifer, and hardwood. The block sizes used as the sampling units were 497 by 500 pixels (picture elements) and 248 by 250 pixels. It is found that, for a given accuracy criterion, the sampling intensity is dependent on the abundance of the cover type of interest in the MSS scene. The results also indicate that, when using the smaller block size, a smaller percentage of the scene has to be classified to obtain a given level of accuracy.
Constrained statistical inference: sample-size tables for ANOVA and regression.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves
2014-01-01
Researchers in the social and behavioral sciences often have clear expectations about the order/direction of the parameters in their statistical model. For example, a researcher might expect that regression coefficient β1 is larger than β2 and β3. The corresponding hypothesis is H: β1 > {β2, β3} and this is known as an (order) constrained hypothesis. A major advantage of testing such a hypothesis is that power can be gained and inherently a smaller sample size is needed. This article discusses this gain in sample size reduction, when an increasing number of constraints is included into the hypothesis. The main goal is to present sample-size tables for constrained hypotheses. A sample-size table contains the necessary sample-size at a pre-specified power (say, 0.80) for an increasing number of constraints. To obtain sample-size tables, two Monte Carlo simulations were performed, one for ANOVA and one for multiple regression. Three results are salient. First, in an ANOVA the needed sample-size decreases with 30-50% when complete ordering of the parameters is taken into account. Second, small deviations from the imposed order have only a minor impact on the power. Third, at the maximum number of constraints, the linear regression results are comparable with the ANOVA results. However, in the case of fewer constraints, ordering the parameters (e.g., β1 > β2) results in a higher power than assigning a positive or a negative sign to the parameters (e.g., β1 > 0).
Sample size requirements for the design of reliability studies: precision consideration.
Shieh, Gwowen
2014-09-01
In multilevel modeling, the intraclass correlation coefficient based on the one-way random-effects model is routinely employed to measure the reliability or degree of resemblance among group members. To facilitate the advocated practice of reporting confidence intervals in future reliability studies, this article presents exact sample size procedures for precise interval estimation of the intraclass correlation coefficient under various allocation and cost structures. Although the suggested approaches do not admit explicit sample size formulas and require special algorithms for carrying out iterative computations, they are more accurate than the closed-form formulas constructed from large-sample approximations with respect to the expected width and assurance probability criteria. This investigation notes the deficiency of existing methods and expands the sample size methodology for the design of reliability studies that have not previously been discussed in the literature.
NASA Astrophysics Data System (ADS)
Reyer, Dorothea; Philipp, Sonja
2014-05-01
It is desirable to enlarge the profit margin of geothermal projects by reducing the total drilling costs considerably. Substantiated assumptions on uniaxial compressive strengths and failure criteria are important to avoid borehole instabilities and adapt the drilling plan to rock mechanical conditions to minimise non-productive time. Because core material is rare we aim at predicting in situ rock properties from outcrop analogue samples which are easy and cheap to provide. The comparability of properties determined from analogue samples with samples from depths is analysed by performing physical characterisation (P-wave velocities, densities), conventional triaxial tests, and uniaxial compressive strength tests of both quarry and equivalent core samples. "Equivalent" means that the quarry sample is of the same stratigraphic age and of comparable sedimentary facies and composition as the correspondent core sample. We determined the parameters uniaxial compressive strength (UCS) and Young's modulus for 35 rock samples from quarries and 14 equivalent core samples from the North German Basin. A subgroup of these samples was used for triaxial tests. For UCS versus Young's modulus, density and P-wave velocity, linear- and non-linear regression analyses were performed. We repeated regression separately for clastic rock samples or carbonate rock samples only as well as for quarry samples or core samples only. Empirical relations were used to calculate UCS values from existing logs of sampled wellbore. Calculated UCS values were then compared with measured UCS of core samples of the same wellbore. With triaxial tests we determined linearized Mohr-Coulomb failure criteria, expressed in both principal stresses and shear and normal stresses, for quarry samples. Comparison with samples from larger depths shows that it is possible to apply the obtained principal stress failure criteria to clastic and volcanic rocks, but less so for carbonates. Carbonate core samples have higher
Bartsch, L.A.; Richardson, W.B.; Naimo, T.J.
1998-01-01
Estimation of benthic macroinvertebrate populations over large spatial scales is difficult due to the high variability in abundance and the cost of sample processing and taxonomic analysis. To determine a cost-effective, statistically powerful sample design, we conducted an exploratory study of the spatial variation of benthic macroinvertebrates in a 37 km reach of the Upper Mississippi River. We sampled benthos at 36 sites within each of two strata, contiguous backwater and channel border. Three standard ponar (525 cm(2)) grab samples were obtained at each site ('Original Design'). Analysis of variance and sampling cost of strata-wide estimates for abundance of Oligochaeta, Chironomidae, and total invertebrates showed that only one ponar sample per site ('Reduced Design') yielded essentially the same abundance estimates as the Original Design, while reducing the overall cost by 63%. A posteriori statistical power analysis (alpha = 0.05, beta = 0.20) on the Reduced Design estimated that at least 18 sites per stratum were needed to detect differences in mean abundance between contiguous backwater and channel border areas for Oligochaeta, Chironomidae, and total invertebrates. Statistical power was nearly identical for the three taxonomic groups. The abundances of several taxa of concern (e.g., Hexagenia mayflies and Musculium fingernail clams) were too spatially variable to estimate power with our method. Resampling simulations indicated that to achieve adequate sampling precision for Oligochaeta, at least 36 sample sites per stratum would be required, whereas a sampling precision of 0.2 would not be attained with any sample size for Hexagenia in channel border areas, or Chironomidae and Musculium in both strata given the variance structure of the original samples. Community-wide diversity indices (Brillouin and 1-Simpsons) increased as sample area per site increased. The backwater area had higher diversity than the channel border area. The number of sampling sites
Calculating of river water quality sampling frequency by the analytic hierarchy process (AHP).
Do, Huu Tuan; Lo, Shang-Lien; Phan Thi, Lan Anh
2013-01-01
River water quality sampling frequency is an important aspect of the river water quality monitoring network. A suitable sampling frequency for each station as well as for the whole network will provide a measure of the real water quality status for the water quality managers as well as the decision makers. The analytic hierarchy process (AHP) is an effective method for decision analysis and calculation of weighting factors based on multiple criteria to solve complicated problems. This study introduces a new procedure to design river water quality sampling frequency by applying the AHP. We introduce and combine weighting factors of variables with the relative weights of stations to select the sampling frequency for each station, monthly and yearly. The new procedure was applied for Jingmei and Xindian rivers, Taipei, Taiwan. The results showed that sampling frequency should be increased at high weighted stations while decreased at low weighted stations. In addition, a detailed monitoring plan for each station and each month could be scheduled from the output results. Finally, the study showed that the AHP is a suitable method to design a system for sampling frequency as it could combine multiple weights and multiple levels for stations and variables to calculate a final weight for stations, variables, and months.
Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review.
Miao, Yinglong; McCammon, J Andrew
Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.
Sleeth, Darrah K
2013-05-01
In 2010, the American Conference of Governmental Industrial Hygienists (ACGIH) formally changed its Threshold Limit Value (TLV) for beryllium from a 'total' particulate sample to an inhalable particulate sample. This change may have important implications for workplace air sampling of beryllium. A history of particle size-selective sampling methods, with a special focus on beryllium, will be provided. The current state of the science on inhalable sampling will also be presented, including a look to the future at what new methods or technology may be on the horizon. This includes new sampling criteria focused on particle deposition in the lung, proposed changes to the existing inhalable convention, as well as how the issues facing beryllium sampling may help drive other changes in sampling technology.
Fujishima, Motonobu; Kawaguchi, Atsushi; Maikusa, Norihide; Kuwano, Ryozo; Iwatsubo, Takeshi; Matsuda, Hiroshi
2016-01-01
Background: Little is known about the sample sizes required for clinical trials of Alzheimer’s disease (AD)-modifying treatments using atrophy measures from serial brain magnetic resonance imaging (MRI) in the Japanese population. Objective: The primary objective of the present study was to estimate how large a sample size would be needed for future clinical trials for AD-modifying treatments in Japan using atrophy measures of the brain as a surrogate biomarker. Methods: Sample sizes were estimated from the rates of change of the whole brain and hippocampus by the k-means normalized boundary shift integral (KN-BSI) and cognitive measures using the data of 537 Japanese Alzheimer’s Neuroimaging Initiative (J-ADNI) participants with a linear mixed-effects model. We also examined the potential use of ApoE status as a trial enrichment strategy. Results: The hippocampal atrophy rate required smaller sample sizes than cognitive measures of AD and mild cognitive impairment (MCI). Inclusion of ApoE status reduced sample sizes for AD and MCI patients in the atrophy measures. Conclusion: These results show the potential use of longitudinal hippocampal atrophy measurement using automated image analysis as a progression biomarker and ApoE status as a trial enrichment strategy in a clinical trial of AD-modifying treatment in Japanese people. PMID:27911297
Shirazi, Mohammadali; Lord, Dominique; Geedipally, Srinivas Reddy
2016-08-01
The Highway Safety Manual (HSM) prediction models are fitted and validated based on crash data collected from a selected number of states in the United States. Therefore, for a jurisdiction to be able to fully benefit from applying these models, it is necessary to calibrate or recalibrate them to local conditions. The first edition of the HSM recommends calibrating the models using a one-size-fits-all sample-size of 30-50 locations with total of at least 100 crashes per year. However, the HSM recommendation is not fully supported by documented studies. The objectives of this paper are consequently: (1) to examine the required sample size based on the characteristics of the data that will be used for the calibration or recalibration process; and, (2) propose revised guidelines. The objectives were accomplished using simulation runs for different scenarios that characterized the sample mean and variance of the data. The simulation results indicate that as the ratio of the standard deviation to the mean (i.e., coefficient of variation) of the crash data increases, a larger sample-size is warranted to fulfill certain levels of accuracy. Taking this observation into account, sample-size guidelines were prepared based on the coefficient of variation of the crash data that are needed for the calibration process. The guidelines were then successfully applied to the two observed datasets. The proposed guidelines can be used for all facility types and both for segment and intersection prediction models.
Demonstration of multi- and single-reader sample size program for diagnostic studies software
NASA Astrophysics Data System (ADS)
Hillis, Stephen L.; Schartz, Kevin M.
2015-03-01
The recently released software Multi- and Single-Reader Sample Size Sample Size Program for Diagnostic Studies, written by Kevin Schartz and Stephen Hillis, performs sample size computations for diagnostic reader-performance studies. The program computes the sample size needed to detect a specified difference in a reader performance measure between two modalities, when using the analysis methods initially proposed by Dorfman, Berbaum, and Metz (DBM) and Obuchowski and Rockette (OR), and later unified and improved by Hillis and colleagues. A commonly used reader performance measure is the area under the receiver-operating-characteristic curve. The program can be used with typical common reader-performance measures which can be estimated parametrically or nonparametrically. The program has an easy-to-use step-by-step intuitive interface that walks the user through the entry of the needed information. Features of the software include the following: (1) choice of several study designs; (2) choice of inputs obtained from either OR or DBM analyses; (3) choice of three different inference situations: both readers and cases random, readers fixed and cases random, and readers random and cases fixed; (4) choice of two types of hypotheses: equivalence or noninferiority; (6) choice of two output formats: power for specified case and reader sample sizes, or a listing of case-reader combinations that provide a specified power; (7) choice of single or multi-reader analyses; and (8) functionality in Windows, Mac OS, and Linux.
Wolf, R; Barkema, H W; De Buck, J; Orsel, K
2015-01-01
Mycobacterium avium subspecies paratuberculosis (MAP), the etiologic agent of Johne's disease, a chronic progressive enteritis, is a common pathogen on dairy farms. Environmental sampling is frequently used to detect MAP-infected herds, because it does not require sample collection from individual animals. The objectives were to determine (1) location-specific odds of MAP-positive environmental sampling results and whether season or herd size affect results; (2) whether season and herd size affect the odds of collection of samples from certain locations; and (3) whether sample-set composition affects the odds of a positive set. Herd veterinarians, producer organization staff, and University of Calgary staff collected 5,588 samples on dairy farms in Alberta and Saskatchewan. Samples from sick-cow and calving pens and samples from dry-cow housing had lower odds of testing MAP-positive than lactating cow-pen samples (odds ratio=0.3 and 0.4, respectively). Samples collected from bedding packs and manure piles were less frequently MAP-positive than those collected from alleyways and lagoons, whereas samples collected in spring and summer more often tested MAP-positive than those collected in winter. Sample sets collected in summer more often included samples from all locations than samples collected in winter; therefore, we inferred that collectors had difficulties accessing certain areas in winter. Substitution of sample locations with others had minor effect on the sensitivity of sample sets containing 6 samples. However, set composition had an effect on the sensitivity of sample sets containing only 2 samples. In that regard, whereas sets with 2 manure-storage-area samples detected 81% of farms with at least one positive environmental sample, sets with only dry, sick, or calving-pen samples detected only 59%. Environmental samples should be collected from areas where manure from numerous cows accumulates and can be well mixed (e.g., alleyways and manure lagoons
Silica glass structure generation for ab initio calculations using small samples of amorphous silica
NASA Astrophysics Data System (ADS)
van Ginhoven, Renée M.; Jónsson, Hannes; Corrales, L. René
2005-01-01
Multiple small samples of amorphous silica have been generated and optimized using classical dynamics and the van Beest-Kramer-van Santen (BKS) empirical potential function. The samples were subsequently optimized and annealed using density functional theory (DFT) with both the local density and the generalized gradient approximations. A thorough analysis of the local and medium-range structure of the optimized samples obtained from the different methods was carried out. The structural characteristics obtained for the average of small systems each containing ca. 100 ions are compared for each of the different methods, and to the BKS simulation of a larger system. The differences found between the DFT and BKS simulations and the effects of volume relaxation on the structures are discussed. Fixed-volume samples are compared to neutron scattering data, with good agreement to 5Å , the length limit of the sample sizes used here. It is shown that by creating multiple small samples, it is possible to achieve a good statistical sampling of structural features consistent with larger simulated glass systems. This study also shows that multiple small samples are necessary to capture the structural distribution of silica glass, and therefore to study more complex processes in glass, such as reactions.
Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach.
Burusco, Kepa K; Bruce, Neil J; Alibay, Irfan; Bryce, Richard A
2015-10-26
Free energy simulations are an established computational tool in modelling chemical change in the condensed phase. However, sampling of kinetically distinct substates remains a challenge to these approaches. As a route to addressing this, we link the methods of thermodynamic integration (TI) and swarm-enhanced sampling molecular dynamics (sesMD), where simulation replicas interact cooperatively to aid transitions over energy barriers. We illustrate the approach by using alchemical alkane transformations in solution, comparing them with the multiple independent trajectory TI (IT-TI) method. Free energy changes for transitions computed by using IT-TI grew increasingly inaccurate as the intramolecular barrier was heightened. By contrast, swarm-enhanced sampling TI (sesTI) calculations showed clear improvements in sampling efficiency, leading to more accurate computed free energy differences, even in the case of the highest barrier height. The sesTI approach, therefore, has potential in addressing chemical change in systems where conformations exist in slow exchange.
Reduced-size plutonium sample processing and packaging for the PAT-2 package
Kuhn, E.; Deron, S.; Aigner, H.; Andersen, J.A.
1982-01-01
A light-water container for the air transport of plutonium safeguards samples, the PAT-2 package, has been developed in the USA and is now licensed by the US NRC (Certificate of Compliance) and the US DOT (IAEA Certificate of Competent Authority). The very limited available space in this package for plutonium-bearing samples required the design of small-size canisters to meet the needs of international safeguards. The suitability of a new small canister and vial for powder and solution samples has been tested in an intralaboratory experiment. The results of the experiment, based on the concept of pre-weighed samples, show that the tested canister and quartz vial can be used successfully for containing small size PuO/sub 2/ powder samples of homogeneous source material, as well as for dried aliguands of plutonium nitrate solutions.
Efficient calculation of SAMPL4 hydration free energies using OMEGA, SZYBKI, QUACPAC, and Zap TK.
Ellingson, Benjamin A; Geballe, Matthew T; Wlodek, Stanislaw; Bayly, Christopher I; Skillman, A Geoffrey; Nicholls, Anthony
2014-03-01
Several submissions for the SAMPL4 hydration free energy set were calculated using OpenEye tools, including many that were among the top performing submissions. All of our best submissions used AM1BCC charges and Poisson-Boltzmann solvation. Three submissions used a single conformer for calculating the hydration free energy and all performed very well with mean unsigned errors ranging from 0.94 to 1.08 kcal/mol. These calculations were very fast, only requiring 0.5-2.0 s per molecule. We observed that our two single-conformer methodologies have different types of failure cases and that these differences could be exploited for determining when the methods are likely to have substantial errors.
Azbouche, Ahmed; Belgaid, Mohamed; Mazrou, Hakim
2015-08-01
A fully detailed Monte Carlo geometrical model of a High Purity Germanium detector with a (152)Eu source, packed in Marinelli beaker, was developed for routine analysis of large volume environmental samples. Then, the model parameters, in particular, the dead layer thickness were adjusted thanks to a specific irradiation configuration together with a fine-tuning procedure. Thereafter, the calculated efficiencies were compared to the measured ones for standard samples containing (152)Eu source filled in both grass and resin matrices packed in Marinelli beaker. From this comparison, a good agreement between experiment and Monte Carlo calculation results was obtained highlighting thereby the consistency of the geometrical computational model proposed in this work. Finally, the computational model was applied successfully to determine the (137)Cs distribution in soil matrix. From this application, instructive results were achieved highlighting, in particular, the erosion and accumulation zone of the studied site.
ERIC Educational Resources Information Center
Dunst, Carl J.; Hamby, Deborah W.
2012-01-01
This paper includes a nontechnical description of methods for calculating effect sizes in intellectual and developmental disability studies. Different hypothetical studies are used to illustrate how null hypothesis significance testing (NHST) and effect size findings can result in quite different outcomes and therefore conflicting results. Whereas…
Bergh, Daniel
2015-01-01
Chi-square statistics are commonly used for tests of fit of measurement models. Chi-square is also sensitive to sample size, which is why several approaches to handle large samples in test of fit analysis have been developed. One strategy to handle the sample size problem may be to adjust the sample size in the analysis of fit. An alternative is to adopt a random sample approach. The purpose of this study was to analyze and to compare these two strategies using simulated data. Given an original sample size of 21,000, for reductions of sample sizes down to the order of 5,000 the adjusted sample size function works as good as the random sample approach. In contrast, when applying adjustments to sample sizes of lower order the adjustment function is less effective at approximating the chi-square value for an actual random sample of the relevant size. Hence, the fit is exaggerated and misfit under-estimated using the adjusted sample size function. Although there are big differences in chi-square values between the two approaches at lower sample sizes, the inferences based on the p-values may be the same.
Comparative studies of grain size separates of 60009. [lunar soil samples
NASA Technical Reports Server (NTRS)
Mckay, D. S.; Morris, R. V.; Dungan, M. A.; Fruland, R. M.; Fuhrman, R.
1976-01-01
Five samples from 60009, the lower half of a double drive tube, were analyzed via grain-size methods, with particle types classified and counted in the coarser grain sizes. Studies were undertaken of particle types and distributions by petrographic methods, of magnetic fractions, of the size splits and magnetic splits as analyzed by ferromagnetic resonance (FMR) techniques, of maturity (based on agglutinate content, FMR index Is/FeO, mean size of sub-cm material, magnetic fraction), of possible reworking or mixing in situ, and of depositional history. Maturity indices are in substantial agreement for all of the five samples. Strong positive correlation of percent agglutinates and percent bedrock-derived lithic fragments, combined with negative correlation of those components with percent single crystal plagioclase, argue against in situ reworking of the same soil.
Group sequential and discretized sample size re-estimation designs: a comparison of flexibility.
Wu, Xiaoru; Cui, Lu
2012-10-30
In clinical trials, researchers usually determine a study sample size prior to the start of the study to provide a sufficient power at a targeted treatment difference. When the targeted treatment difference deviates from the true one, the study may either have insufficient power or use more subjects than necessary. To address the difficulty in sample size planning, researchers have developed various flexible sample size designs and compared their performances. Some previous work suggests that re-estimation designs are inefficient and that one can improve uniformly by using standard group sequential likelihood ratio tests, although more interim analyses are involved. However, researchers need to further study the statement and the minimal number of tests needed before a standard group sequential test might outperform a re-estimation design. In this paper, we conducted simulation studies to answer these questions using various optimality criteria.
Optimal sample sizes for the design of reliability studies: power consideration.
Shieh, Gwowen
2014-09-01
Intraclass correlation coefficients are used extensively to measure the reliability or degree of resemblance among group members in multilevel research. This study concerns the problem of the necessary sample size to ensure adequate statistical power for hypothesis tests concerning the intraclass correlation coefficient in the one-way random-effects model. In view of the incomplete and problematic numerical results in the literature, the approximate sample size formula constructed from Fisher's transformation is reevaluated and compared with an exact approach across a wide range of model configurations. These comprehensive examinations showed that the Fisher transformation method is appropriate only under limited circumstances, and therefore it is not recommended as a general method in practice. For advance design planning of reliability studies, the exact sample size procedures are fully described and illustrated for various allocation and cost schemes. Corresponding computer programs are also developed to implement the suggested algorithms.
MRI derived brain atrophy in PSP and MSA-P. Determining sample size to detect treatment effects.
Paviour, Dominic C; Price, Shona L; Lees, Andrew J; Fox, Nick C
2007-04-01
Progressive supranuclear palsy (PSP) and multiple system (MSA) atrophy are associated with progressive brain atrophy. Serial MRI can be applied in order to measure this change in brain volume and to calculate atrophy rates. We evaluated MRI derived whole brain and regional atrophy rates as potential markers of progression in PSP and the Parkinsonian variant of multiple system atrophy (MSA-P). 17 patients with PSP, 9 with MSA-P and 18 healthy controls underwent two MRI brain scans. MRI scans were registered, and brain and regional atrophy rates (midbrain, pons, cerebellum, third and lateral ventricles) measured. Sample sizes required to detect the effect of a proposed disease-modifying treatment were estimated. The effect of scan interval on the variance of the atrophy rates and sample size was assessed. Based on the calculated yearly rates of atrophy, for a drug effect equivalent to a 30% reduction in atrophy, fewer PSP subjects are required in each treatment arm when using midbrain rather than whole brain atrophy rates (183 cf. 499). Fewer MSA-P subjects are required, using pontine/cerebellar, rather than whole brain atrophy rates (164/129 cf. 794). A reduction in the variance of measured atrophy rates was observed with a longer scan interval. Regional rather than whole brain atrophy rates calculated from volumetric serial MRI brain scans in PSP and MSA-P provide a more practical and powerful means of monitoring disease progression in clinical trials.
Mesh-size effects on drift sample composition as determined with a triple net sampler
Slack, K.V.; Tilley, L.J.; Kennelly, S.S.
1991-01-01
Nested nets of three different mesh apertures were used to study mesh-size effects on drift collected in a small mountain stream. The innermost, middle, and outermost nets had, respectively, 425 ??m, 209 ??m and 106 ??m openings, a design that reduced clogging while partitioning collections into three size groups. The open area of mesh in each net, from largest to smallest mesh opening, was 3.7, 5.7 and 8.0 times the area of the net mouth. Volumes of filtered water were determined with a flowmeter. The results are expressed as (1) drift retained by each net, (2) drift that would have been collected by a single net of given mesh size, and (3) the percentage of total drift (the sum of the catches from all three nets) that passed through the 425 ??m and 209 ??m nets. During a two day period in August 1986, Chironomidae larvae were dominant numerically in all 209 ??m and 106 ??m samples and midday 425 ??m samples. Large drifters (Ephemerellidae) occurred only in 425 ??m or 209 ??m nets, but the general pattern was an increase in abundance and number of taxa with decreasing mesh size. Relatively more individuals occurred in the larger mesh nets at night than during the day. The two larger mesh sizes retained 70% of the total sediment/detritus in the drift collections, and this decreased the rate of clogging of the 106 ??m net. If an objective of a sampling program is to compare drift density or drift rate between areas or sampling dates, the same mesh size should be used for all sample collection and processing. The mesh aperture used for drift collection should retain all species and life stages of significance in a study. The nested net design enables an investigator to test the adequacy of drift samples. ?? 1991 Kluwer Academic Publishers.
A new method for choosing sample size for confidence interval-based inferences.
Jiroutek, Michael R; Muller, Keith E; Kupper, Lawrence L; Stewart, Paul W
2003-09-01
Scientists often need to test hypotheses and construct corresponding confidence intervals. In designing a study to test a particular null hypothesis, traditional methods lead to a sample size large enough to provide sufficient statistical power. In contrast, traditional methods based on constructing a confidence interval lead to a sample size likely to control the width of the interval. With either approach, a sample size so large as to waste resources or introduce ethical concerns is undesirable. This work was motivated by the concern that existing sample size methods often make it difficult for scientists to achieve their actual goals. We focus on situations which involve a fixed, unknown scalar parameter representing the true state of nature. The width of the confidence interval is defined as the difference between the (random) upper and lower bounds. An event width is said to occur if the observed confidence interval width is less than a fixed constant chosen a priori. An event validity is said to occur if the parameter of interest is contained between the observed upper and lower confidence interval bounds. An event rejection is said to occur if the confidence interval excludes the null value of the parameter. In our opinion, scientists often implicitly seek to have all three occur: width, validity, and rejection. New results illustrate that neglecting rejection or width (and less so validity) often provides a sample size with a low probability of the simultaneous occurrence of all three events. We recommend considering all three events simultaneously when choosing a criterion for determining a sample size. We provide new theoretical results for any scalar (mean) parameter in a general linear model with Gaussian errors and fixed predictors. Convenient computational forms are included, as well as numerical examples to illustrate our methods.
Eberl, D.D.; Drits, V.A.; Srodon, Jan; Nuesch, R.
1996-01-01
Particle size may strongly influence the physical and chemical properties of a substance (e.g. its rheology, surface area, cation exchange capacity, solubility, etc.), and its measurement in rocks may yield geological information about ancient environments (sediment provenance, degree of metamorphism, degree of weathering, current directions, distance to shore, etc.). Therefore mineralogists, geologists, chemists, soil scientists, and others who deal with clay-size material would like to have a convenient method for measuring particle size distributions. Nano-size crystals generally are too fine to be measured by light microscopy. Laser scattering methods give only average particle sizes; therefore particle size can not be measured in a particular crystallographic direction. Also, the particles measured by laser techniques may be composed of several different minerals, and may be agglomerations of individual crystals. Measurement by electron and atomic force microscopy is tedious, expensive, and time consuming. It is difficult to measure more than a few hundred particles per sample by these methods. This many measurements, often taking several days of intensive effort, may yield an accurate mean size for a sample, but may be too few to determine an accurate distribution of sizes. Measurement of size distributions by X-ray diffraction (XRD) solves these shortcomings. An X-ray scan of a sample occurs automatically, taking a few minutes to a few hours. The resulting XRD peaks average diffraction effects from billions of individual nano-size crystals. The size that is measured by XRD may be related to the size of the individual crystals of the mineral in the sample, rather than to the size of particles formed from the agglomeration of these crystals. Therefore one can determine the size of a particular mineral in a mixture of minerals, and the sizes in a particular crystallographic direction of that mineral.
Bias correction of EU-ENSEMBLES precipitation data with focus on the effect of sample size
NASA Astrophysics Data System (ADS)
Reiter, Philipp; Gutjahr, Oliver; Schefczyk, Lukas; Heinemann, Günther; Casper, Markus C.
2015-04-01
The precipitation output of climate models often shows a bias when compared to observed data, so that a bias correction is necessary before using it as climate forcing in impact modeling. We expect the performance of the bias correction to strongly depend on the sample size used for its calibration. This raises the question: how long does a time series need to be to achieve a sufficient bias correction? We carry out experiments using 40 years of daily precipitation data from 10 regional climate models (RCM) of the EU-ENSEMBLES project, splitting them into a 30 year calibration period and a 10 year validation period. The RCM data are bias corrected using decreasing sample sizes out of the calibration period. By applying skill scores we quantify the critical sample size ncrit, at which the quality of the bias correction becomes statistically worse compared to the correction based on 30 years. In order to analyze whether the effect of the sample size depends on the chosen correction method and the calibration period, we applied four variations of the quantile matching (QM) approach and 3 different calibration/validation periods in this study. The results show that the spread of ncrit is large, ranging from 28 years to approximately 10 years. This indicates that even a small decrease in sample size for the calibration can result in a statistical significant degradation of the bias correction. Corrections with sample sizes smaller than 10 years always perform significantly worse than the 'best fit' with 30 years. The chosen QM approach influences ncrit in dependence of its degrees of freedom: the higher the degrees of freedom the larger ncrit. We also found that the choice of the calibration period affects the ncrit values. In conclusion we recommend to use time series as long as possible for bias correction of precipitation data. However, there is a large transition zone of the critical sample size where shorter time series can perform sufficiently well, depending on
NASA Technical Reports Server (NTRS)
Morgera, S. D.; Cooper, D. B.
1976-01-01
The experimental observation that a surprisingly small sample size vis-a-vis dimension is needed to achieve good signal-to-interference ratio (SIR) performance with an adaptive predetection filter is explained. The adaptive filter requires estimates as obtained by a recursive stochastic algorithm of the inverse of the filter input data covariance matrix. The SIR performance with sample size is compared for the situations where the covariance matrix estimates are of unstructured (generalized) form and of structured (finite Toeplitz) form; the latter case is consistent with weak stationarity of the input data stochastic process.
Estimation of grain size in asphalt samples using digital image analysis
NASA Astrophysics Data System (ADS)
Källén, Hanna; Heyden, Anders; Lindh, Per
2014-09-01
Asphalt is made of a mixture of stones of different sizes and a binder called bitumen, the size distribution of the stones is determined by the recipe of the asphalt. One quality check of asphalt is to see if the real size distribution of asphalt samples is consistent with the recipe. This is usually done by first extracting the binder using methylenchloride and the sieving the stones and see how much that pass every sieve size. Methylenchloride is highly toxic and it is desirable to find the size distribution in some other way. In this paper we find the size distribution by slicing up the asphalt sample and using image analysis techniques to analyze the cross-sections. First the stones are segmented from the background, bitumen, and then rectangles are fit to the detected stones. We then estimate the sizes of the stones by using the width of the rectangle. The result is compared with both the recipe for the asphalt and with the result from the standard analysis method, and our method shows good correlation with those.
Hoyle, Rick H; Gottfredson, Nisha C
2015-10-01
When the goal of prevention research is to capture in statistical models some measure of the dynamic complexity in structures and processes implicated in problem behavior and its prevention, approaches such as multilevel modeling (MLM) and structural equation modeling (SEM) are indicated. Yet the assumptions that must be satisfied if these approaches are to be used responsibly raise concerns regarding their use in prevention research involving smaller samples. In this article, we discuss in nontechnical terms the role of sample size in MLM and SEM and present findings from the latest simulation work on the performance of each approach at sample sizes typical of prevention research. For each statistical approach, we draw from extant simulation studies to establish lower bounds for sample size (e.g., MLM can be applied with as few as ten groups comprising ten members with normally distributed data, restricted maximum likelihood estimation, and a focus on fixed effects; sample sizes as small as N = 50 can produce reliable SEM results with normally distributed data and at least three reliable indicators per factor) and suggest strategies for making the best use of the modeling approach when N is near the lower bound.
Hoyle, Rick H.; Gottfredson, Nisha C.
2014-01-01
When the goal of prevention research is to capture in statistical models some measure of the dynamic complexity in structures and processes implicated in problem behavior and its prevention, approaches such as multilevel modeling (MLM) and structural equation modeling (SEM) are indicated. Yet the assumptions that must be satisfied if these approaches are to be used responsibly raise concerns regarding their use in prevention research involving smaller samples. In this manuscript we discuss in nontechnical terms the role of sample size in MLM and SEM and present findings from the latest simulation work on the performance of each approach at sample sizes typical of prevention research. For each statistical approach, we draw from extant simulation studies to establish lower bounds for sample size (e.g., MLM can be applied with as few as 10 groups comprising 10 members with normally distributed data, restricted maximum likelihood estimation, and a focus on fixed effects; sample sizes as small as N = 50 can produce reliable SEM results with normally distributed data and at least three reliable indicators per factor) and suggest strategies for making the best use of the modeling approach when N is near the lower bound. PMID:24752569
Simulation analyses of space use: Home range estimates, variability, and sample size
Bekoff, M.; Mech, L.D.
1984-01-01
Simulations of space use by animals were run to determine the relationship among home range area estimates, variability, and sample size {number of locations}. As sample size increased, home range size increased asymptotically, whereas variability decreased among mean home range area estimates generated by multiple simulations for the same sample size. Our results suggest that field workers should ascertain between 100 and 200 locations in order to estimate reliably home range area. In some cases, this suggested guideline is higher than values found in the few published studies in which the relationship between home range area and number of locations is addressed. Sampling differences for small species occupying relatively small home ranges indicate that fewer locations may be sufficient to allow for a reliable estimate of home range. Intraspecffic variability in social status (group member, loner, resident, transient), age, sex, reproductive condition, and food resources also have to be considered, as do season, habitat, and differences in sampling and analytical methods. Comparative data still are needed.
Big data and large sample size: a cautionary note on the potential for bias.
Kaplan, Robert M; Chambers, David A; Glasgow, Russell E
2014-08-01
A number of commentaries have suggested that large studies are more reliable than smaller studies and there is a growing interest in the analysis of "big data" that integrates information from many thousands of persons and/or different data sources. We consider a variety of biases that are likely in the era of big data, including sampling error, measurement error, multiple comparisons errors, aggregation error, and errors associated with the systematic exclusion of information. Using examples from epidemiology, health services research, studies on determinants of health, and clinical trials, we conclude that it is necessary to exercise greater caution to be sure that big sample size does not lead to big inferential errors. Despite the advantages of big studies, large sample size can magnify the bias associated with error resulting from sampling or study design.
Williamson, A.D.; Farthing, W.E.; Ward, T.E.; Midgett, M.R.
1987-05-01
In several particle-sizing samplers, the sample extraction nozzle is necessarily closely coupled to the first inertial sizing stage. Devices of this type include small sampling cyclones, right-angle impactor precollectors for in-stack impactors, and the first impaction stage of several cascade impactors. In a recent laboratory study of a stack-sampling cyclone with various sampling nozzles, significant perturbations were observed in the actual D50 when some of the nozzles were used. Some nozzles caused the D50 of the cyclone to be reduced from 10 micrometers to less than 6 micrometers. Several alternate nozzle designs were considered to alleviate this behavior. Simple extension of the nozzle length was sufficient to restore the 10-micrometers sampler D50, but at the expense of enhanced deposition of the test-aerosol particles on the nozzle walls.
Wong, Esther; Sastri, Akash R; Lin, Fan-Sian; Hsieh, Chih-Hao
2017-01-01
We have developed a modified FlowCAM procedure for efficiently quantifying the size distribution of zooplankton. The modified method offers the following new features: 1) prevents animals from settling and clogging with constant bubbling in the sample container; 2) prevents damage to sample animals and facilitates recycling by replacing the built-in peristaltic pump with an external syringe pump, in order to generate negative pressure, creates a steady flow by drawing air from the receiving conical flask (i.e. vacuum pump), and transfers plankton from the sample container toward the main flowcell of the imaging system and finally into the receiving flask; 3) aligns samples in advance of imaging and prevents clogging with an additional flowcell placed ahead of the main flowcell. These modifications were designed to overcome the difficulties applying the standard FlowCAM procedure to studies where the number of individuals per sample is small, and since the FlowCAM can only image a subset of a sample. Our effective recycling procedure allows users to pass the same sample through the FlowCAM many times (i.e. bootstrapping the sample) in order to generate a good size distribution. Although more advanced FlowCAM models are equipped with syringe pump and Field of View (FOV) flowcells which can image all particles passing through the flow field; we note that these advanced setups are very expensive, offer limited syringe and flowcell sizes, and do not guarantee recycling. In contrast, our modifications are inexpensive and flexible. Finally, we compared the biovolumes estimated by automated FlowCAM image analysis versus conventional manual measurements, and found that the size of an individual zooplankter can be estimated by the FlowCAM image system after ground truthing.
Size-dependent Turbidimatric Quantification of Mobile Colloids in Field Samples
NASA Astrophysics Data System (ADS)
Yan, J.; Meng, X.; Jin, Y.
2015-12-01
Natural colloids, often defined as entities with sizes < 1.0 μm, have attracted much research attention because of their ability to facilitate the transport of contaminants in the subsurface environment. However, due to their small size and generally low concentrations in field samples, quantification of mobile colloids, especially the smaller fractions (< 0.45 µm), which are operationally defined as dissolved, is largely impeded and hence the natural colloidal pool is greatly overlooked and underestimated. The main objectives of this study are to: (1) develop an experimentally and economically efficient methodology to quantify natural colloids in different size fractions (0.1-0.45 and 0.45-1 µm); (2) quantify mobile colloids including small colloids, < 0.45 µm particularly, in different natural aquatic samples. We measured and generated correlations between mass concentration and turbidity of colloid suspensions, made by extracting and fractionating water dispersible colloids in 37 soils from different areas in the U.S. and Denmark, for colloid size fractions 0.1-0.45 and 0.45-1 µm. Results show that the correlation between turbidity and colloid mass concentration is largely affected by colloid size and iron content, indicating the need to generate different correlations for colloids with constrained size range and iron content. This method enabled quick quantification of colloid concentrations in a large number of field samples collected from freshwater, wetland and estuaries in different size fractions. As a general trend, we observed high concentrations of colloids in the < 0.45 µm fraction, which constitutes a significant percentage of the total mobile colloidal pool (< 1 µm). This observation suggests that the operationally defined cut-off size for "dissolved" phase can greatly underestimate colloid concentration therefore the role that colloids play in the transport of associated contaminants or other elements.
Janja Tursic; Irena Grgic; Axel Berner; Jaroslav Skantar; Igor Cuhalev
2008-02-01
A special sampling system for measurements of size-segregated particles directly at the source of emission was designed and constructed. The central part of this system is a low-pressure cascade impactor with 10 collection stages for the size ranges between 15 nm and 16 {mu}m. Its capability and suitability was proven by sampling particles at the stack (100{sup o}C) of a coal-fired power station in Slovenia. These measurements showed very reasonable results in comparison with a commercial cascade impactor for PM10 and PM2.5 and with a plane device for total suspended particulate matter (TSP). The best agreement with the measurements made by a commercial impactor was found for concentrations of TSP above 10 mg m{sup -3}, i.e., the average PM2.5/PM10 ratios obtained by a commercial impactor and by our impactor were 0.78 and 0.80, respectively. Analysis of selected elements in size-segregated emission particles additionally confirmed the suitability of our system. The measurements showed that the mass size distributions were generally bimodal, with the most pronounced mass peak in the 1-2 {mu}m size range. The first results of elemental mass size distributions showed some distinctive differences in comparison to the most common ambient anthropogenic sources (i.e., traffic emissions). For example, trace elements, like Pb, Cd, As, and V, typically related to traffic emissions, are usually more abundant in particles less than 1 {mu}m in size, whereas in our specific case they were found at about 2 {mu}m. Thus, these mass size distributions can be used as a signature of this source. Simultaneous measurements of size-segregated particles at the source and in the surrounding environment can therefore significantly increase the sensitivity of the contribution of a specific source to the actual ambient concentrations. 25 refs., 3 figs., 2 tabs.
Fang, Hong-Bin; Tian, Guo-Liang; Li, Wei; Tan, Ming
2009-07-01
The study of drug combinations has become important in drug development due to its potential for efficacy at lower, less toxic doses and the need to move new therapies rapidly into clinical trials. The goal is to identify which combinations are additive, synergistic, or antagonistic. Although there exists statistical framework for finding doses and sample sizes needed to detect departure from additivity, e.g., the power maximized F-test, different classes of drugs of different does-response shapes require different derivation for calculating sample size and finding doses. Motivated by two anticancer combination studies that we are involved with, this article proposes dose-finding and sample size method for detecting departures from additivity of two drugs with linear and log-linear single dose-response curves. The first study involves combination of two drugs, where one single drug dose-response curve is linear and the other is log-linear. The second study involves combinations of drugs whose single drug dose-response curves are linear. The experiment had been planned with the common fixed ratio design before we were consulted, but the resulting data missed the synergistic combinations. However, the experiment based on the proposed design was able to identify the synergistic combinations as anticipated. Thus we shall summarize the analysis of the data collected according to the proposed design and discuss why the commonly used fixed ratio method failed and the implications of the proposed method for other combination studies.
ERIC Educational Resources Information Center
Fan, Xitao; Wang, Lin; Thompson, Bruce
1999-01-01
A Monte Carlo simulation study investigated the effects on 10 structural equation modeling fit indexes of sample size, estimation method, and model specification. Some fit indexes did not appear to be comparable, and it was apparent that estimation method strongly influenced almost all fit indexes examined, especially for misspecified models. (SLD)
Sideridis, Georgios; Simos, Panagiotis; Papanicolaou, Andrew; Fletcher, Jack
2014-10-01
The present study assessed the impact of sample size on the power and fit of structural equation modeling applied to functional brain connectivity hypotheses. The data consisted of time-constrained minimum norm estimates of regional brain activity during performance of a reading task obtained with magnetoencephalography. Power analysis was first conducted for an autoregressive model with 5 latent variables (brain regions), each defined by 3 indicators (successive activity time bins). A series of simulations were then run by generating data from an existing pool of 51 typical readers (aged 7.5-12.5 years). Sample sizes ranged between 20 and 1,000 participants and for each sample size 1,000 replications were run. Results were evaluated using chi-square Type I errors, model convergence, mean RMSEA (root mean square error of approximation) values, confidence intervals of the RMSEA, structural path stability, and D-Fit index values. Results suggested that 70 to 80 participants were adequate to model relationships reflecting close to not so close fit as per MacCallum et al.'s recommendations. Sample sizes of 50 participants were associated with satisfactory fit. It is concluded that structural equation modeling is a viable methodology to model complex regional interdependencies in brain activation in pediatric populations.
ERIC Educational Resources Information Center
Sideridis, Georgios; Simos, Panagiotis; Papanicolaou, Andrew; Fletcher, Jack
2014-01-01
The present study assessed the impact of sample size on the power and fit of structural equation modeling applied to functional brain connectivity hypotheses. The data consisted of time-constrained minimum norm estimates of regional brain activity during performance of a reading task obtained with magnetoencephalography. Power analysis was first…
Introduction to Sample Size Choice for Confidence Intervals Based on "t" Statistics
ERIC Educational Resources Information Center
Liu, Xiaofeng Steven; Loudermilk, Brandon; Simpson, Thomas
2014-01-01
Sample size can be chosen to achieve a specified width in a confidence interval. The probability of obtaining a narrow width given that the confidence interval includes the population parameter is defined as the power of the confidence interval, a concept unfamiliar to many practitioners. This article shows how to utilize the Statistical Analysis…
Analysis of variograms with various sample sizes from a multispectral image
Technology Transfer Automated Retrieval System (TEKTRAN)
Variogram plays a crucial role in remote sensing application and geostatistics. It is very important to estimate variogram reliably from sufficient data. In this study, the analysis of variograms with various sample sizes of remotely sensed data was conducted. A 100x100-pixel subset was chosen from ...
Analysis of variograms with various sample sizes from a multispectral image
Technology Transfer Automated Retrieval System (TEKTRAN)
Variograms play a crucial role in remote sensing application and geostatistics. In this study, the analysis of variograms with various sample sizes of remotely sensed data was conducted. A 100 X 100 pixel subset was chosen from an aerial multispectral image which contained three wavebands, green, ...
Sample Size Determination for Estimation of Sensor Detection Probabilities Based on a Test Variable
2007-06-01
interest. 15. NUMBER OF PAGES 121 14. SUBJECT TERMS Sample Size, Binomial Proportion, Confidence Interval , Coverage Probability, Experimental...THE STUDY ..........................5 II. LITERATURE REVIEW .......................................7 A. CONFIDENCE INTERVAL METHODS FOR THE...BINOMIAL PROPORTION .........................................7 1. The Wald Confidence Interval ..................7 2. The Wilson Score Confidence Interval .........13
Sample size determination for alternate periods of use study designs with binary responses.
Morel, Jorge G; Neerchal, Nagaraj K
2012-01-01
In this article, we consider several study designs that arise in practice, which are variations of standard crossover designs. Often, they may result from modifications made to a standard crossover design due to practical considerations. Characteristic features of the studies we are concerned with are (a) treatments consist of external use of products with little or no possibility of carry over effects, and (b) the periods of use are dictated by the subjects or by some specific event, such as diaper leakage or menstrual flow. We consider a number of such study designs for estimating the difference in the efficacy of two treatments or test products. We provide brief descriptions of studies to motivate the study design, the underlying data structure, and computations of the variances of the usual unbiased estimators of the difference in efficacy, and the sample size formulas. The situations considered here cover a number of popular crossover designs. The objective of our work is to provide guidance to members of a wide audience on how to answer the sample size question for their own nonstandard situations. We conclude the article with a brief report on a simulation study we conducted to investigate the impact of estimation on the sample size determination and consequently on the actual power realized in an effort to promote the "best practice" of checking whether the recommended sample sizes indeed achieve the desired level of power.
ERIC Educational Resources Information Center
Kim, Su-Young
2012-01-01
Just as growth mixture models are useful with single-phase longitudinal data, multiphase growth mixture models can be used with multiple-phase longitudinal data. One of the practically important issues in single- and multiphase growth mixture models is the sample size requirements for accurate estimation. In a Monte Carlo simulation study, the…
40 CFR 761.243 - Standard wipe sample method and size.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Standard wipe sample method and size. 761.243 Section 761.243 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) TOXIC SUBSTANCES CONTROL ACT POLYCHLORINATED BIPHENYLS (PCBs) MANUFACTURING, PROCESSING, DISTRIBUTION IN...
Sample size and robust marginal methods for cluster-randomized trials with censored event times.
Zhong, Yujie; Cook, Richard J
2015-03-15
In cluster-randomized trials, intervention effects are often formulated by specifying marginal models, fitting them under a working independence assumption, and using robust variance estimates to address the association in the responses within clusters. We develop sample size criteria within this framework, with analyses based on semiparametric Cox regression models fitted with event times subject to right censoring. At the design stage, copula models are specified to enable derivation of the asymptotic variance of estimators from a marginal Cox regression model and to compute the number of clusters necessary to satisfy power requirements. Simulation studies demonstrate the validity of the sample size formula in finite samples for a range of cluster sizes, censoring rates, and degrees of within-cluster association among event times. The power and relative efficiency implications of copula misspecification is studied, as well as the effect of within-cluster dependence in the censoring times. Sample size criteria and other design issues are also addressed for the setting where the event status is only ascertained at periodic assessments and times are interval censored.
One-Sided Nonparametric Comparison of Treatments with a Standard for Unequal Sample Sizes.
ERIC Educational Resources Information Center
Chakraborti, S.; Gibbons, Jean D.
1992-01-01
The one-sided problem of comparing treatments with a standard on the basis of data available in the context of a one-way analysis of variance is examined, and the methodology of S. Chakraborti and J. D. Gibbons (1991) is extended to the case of unequal sample sizes. (SLD)
Bolton tooth size ratio among Sudanese Population sample: A preliminary study
Abdalla Hashim, Ala’a Hayder; Eldin, AL-Hadi Mohi; Hashim, Hayder Abdalla
2015-01-01
Background: The study of the mesiodistal size, the morphology of teeth and dental arch may play an important role in clinical dentistry, as well as other sciences such as Forensic Dentistry and Anthropology. Aims: The aims of the present study were to establish tooth-size ratio in Sudanese sample with Class I normal occlusion, to compare the tooth-size ratio between the present study and Bolton's study and between genders. Materials and Methods: The sample consisted of dental casts of 60 subjects (30 males and 30 females). Bolton formula was used to compute the overall and anterior ratio. The correlation coefficient between the anterior ratio and overall ratio was tested, and Student's t-test was used to compare tooth-size ratios between males and females, and between the present study and Bolton's result. Results: The results of the overall and anterior ratio was relatively similar to the mean values reported by Bolton, and there were no statistically significant differences between the mean values of the anterior ratio and the overall ratio between males and females. The correlation coefficient was (r = 0.79). Conclusions: The result obtained was similar to the Caucasian race. However, the reality indicates that the Sudanese population consisted of different racial groups; therefore, the firm conclusion is difficult to draw. Since this sample is not representative for the Sudanese population, hence, a further study with a large sample collected from the different parts of the Sudan is required. PMID:26229948
Support vector regression to predict porosity and permeability: Effect of sample size
NASA Astrophysics Data System (ADS)
Al-Anazi, A. F.; Gates, I. D.
2012-02-01
Porosity and permeability are key petrophysical parameters obtained from laboratory core analysis. Cores, obtained from drilled wells, are often few in number for most oil and gas fields. Porosity and permeability correlations based on conventional techniques such as linear regression or neural networks trained with core and geophysical logs suffer poor generalization to wells with only geophysical logs. The generalization problem of correlation models often becomes pronounced when the training sample size is small. This is attributed to the underlying assumption that conventional techniques employing the empirical risk minimization (ERM) inductive principle converge asymptotically to the true risk values as the number of samples increases. In small sample size estimation problems, the available training samples must span the complexity of the parameter space so that the model is able both to match the available training samples reasonably well and to generalize to new data. This is achieved using the structural risk minimization (SRM) inductive principle by matching the capability of the model to the available training data. One method that uses SRM is support vector regression (SVR) network. In this research, the capability of SVR to predict porosity and permeability in a heterogeneous sandstone reservoir under the effect of small sample size is evaluated. Particularly, the impact of Vapnik's ɛ-insensitivity loss function and least-modulus loss function on generalization performance was empirically investigated. The results are compared to the multilayer perception (MLP) neural network, a widely used regression method, which operates under the ERM principle. The mean square error and correlation coefficients were used to measure the quality of predictions. The results demonstrate that SVR yields consistently better predictions of the porosity and permeability with small sample size than the MLP method. Also, the performance of SVR depends on both kernel function
The effect of sample size and disease prevalence on supervised machine learning of narrative data.
McKnight, Lawrence K.; Wilcox, Adam; Hripcsak, George
2002-01-01
This paper examines the independent effects of outcome prevalence and training sample sizes on inductive learning performance. We trained 3 inductive learning algorithms (MC4, IB, and Naïve-Bayes) on 60 simulated datasets of parsed radiology text reports labeled with 6 disease states. Data sets were constructed to define positive outcome states at 4 prevalence rates (1, 5, 10, 25, and 50%) in training set sizes of 200 and 2,000 cases. We found that the effect of outcome prevalence is significant when outcome classes drop below 10% of cases. The effect appeared independent of sample size, induction algorithm used, or class label. Work is needed to identify methods of improving classifier performance when output classes are rare. PMID:12463878
Text classification performance: is the sample size the only factor to be considered?
Figueroa, Rosa L; Zeng-Treitler, Qing
2013-01-01
The use of text mining and supervised machine learning algorithms on biomedical databases has become increasingly common. However, a question remains: How much data must be annotated to create a suitable training set for a machine learning classifier? In prior research with active learning in medical text classification, we found evidence that not only sample size but also some of the intrinsic characteristics of the texts being analyzed-such as the size of the vocabulary and the length of a document-may also influence the resulting classifier's performance. This study is an attempt to create a regression model to predict performance based on sample size and other text features. While the model needs to be trained on existing datasets, we believe it is feasible to predict performance without obtaining annotations from new datasets once the model is built.
Kelley, Ken; Rausch, Joseph R
2011-12-01
Longitudinal studies are necessary to examine individual change over time, with group status often being an important variable in explaining some individual differences in change. Although sample size planning for longitudinal studies has focused on statistical power, recent calls for effect sizes and their corresponding confidence intervals underscore the importance of obtaining sufficiently accurate estimates of group differences in change. We derived expressions that allow researchers to plan sample size to achieve the desired confidence interval width for group differences in change for orthogonal polynomial change parameters. The approaches developed provide the expected confidence interval width to be sufficiently narrow, with an extension that allows some specified degree of assurance (e.g., 99%) that the confidence interval will be sufficiently narrow. We make computer routines freely available, so that the methods developed can be used by researchers immediately.
NASA Astrophysics Data System (ADS)
Azimi, Ehsan; Behrad, Alireza; Ghaznavi-Ghoushchi, Mohammad Bagher; Shanbehzadeh, Jamshid
2016-11-01
The projective model is an important mapping function for the calculation of global transformation between two images. However, its hardware implementation is challenging because of a large number of coefficients with different required precisions for fixed point representation. A VLSI hardware architecture is proposed for the calculation of a global projective model between input and reference images and refining false matches using random sample consensus (RANSAC) algorithm. To make the hardware implementation feasible, it is proved that the calculation of the projective model can be divided into four submodels comprising two translations, an affine model and a simpler projective mapping. This approach makes the hardware implementation feasible and considerably reduces the required number of bits for fixed point representation of model coefficients and intermediate variables. The proposed hardware architecture for the calculation of a global projective model using the RANSAC algorithm was implemented using Verilog hardware description language and the functionality of the design was validated through several experiments. The proposed architecture was synthesized by using an application-specific integrated circuit digital design flow utilizing 180-nm CMOS technology as well as a Virtex-6 field programmable gate array. Experimental results confirm the efficiency of the proposed hardware architecture in comparison with software implementation.
Forestry inventory based on multistage sampling with probability proportional to size
NASA Technical Reports Server (NTRS)
Lee, D. C. L.; Hernandez, P., Jr.; Shimabukuro, Y. E.
1983-01-01
A multistage sampling technique, with probability proportional to size, is developed for a forest volume inventory using remote sensing data. The LANDSAT data, Panchromatic aerial photographs, and field data are collected. Based on age and homogeneity, pine and eucalyptus classes are identified. Selection of tertiary sampling units is made through aerial photographs to minimize field work. The sampling errors for eucalyptus and pine ranged from 8.34 to 21.89 percent and from 7.18 to 8.60 percent, respectively.
ERIC Educational Resources Information Center
Shieh, Gwowen
2006-01-01
This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple…
Gutenberg-Richter b-value maximum likelihood estimation and sample size
NASA Astrophysics Data System (ADS)
Nava, F. A.; Márquez-Ramírez, V. H.; Zúñiga, F. R.; Ávila-Barrientos, L.; Quinteros, C. B.
2017-01-01
The Aki-Utsu maximum likelihood method is widely used for estimation of the Gutenberg-Richter b-value, but not all authors are conscious of the method's limitations and implicit requirements. The Aki/Utsu method requires a representative estimate of the population mean magnitude; a requirement seldom satisfied in b-value studies, particularly in those that use data from small geographic and/or time windows, such as b-mapping and b-vs-time studies. Monte Carlo simulation methods are used to determine how large a sample is necessary to achieve representativity, particularly for rounded magnitudes. The size of a representative sample weakly depends on the actual b-value. It is shown that, for commonly used precisions, small samples give meaningless estimations of b. Our results give estimates on the probabilities of getting correct estimates of b for a given desired precision for samples of different sizes. We submit that all published studies reporting b-value estimations should include information about the size of the samples used.
Minimum sample sizes for population genomics: an empirical study from an Amazonian plant species.
Nazareno, Alison G; Bemmels, Jordan B; Dick, Christopher W; Lohmann, Lúcia G
2017-01-12
High-throughput DNA sequencing facilitates the analysis of large portions of the genome in nonmodel organisms, ensuring high accuracy of population genetic parameters. However, empirical studies evaluating the appropriate sample size for these kinds of studies are still scarce. In this study, we use double-digest restriction-associated DNA sequencing (ddRADseq) to recover thousands of single nucleotide polymorphisms (SNPs) for two physically isolated populations of Amphirrhox longifolia (Violaceae), a nonmodel plant species for which no reference genome is available. We used resampling techniques to construct simulated populations with a random subset of individuals and SNPs to determine how many individuals and biallelic markers should be sampled for accurate estimates of intra- and interpopulation genetic diversity. We identified 3646 and 4900 polymorphic SNPs for the two populations of A. longifolia, respectively. Our simulations show that, overall, a sample size greater than eight individuals has little impact on estimates of genetic diversity within A. longifolia populations, when 1000 SNPs or higher are used. Our results also show that even at a very small sample size (i.e. two individuals), accurate estimates of FST can be obtained with a large number of SNPs (≥1500). These results highlight the potential of high-throughput genomic sequencing approaches to address questions related to evolutionary biology in nonmodel organisms. Furthermore, our findings also provide insights into the optimization of sampling strategies in the era of population genomics.
Size selective isocyanate aerosols personal air sampling using porous plastic foams
NASA Astrophysics Data System (ADS)
Khanh Huynh, Cong; Duc, Trinh Vu
2009-02-01
As part of a European project (SMT4-CT96-2137), various European institutions specialized in occupational hygiene (BGIA, HSL, IOM, INRS, IST, Ambiente e Lavoro) have established a program of scientific collaboration to develop one or more prototypes of European personal samplers for the collection of simultaneous three dust fractions: inhalable, thoracic and respirable. These samplers based on existing sampling heads (IOM, GSP and cassettes) use Polyurethane Plastic Foam (PUF) according to their porosity to support sampling and separator size of the particles. In this study, the authors present an original application of size selective personal air sampling using chemical impregnated PUF to perform isocyanate aerosols capturing and derivatizing in industrial spray-painting shops.
Nagy, Tibor; Vikár, Anna; Lendvay, György
2016-01-07
The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH{sub 4} + H → CH{sub 3} + H{sub 2} and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C–H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C–H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling.
NASA Technical Reports Server (NTRS)
Cavalleri, R. J.; Agnone, A. M.
1972-01-01
A computer program for calculating internal supersonic flow fields with chemical reactions and shock waves typical of supersonic combustion chambers with either wall or mid-stream injectors is described. The usefulness and limitations of the program are indicated. The program manual and listing are presented along with a sample calculation.
NASA Astrophysics Data System (ADS)
Jha, Anjani K.
Particulate materials are routinely handled in large quantities by industries such as, agriculture, electronic, ceramic, chemical, cosmetic, fertilizer, food, nutraceutical, pharmaceutical, power, and powder metallurgy. These industries encounter segregation due to the difference in physical and mechanical properties of particulates. The general goal of this research was to study percolation segregation in multi-size and multi-component particulate mixtures, especially measurement, sampling, and modeling. A second generation primary segregation shear cell (PSSC-II), an industrial vibrator, a true cubical triaxial tester, and two samplers (triers) were used as primary test apparatuses for quantifying segregation and flowability; furthermore, to understand and propose strategies to mitigate segregation in particulates. Toward this end, percolation segregation in binary, ternary, and quaternary size mixtures for two particulate types: urea (spherical) and potash (angular) were studied. Three coarse size ranges 3,350-4,000 mum (mean size = 3,675 mum), 2,800-3,350 mum (3,075 mum), and 2,360-2,800 mum (2,580 mum) and three fines size ranges 2,000-2,360 mum (2,180 mum), 1,700-2,000 mum (1,850 mum), and 1,400-1,700 mum (1,550 mum) for angular-shaped and spherical-shaped were selected for tests. Since the fines size 1,550 mum of urea was not available in sufficient quantity; therefore, it was not included in tests. Percolation segregation in fertilizer bags was tested also at two vibration frequencies of 5 Hz and 7Hz. The segregation and flowability of binary mixtures of urea under three equilibrium relative humidities (40%, 50%, and 60%) were also tested. Furthermore, solid fertilizer sampling was performed to compare samples obtained from triers of opening widths 12.7 mm and 19.1 mm and to determine size segregation in blend fertilizers. Based on experimental results, the normalized segregation rate (NSR) of binary mixtures was dependent on size ratio, mixing ratio
Estimating the Correlation in Bivariate Normal Data with Known Variances and Small Sample Sizes1
Fosdick, Bailey K.; Raftery, Adrian E.
2013-01-01
We consider the problem of estimating the correlation in bivariate normal data when the means and variances are assumed known, with emphasis on the small sample case. We consider eight different estimators, several of them considered here for the first time in the literature. In a simulation study, we found that Bayesian estimators using the uniform and arc-sine priors outperformed several empirical and exact or approximate maximum likelihood estimators in small samples. The arc-sine prior did better for large values of the correlation. For testing whether the correlation is zero, we found that Bayesian hypothesis tests outperformed significance tests based on the empirical and exact or approximate maximum likelihood estimators considered in small samples, but that all tests performed similarly for sample size 50. These results lead us to suggest using the posterior mean with the arc-sine prior to estimate the correlation in small samples when the variances are assumed known. PMID:23378667
Vertical grain size distribution in dust devils: Analyses of in situ samples from southern Morocco
NASA Astrophysics Data System (ADS)
Raack, J.; Reiss, D.; Ori, G. G.; Taj-Eddine, K.
2014-04-01
Dust devils are vertical convective vortices occurring on Earth and Mars [1]. Entrained particle sizes such as dust and sand lifted by dust devils make them visible [1]. On Earth, finer particles (<~50 μm) can be entrained in the boundary layer and transported over long distances [e.g., 2]. The lifetime of entrained particles in the atmosphere depends on their size, where smaller particles maintain longer into the atmosphere [3]. Mineral aerosols such as desert dust are important for human health, weather, climate, and biogeochemistry [4]. The entrainment of dust particles by dust devil and its vertical grain size distribution is not well constrained. In situ grain size samples from active dust devils were so far derived by [5,6,7] in three different continents: Africa, Australia, and North America, respectively. In this study we report about in situ samples directly derived from active dust devils in the Sahara Desert (Erg Chegaga) in southern Morocco in 2012 to characterize the vertical grain size distribution within dust devils.
Srivastava, S; Das, I; Cheng, C
2014-06-01
Purpose: IMRT has become standard of care for complex treatments to optimize dose to target and spare normal tissues. However, the impact of calculation grid size is not widely known especially dose distribution, tumor control probability (TCP) and normal tissue complication probability (NTCP) which is investigated in this study. Methods: Ten head and neck IMRT patients treated with 6 MV photons were chosen for this study. Using Eclipse TPS, treatment plans were generated for different grid sizes in the range 1–5 mm for the same optimization criterion with specific dose-volume constraints. The dose volume histogram (DVH) was calculated for all IMRT plans and dosimetric data were compared. ICRU-83 dose points such as D2%, D50%, D98%, as well as the homogeneity and conformity indices (HI, CI) were calculated. In addition, TCP and NTCP were calculated from DVH data. Results: The PTV mean dose and TCP decreases with increasing grid size with an average decrease in mean dose by 2% and TCP by 3% respectively. Increasing grid size from 1–5 mm grid size, the average mean dose and NTCP for left parotid was increased by 6.0% and 8.0% respectively. Similar patterns were observed for other OARs such as cochlea, parotids and spinal cord. The HI increases up to 60% and CI decreases on average by 3.5% between 1 and 5 mm grid that resulted in decreased TCP and increased NTCP values. The number of points meeting the gamma criteria of ±3% dose difference and ±3mm DTA was higher with a 1 mm on average (97.2%) than with a 5 mm grid (91.3%). Conclusion: A smaller calculation grid provides superior dosimetry with improved TCP and reduced NTCP values. The effect is more pronounced for smaller OARs. Thus, the smallest possible grid size should be used for accurate dose calculation especially in H and N planning.
Glushkov, Alexander V.; Gurnitskaya, E.P.; Loboda, A.V.
2005-10-26
Advanced quantum approach to calculation of spectra for superheavy ions with an account of relativistic, correlation, nuclear, radiative effects is developed and based on the gauge invariant quantum electrodynamics (QED) perturbation theory (PT). The Lamb shift polarization part is calculated in the Ueling approximation, self-energy part is defined within a new non-PT procedure of Ivanov-Ivanova. Calculation results for energy levels, hyperfine structure parameters of some heavy elements ions are presented.
Estimating the Size of Populations at High Risk for HIV Using Respondent-Driven Sampling Data
Handcock, Mark S.; Gile, Krista J.; Mar, Corinne M.
2015-01-01
Summary The study of hard-to-reach populations presents significant challenges. Typically, a sampling frame is not available, and population members are difficult to identify or recruit from broader sampling frames. This is especially true of populations at high risk for HIV/AIDS. Respondent-driven sampling (RDS) is often used in such settings with the primary goal of estimating the prevalence of infection. In such populations, the number of people at risk for infection and the number of people infected are of fundamental importance. This article presents a case-study of the estimation of the size of the hard-to-reach population based on data collected through RDS. We study two populations of female sex workers and men-who-have-sex-with-men in El Salvador. The approach is Bayesian and we consider different forms of prior information, including using the UNAIDS population size guidelines for this region. We show that the method is able to quantify the amount of information on population size available in RDS samples. As separate validation, we compare our results to those estimated by extrapolating from a capture–recapture study of El Salvadorian cities. The results of our case-study are largely comparable to those of the capture–recapture study when they differ from the UNAIDS guidelines. Our method is widely applicable to data from RDS studies and we provide a software package to facilitate this. PMID:25585794
The role of the upper sample size limit in two-stage bioequivalence designs.
Karalis, Vangelis
2013-11-01
Two-stage designs (TSDs) are currently recommended by the regulatory authorities for bioequivalence (BE) assessment. The TSDs presented until now rely on an assumed geometric mean ratio (GMR) value of the BE metric in stage I in order to avoid inflation of type I error. In contrast, this work proposes a more realistic TSD design where sample re-estimation relies not only on the variability of stage I, but also on the observed GMR. In these cases, an upper sample size limit (UL) is introduced in order to prevent inflation of type I error. The aim of this study is to unveil the impact of UL on two TSD bioequivalence approaches which are based entirely on the interim results. Monte Carlo simulations were used to investigate several different scenarios of UL levels, within-subject variability, different starting number of subjects, and GMR. The use of UL leads to no inflation of type I error. As UL values increase, the % probability of declaring BE becomes higher. The starting sample size and the variability of the study affect type I error. Increased UL levels result in higher total sample sizes of the TSD which are more pronounced for highly variable drugs.
Tang, Yongqiang
2017-02-22
We derive the closed-form restricted maximum likelihood estimator and Kenward-Roger's variance estimator for fixed effects in the mixed effects model for repeated measures (MMRM) when the missing data pattern is monotone. As an important application of the analytic result, we present the formula for calculating the power of treatment comparison using the Wald t-test with the Kenward-Roger adjusted variance estimate in MMRM. It allows adjustment for baseline covariates without the need to specify the covariate distribution in randomized trials. A simple two-step procedure is proposed to determine the sample size needed to achieve the targeted power. The proposed method performs well for both normal and moderately non-normal data even in small samples (n=20) in simulations. An antidepressant trial is analyzed for illustrative purposes. Copyright © 2017 John Wiley & Sons, Ltd.
The use of a pocket-size, programmable calculator for phenotype tallying of a three-point cross.
Adams, J N; De Jone, G; Adams, B E
1975-01-01
A program is presented which permits use of a pocket-size programmable calculator, the HP-65, to tally phenotypes resulting from a three-point cross. For practical purposes the total number recorded for any of the eight possibel phenotypic combinations is unlimited. Although programmed operation of the calculator for tallying purposes is slower than a single purpose instrument designed for tallying, this deficiency is componensated by the computational capability of this instrument.
Multiple Approaches to Down Sizing of the Lunar Sample Return Collection
NASA Technical Reports Server (NTRS)
Lofgren, Gary E.; Horz, F.
2010-01-01
Future Lunar missions are planned for at least 7 days, significantly longer than the 3 days of the later Apollo missions. The last of those missions, A-17, returned 111 kg of samples plus another 20 kg of containers. The current Constellation program requirements for return weight for science is 100 kg with the hope of raising that limit to near 250 kg including containers and other non-geological materials. The estimated return weight for rock and soil samples will, at best, be about 175 kg. One method proposed to accomplish down-sizing of the collection is the use of a Geo-Lab in the lunar habitat to complete a preliminary examination of selected samples and facilitate prioritizing the return samples.
Optimizing stream water mercury sampling for calculation of fish bioaccumulation factors
Riva-Murray, Karen; Bradley, Paul M.; Journey, Celeste; Brigham, Mark E.; Scudder Eikenberry, Barbara C.; Knightes, Christopher; Button, Daniel T.
2013-01-01
Mercury (Hg) bioaccumulation factors (BAFs) for game fishes are widely employed for monitoring, assessment, and regulatory purposes. Mercury BAFs are calculated as the fish Hg concentration (Hgfish) divided by the water Hg concentration (Hgwater) and, consequently, are sensitive to sampling and analysis artifacts for fish and water. We evaluated the influence of water sample timing, filtration, and mercury species on the modeled relation between game fish and water mercury concentrations across 11 streams and rivers in five states in order to identify optimum Hgwater sampling approaches. Each model included fish trophic position, to account for a wide range of species collected among sites, and flow-weighted Hgwater estimates. Models were evaluated for parsimony, using Akaike’s Information Criterion. Better models included filtered water methylmercury (FMeHg) or unfiltered water methylmercury (UMeHg), whereas filtered total mercury did not meet parsimony requirements. Models including mean annual FMeHg were superior to those with mean FMeHg calculated over shorter time periods throughout the year. FMeHg models including metrics of high concentrations (80th percentile and above) observed during the year performed better, in general. These higher concentrations occurred most often during the growing season at all sites. Streamflow was significantly related to the probability of achieving higher concentrations during the growing season at six sites, but the direction of influence varied among sites. These findings indicate that streamwater Hg collection can be optimized by evaluating site-specific FMeHg - UMeHg relations, intra-annual temporal variation in their concentrations, and streamflow-Hg dynamics.
Schmidt, Wolf-Peter; Genser, Bernd; Luby, Stephen P; Chalabi, Zaid
2011-08-01
There is an ongoing interest in studying the effect of common recurrent infections and conditions, such as diarrhoea, respiratory infections, and fever, on the nutritional status of children at risk of malnutrition. Epidemiological studies exploring this association need to measure infections with sufficient accuracy to minimize bias in the effect estimates. A versatile model of common recurrent infections was used for exploring how many repeated measurements of disease are required to maximize the power and logistical efficiency of studies investigating the effect of infectious diseases on malnutrition without compromising the validity of the estimates. Depending on the prevalence and distribution of disease within a population, 15-30 repeat measurements per child over one year should be sufficient to provide unbiased estimates of the association between infections and nutritional status. Less-frequent measurements lead to a bias in the effect size towards zero, especially if disease is rare. In contrast, recall error can lead to exaggerated effect sizes. Recall periods of three days or shorter may be preferable compared to longer recall periods. The results showed that accurate estimation of the association between recurrent infections and nutritional status required closer follow-up of study participants than studies using recurrent infections as an outcome measure. The findings of the study provide guidance for choosing an appropriate sampling strategy to explore this association.
Sample size and the width of the confidence interval for mean difference.
Liu, Xiaofeng Steven
2009-05-01
The width of the confidence interval for mean difference can be viewed as a random variable. Overlooking its stochastic nature may lead to a serious underestimate of the sample size required to obtain an adequate probability of achieving the desired width for the confidence interval. The probability of achieving a certain width can either be an unconditional probability or a conditional probability given that the confidence interval includes the true parameter. We reconciled the difference between the unconditional and conditional probabilities by deriving the lower bound of the conditional probability. Additionally, we used the harmonic mean to determine unequal sample sizes for the confidence intervals for the two-mean comparison and multiple-mean comparisons.
Esserman, Denise; Zhao, Yingqi; Tang, Yiyun; Cai, Jianwen
2013-05-30
We present closed form sample size and power formulas motivated by the study of a psycho-social intervention in which the experimental group has the intervention delivered in teaching subgroups whereas the control group receives usual care. This situation is different from the usual clustered randomized trial because subgroup heterogeneity only exists in one arm. We take this modification into consideration and present formulas for the situation in which we compare a continuous outcome at both a single point in time and longitudinally over time. In addition, we present the optimal combination of parameters such as the number of subgroups and number of time points for minimizing sample size and maximizing power subject to constraints such as the maximum number of measurements that can be taken (i.e., a proxy for cost).
NASA Technical Reports Server (NTRS)
Hirleman, E. D.; Oechsle, V.; Chigier, N. A.
1984-01-01
The response characteristics of laser diffraction particle sizing instruments were studied theoretically and experimentally. In particular, the extent of optical sample volume and the effects of receiving lens properties were investigated in detail. The experimental work was performed with a particle size analyzer using a calibration reticle containing a two-dimensional array of opaque circular disks on a glass substrate. The calibration slide simulated the forward-scattering characteristics of a Rosin-Rammler droplet size distribution. The reticle was analyzed with collection lenses of 63 mm, 100 mm, and 300 mm focal lengths using scattering inversion software that determined best-fit Rosin-Rammler size distribution parameters. The data differed from the predicted response for the reticle by about 10 percent. A set of calibration factor for the detector elements was determined that corrected for the nonideal response of the instrument. The response of the instrument was also measured as a function of reticle position, and the results confirmed a theoretical optical sample volume model presented here.
NASA Astrophysics Data System (ADS)
Kitao, Akio; Harada, Ryuhei; Nishihara, Yasutaka; Tran, Duy Phuoc
2016-12-01
Parallel Cascade Selection Molecular Dynamics (PaCS-MD) was proposed as an efficient conformational sampling method to investigate conformational transition pathway of proteins. In PaCS-MD, cycles of (i) selection of initial structures for multiple independent MD simulations and (ii) conformational sampling by independent MD simulations are repeated until the convergence of the sampling. The selection is conducted so that protein conformation gradually approaches a target. The selection of snapshots is a key to enhance conformational changes by increasing the probability of rare event occurrence. Since the procedure of PaCS-MD is simple, no modification of MD programs is required; the selections of initial structures and the restart of the next cycle in the MD simulations can be handled with relatively simple scripts with straightforward implementation. Trajectories generated by PaCS-MD were further analyzed by the Markov state model (MSM), which enables calculation of free energy landscape. The combination of PaCS-MD and MSM is reported in this work.
A contemporary decennial global Landsat sample of changing agricultural field sizes
NASA Astrophysics Data System (ADS)
White, Emma; Roy, David
2014-05-01
Agriculture has caused significant human induced Land Cover Land Use (LCLU) change, with dramatic cropland expansion in the last century and significant increases in productivity over the past few decades. Satellite data have been used for agricultural applications including cropland distribution mapping, crop condition monitoring, crop production assessment and yield prediction. Satellite based agricultural applications are less reliable when the sensor spatial resolution is small relative to the field size. However, to date, studies of agricultural field size distributions and their change have been limited, even though this information is needed to inform the design of agricultural satellite monitoring systems. Moreover, the size of agricultural fields is a fundamental description of rural landscapes and provides an insight into the drivers of rural LCLU change. In many parts of the world field sizes may have increased. Increasing field sizes cause a subsequent decrease in the number of fields and therefore decreased landscape spatial complexity with impacts on biodiversity, habitat, soil erosion, plant-pollinator interactions, and impacts on the diffusion of herbicides, pesticides, disease pathogens, and pests. The Landsat series of satellites provide the longest record of global land observations, with 30m observations available since 1982. Landsat data are used to examine contemporary field size changes in a period (1980 to 2010) when significant global agricultural changes have occurred. A multi-scale sampling approach is used to locate global hotspots of field size change by examination of a recent global agricultural yield map and literature review. Nine hotspots are selected where significant field size change is apparent and where change has been driven by technological advancements (Argentina and U.S.), abrupt societal changes (Albania and Zimbabwe), government land use and agricultural policy changes (China, Malaysia, Brazil), and/or constrained by
A Bayesian adaptive blinded sample size adjustment method for risk differences.
Hartley, Andrew Montgomery
2015-01-01
Adaptive sample size adjustment (SSA) for clinical trials consists of examining early subsets of on trial data to adjust estimates of sample size requirements. Blinded SSA is often preferred over unblinded SSA because it obviates many logistical complications of the latter and generally introduces less bias. On the other hand, current blinded SSA methods for binary data offer little to no new information about the treatment effect, ignore uncertainties associated with the population treatment proportions, and/or depend on enhanced randomization schemes that risk partial unblinding. I propose an innovative blinded SSA method for use when the primary analysis is a non-inferiority or superiority test regarding a risk difference. The method incorporates evidence about the treatment effect via the likelihood function of a mixture distribution. I compare the new method with an established one and with the fixed sample size study design, in terms of maximization of an expected utility function. The new method maximizes the expected utility better than do the comparators, under a range of assumptions. I illustrate the use of the proposed method with an example that incorporates a Bayesian hierarchical model. Lastly, I suggest topics for future study regarding the proposed methods.
Biau, David Jean; Kernéis, Solen; Porcher, Raphaël
2008-09-01
The increasing volume of research by the medical community often leads to increasing numbers of contradictory findings and conclusions. Although the differences observed may represent true differences, the results also may differ because of sampling variability as all studies are performed on a limited number of specimens or patients. When planning a study reporting differences among groups of patients or describing some variable in a single group, sample size should be considered because it allows the researcher to control for the risk of reporting a false-negative finding (Type II error) or to estimate the precision his or her experiment will yield. Equally important, readers of medical journals should understand sample size because such understanding is essential to interpret the relevance of a finding with regard to their own patients. At the time of planning, the investigator must establish (1) a justifiable level of statistical significance, (2) the chances of detecting a difference of given magnitude between the groups compared, ie, the power, (3) this targeted difference (ie, effect size), and (4) the variability of the data (for quantitative data). We believe correct planning of experiments is an ethical issue of concern to the entire community.
Bayesian sample size determination for case-control studies when exposure may be misclassified.
Joseph, Lawrence; Bélisle, Patrick
2013-12-01
Odds ratios are frequently used for estimating the effect of an exposure on the probability of disease in case-control studies. In planning such studies, methods for sample size determination are required to ensure sufficient accuracy in estimating odds ratios once the data are collected. Often, the exposure used in epidemiologic studies is not perfectly ascertained. This can arise from recall bias, the use of a proxy exposure measurement, uncertain work exposure history, and laboratory or other errors. The resulting misclassification can have large impacts on the accuracy and precision of estimators, and specialized estimation techniques have been developed to adjust for these biases. However, much less work has been done to account for the anticipated decrease in the precision of estimators at the design stage. Here, we develop methods for sample size determination for odds ratios in the presence of exposure misclassification by using several interval-based Bayesian criteria. By using a series of prototypical examples, we compare sample size requirements after adjustment for misclassification with those required when this problem is ignored. We illustrate the methods by planning a case-control study of the effect of late introduction of peanut to the diet of children to the subsequent development of peanut allergy.
Sub-sampling genetic data to estimate black bear population size: A case study
Tredick, C.A.; Vaughan, M.R.; Stauffer, D.F.; Simek, S.L.; Eason, T.
2007-01-01
Costs for genetic analysis of hair samples collected for individual identification of bears average approximately US$50 [2004] per sample. This can easily exceed budgetary allowances for large-scale studies or studies of high-density bear populations. We used 2 genetic datasets from 2 areas in the southeastern United States to explore how reducing costs of analysis by sub-sampling affected precision and accuracy of resulting population estimates. We used several sub-sampling scenarios to create subsets of the full datasets and compared summary statistics, population estimates, and precision of estimates generated from these subsets to estimates generated from the complete datasets. Our results suggested that bias and precision of estimates improved as the proportion of total samples used increased, and heterogeneity models (e.g., Mh[CHAO]) were more robust to reduced sample sizes than other models (e.g., behavior models). We recommend that only high-quality samples (>5 hair follicles) be used when budgets are constrained, and efforts should be made to maximize capture and recapture rates in the field.
NASA Astrophysics Data System (ADS)
Holmes, Jesse Curtis
established that depends on uncertainties in the physics models and methodology employed to produce the DOS. Through Monte Carlo sampling of perturbations from the reference phonon spectrum, an S(alpha, beta) covariance matrix may be generated. In this work, density functional theory and lattice dynamics in the harmonic approximation are used to calculate the phonon DOS for hexagonal crystalline graphite. This form of graphite is used as an example material for the purpose of demonstrating procedures for analyzing, calculating and processing thermal neutron inelastic scattering uncertainty information. Several sources of uncertainty in thermal neutron inelastic scattering calculations are examined, including sources which cannot be directly characterized through a description of the phonon DOS uncertainty, and their impacts are evaluated. Covariances for hexagonal crystalline graphite S(alpha, beta) data are quantified by coupling the standard methodology of LEAPR with a Monte Carlo sampling process. The mechanics of efficiently representing and processing this covariance information is also examined. Finally, with appropriate sensitivity information, it is shown that an S(alpha, beta) covariance matrix can be propagated to generate covariance data for integrated cross sections, secondary energy distributions, and coupled energy-angle distributions. This approach enables a complete description of thermal neutron inelastic scattering cross section uncertainties which may be employed to improve the simulation of nuclear systems.
Wei, Jinwu; Wang, Jianbo; Liu, Qingfang; Li, Xiaoyu; Cao, Derang; Sun, Xiaojun
2014-05-01
A new analytical method has been proposed by utilizing an electromagnetic induction principle with a short-circuited microstrip line jig and the complex permeability spectra can be calculated without a known reference sample. The new method using the short-circuited microstrip line can exhibit higher sensitivity and a wider frequency band than coplanar waveguide and pick-up coil. Two magnetic thin films having a good in-plane uniaxial anisotropy are measured by using the induction method. The results show typical complex permeability spectra in good agreement with the theoretical analytical results. The measured permeability values are verified by comparing with the initial susceptibility derived from the sweeping field results. The difference of measured permeability values is less than 5%.
NASA Astrophysics Data System (ADS)
Gallicchio, Emilio; Deng, Nanjie; He, Peng; Wickstrom, Lauren; Perryman, Alexander L.; Santiago, Daniel N.; Forli, Stefano; Olson, Arthur J.; Levy, Ronald M.
2014-04-01
As part of the SAMPL4 blind challenge, filtered AutoDock Vina ligand docking predictions and large scale binding energy distribution analysis method binding free energy calculations have been applied to the virtual screening of a focused library of candidate binders to the LEDGF site of the HIV integrase protein. The computational protocol leveraged docking and high level atomistic models to improve enrichment. The enrichment factor of our blind predictions ranked best among all of the computational submissions, and second best overall. This work represents to our knowledge the first example of the application of an all-atom physics-based binding free energy model to large scale virtual screening. A total of 285 parallel Hamiltonian replica exchange molecular dynamics absolute protein-ligand binding free energy simulations were conducted starting from docked poses. The setup of the simulations was fully automated, calculations were distributed on multiple computing resources and were completed in a 6-weeks period. The accuracy of the docked poses and the inclusion of intramolecular strain and entropic losses in the binding free energy estimates were the major factors behind the success of the method. Lack of sufficient time and computing resources to investigate additional protonation states of the ligands was a major cause of mispredictions. The experiment demonstrated the applicability of binding free energy modeling to improve hit rates in challenging virtual screening of focused ligand libraries during lead optimization.
Gallicchio, Emilio; Deng, Nanjie; He, Peng; Wickstrom, Lauren; Perryman, Alexander L.; Santiago, Daniel N.; Forli, Stefano; Olson, Arthur J.; Levy, Ronald M.
2014-01-01
As part of the SAMPL4 blind challenge, filtered AutoDock Vina ligand docking predictions and large scale binding energy distribution analysis method binding free energy calculations have been applied to the virtual screening of a focused library of candidate binders to the LEDGF site of the HIV integrase protein. The computational protocol leveraged docking and high level atomistic models to improve enrichment. The enrichment factor of our blind predictions ranked best among all of the computational submissions, and second best overall. This work represents to our knowledge the first example of the application of an all-atom physics-based binding free energy model to large scale virtual screening. A total of 285 parallel Hamiltonian replica exchange molecular dynamics absolute protein-ligand binding free energy simulations were conducted starting from docked poses. The setup of the simulations was fully automated, calculations were distributed on multiple computing resources and were completed in a 6-weeks period. The accuracy of the docked poses and the inclusion of intramolecular strain and entropic losses in the binding free energy estimates were the major factors behind the success of the method. Lack of sufficient time and computing resources to investigate additional protonation states of the ligands was a major cause of mispredictions. The experiment demonstrated the applicability of binding free energy modeling to improve hit rates in challenging virtual screening of focused ligand libraries during lead optimization. PMID:24504704
Forest inventory using multistage sampling with probability proportional to size. [Brazil
NASA Technical Reports Server (NTRS)
Parada, N. D. J. (Principal Investigator); Lee, D. C. L.; Hernandezfilho, P.; Shimabukuro, Y. E.; Deassis, O. R.; Demedeiros, J. S.
1984-01-01
A multistage sampling technique, with probability proportional to size, for forest volume inventory using remote sensing data is developed and evaluated. The study area is located in the Southeastern Brazil. The LANDSAT 4 digital data of the study area are used in the first stage for automatic classification of reforested areas. Four classes of pine and eucalypt with different tree volumes are classified utilizing a maximum likelihood classification algorithm. Color infrared aerial photographs are utilized in the second stage of sampling. In the third state (ground level) the time volume of each class is determined. The total time volume of each class is expanded through a statistical procedure taking into account all the three stages of sampling. This procedure results in an accurate time volume estimate with a smaller number of aerial photographs and reduced time in field work.
Moser, Barry Kurt; Halabi, Susan
2013-01-01
In this paper we develop the methodology for designing clinical trials with any factorial arrangement when the primary outcome is time to event. We provide a matrix formulation for calculating the sample size and study duration necessary to test any effect with a pre-specified type I error rate and power. Assuming that a time to event follows an exponential distribution, we describe the relationships between the effect size, the power, and the sample size. We present examples for illustration purposes. We provide a simulation study to verify the numerical calculations of the expected number of events and the duration of the trial. The change in the power produced by a reduced number of observations or by accruing no patients to certain factorial combinations is also described. PMID:25530661
Dwivedi, Alok Kumar; Mallawaarachchi, Indika; Alvarado, Luis A
2017-03-09
Experimental studies in biomedical research frequently pose analytical problems related to small sample size. In such studies, there are conflicting findings regarding the choice of parametric and nonparametric analysis, especially with non-normal data. In such instances, some methodologists questioned the validity of parametric tests and suggested nonparametric tests. In contrast, other methodologists found nonparametric tests to be too conservative and less powerful and thus preferred using parametric tests. Some researchers have recommended using a bootstrap test; however, this method also has small sample size limitation. We used a pooled method in nonparametric bootstrap test that may overcome the problem related with small samples in hypothesis testing. The present study compared nonparametric bootstrap test with pooled resampling method corresponding to parametric, nonparametric, and permutation tests through extensive simulations under various conditions and using real data examples. The nonparametric pooled bootstrap t-test provided equal or greater power for comparing two means as compared with unpaired t-test, Welch t-test, Wilcoxon rank sum test, and permutation test while maintaining type I error probability for any conditions except for Cauchy and extreme variable lognormal distributions. In such cases, we suggest using an exact Wilcoxon rank sum test. Nonparametric bootstrap paired t-test also provided better performance than other alternatives. Nonparametric bootstrap test provided benefit over exact Kruskal-Wallis test. We suggest using nonparametric bootstrap test with pooled resampling method for comparing paired or unpaired means and for validating the one way analysis of variance test results for non-normal data in small sample size studies. Copyright © 2017 John Wiley & Sons, Ltd.
Statistical characterization of a large geochemical database and effect of sample size
Zhang, C.; Manheim, F. T.; Hinde, J.; Grossman, J.N.
2005-01-01
smaller numbers of data points showed that few elements passed standard statistical tests for normality or log-normality until sample size decreased to a few hundred data points. Large sample size enhances the power of statistical tests, and leads to rejection of most statistical hypotheses for real data sets. For large sample sizes (e.g., n > 1000), graphical methods such as histogram, stem-and-leaf, and probability plots are recommended for rough judgement of probability distribution if needed. ?? 2005 Elsevier Ltd. All rights reserved.
Back to basics: explaining sample size in outcome trials, are statisticians doing a thorough job?
Carroll, Kevin J
2009-01-01
Time to event outcome trials in clinical research are typically large, expensive and high-profile affairs. Such trials are commonplace in oncology and cardiovascular therapeutic areas but are also seen in other areas such as respiratory in indications like chronic obstructive pulmonary disease. Their progress is closely monitored and results are often eagerly awaited. Once available, the top line result is often big news, at least within the therapeutic area in which it was conducted, and the data are subsequently fully scrutinized in a series of high-profile publications. In such circumstances, the statistician has a vital role to play in the design, conduct, analysis and reporting of the trial. In particular, in drug development it is incumbent on the statistician to ensure at the outset that the sizing of the trial is fully appreciated by their medical, and other non-statistical, drug development team colleagues and that the risk of delivering a statistically significant but clinically unpersuasive result is minimized. The statistician also has a key role in advising the team when, early in the life of an outcomes trial, a lower than anticipated event rate appears to be emerging. This paper highlights some of the important features relating to outcome trial sample sizing and makes a number of simple recommendations aimed at ensuring a better, common understanding of the interplay between sample size and power and the final result required to provide a statistically positive and clinically persuasive outcome.
Reducing sample size in experiments with animals: historical controls and related strategies.
Kramer, Matthew; Font, Enrique
2017-02-01
Reducing the number of animal subjects used in biomedical experiments is desirable for ethical and practical reasons. Previous reviews of the benefits of reducing sample sizes have focused on improving experimental designs and methods of statistical analysis, but reducing the size of control groups has been considered rarely. We discuss how the number of current control animals can be reduced, without loss of statistical power, by incorporating information from historical controls, i.e. subjects used as controls in similar previous experiments. Using example data from published reports, we describe how to incorporate information from historical controls under a range of assumptions that might be made in biomedical experiments. Assuming more similarities between historical and current controls yields higher savings and allows the use of smaller current control groups. We conducted simulations, based on typical designs and sample sizes, to quantify how different assumptions about historical controls affect the power of statistical tests. We show that, under our simulation conditions, the number of current control subjects can be reduced by more than half by including historical controls in the analyses. In other experimental scenarios, control groups may be unnecessary. Paying attention to both the function and to the statistical requirements of control groups would result in reducing the total number of animals used in experiments, saving time, effort and money, and bringing research with animals within ethically acceptable bounds.
Adjustable virtual pore-size filter for automated sample preparation using acoustic radiation force
Jung, B; Fisher, K; Ness, K; Rose, K; Mariella, R
2008-05-22
We present a rapid and robust size-based separation method for high throughput microfluidic devices using acoustic radiation force. We developed a finite element modeling tool to predict the two-dimensional acoustic radiation force field perpendicular to the flow direction in microfluidic devices. Here we compare the results from this model with experimental parametric studies including variations of the PZT driving frequencies and voltages as well as various particle sizes and compressidensities. These experimental parametric studies also provide insight into the development of an adjustable 'virtual' pore-size filter as well as optimal operating conditions for various microparticle sizes. We demonstrated the separation of Saccharomyces cerevisiae and MS2 bacteriophage using acoustic focusing. The acoustic radiation force did not affect the MS2 viruses, and their concentration profile remained unchanged. With optimized design of our microfluidic flow system we were able to achieve yields of > 90% for the MS2 with > 80% of the S. cerevisiae being removed in this continuous-flow sample preparation device.
Weighted skewness and kurtosis unbiased by sample size and Gaussian uncertainties
NASA Astrophysics Data System (ADS)
Rimoldini, Lorenzo
2014-07-01
Central moments and cumulants are often employed to characterize the distribution of data. The skewness and kurtosis are particularly useful for the detection of outliers, the assessment of departures from normally distributed data, automated classification techniques and other applications. Estimators of higher order moments that are robust against outliers are more stable but might miss characteristic features of the data, as in the case of astronomical time series exhibiting brief events like stellar bursts or eclipses of binary systems, while weighting can help identify reliable measurements from uncertain or spurious outliers. Furthermore, noise is an unavoidable part of most measurements and their uncertainties need to be taken properly into account during the data analysis or biases are likely to emerge in the results, including basic descriptive statistics. This work provides unbiased estimates of the weighted skewness and kurtosis moments and cumulants, corrected for biases due to sample size and Gaussian noise, under the assumption of independent data. A comparison of biased and unbiased weighted estimators is illustrated with simulations as a function of sample size and signal-to-noise ratio, employing different data distributions and weighting schemes related to measurement uncertainties and the sampling of the signal. Detailed derivations and figures of simulation results are presented in the Appendices available online.
Höschen, Carmen; Höschen, Till; Mueller, Carsten W; Lugmeier, Johann; Elgeti, Stefan; Rennert, Thilo; Kögel-Knabner, Ingrid
2015-08-18
Microscale processes occurring at biogeochemical interfaces in soils and sediments have fundamental impacts on phenomena at larger scales. To obtain the organo-mineral associations necessary for the study of biogeochemical interfaces, bulk samples are usually fractionated into microaggregates or micrometer-sized single particles. Such fine-grained mineral particles are often prepared for nanoscale secondary ion mass spectroscopy (NanoSIMS) investigations by depositing them on a carrier. This introduces topographic differences, which can strongly affect local sputtering efficiencies. Embedding in resin causes undesired C impurities. We present a novel method for preparing polished cross-sections of micrometer-sized primary soil particles that overcomes the problems of topography and C contamination. The particles are coated with a marker layer, embedded, and well-polished. The interpretation of NanoSIMS data is assisted by energy-dispersive X-ray spectroscopy on cross-sections prepared by a focused ion beam. In the cross-sections, organic assemblages on the primary soil particles become visible. This novel method significantly improves the quality of NanoSIMS measurements on grainy mineral samples, enabling better characterization of soil biogeochemical interfaces. In addition, this sample preparation technique may also improve results from other (spectro-) microscopic techniques.
Stevens, June; Bryant, Maria; Wang, Chin-Hua; Cai, Jianwen; Bentley, Margaret E
2012-06-01
Measurement of the home food environment is of interest to researchers because it affects food intake and is a feasible target for nutrition interventions. The objective of this study was to provide estimates to aid the calculation of sample size and number of repeated measures needed in studies of nutrients and foods in the home. We inventoried all foods in the homes of 80 African-American first-time mothers and determined 6 nutrient-related attributes. Sixty-three households were measured 3 times, 11 were measured twice, and 6 were measured once, producing 217 inventories collected at ~2-mo intervals. Following log transformations, number of foods, total energy, dietary fiber, and fat required only one measurement per household to achieve a correlation of 0.8 between the observed and true values. For percent energy from fat and energy density, 3 and 2 repeated measurements, respectively, were needed to achieve a correlation of 0.8. A sample size of 252 was needed to detect a difference of 25% of an SD in total energy with one measurement compared with 213 with 3 repeated measurements. Macronutrient characteristics of household foods appeared relatively stable over a 6-mo period and only 1 or 2 repeated measures of households may be sufficient for an efficient study design.
A Bayesian cost-benefit approach to the determination of sample size in clinical trials.
Kikuchi, Takashi; Pezeshk, Hamid; Gittins, John
2008-01-15
Current practice for sample size computations in clinical trials is largely based on frequentist or classical methods. These methods have the drawback of requiring a point estimate of the variance of the treatment effect and are based on arbitrary settings of type I and II errors. They also do not directly address the question of achieving the best balance between the cost of the trial and the possible benefits from using the new treatment, and fail to consider the important fact that the number of users depends on the evidence for improvement compared with the current treatment. Our approach, Behavioural Bayes (or BeBay for short), assumes that the number of patients switching to the new medical treatment depends on the strength of the evidence that is provided by clinical trials, and takes a value between zero and the number of potential patients. The better a new treatment, the more the number of patients who want to switch to it and the more the benefit is obtained. We define the optimal sample size to be the sample size that maximizes the expected net benefit resulting from a clinical trial. Gittins and Pezeshk (Drug Inf. Control 2000; 34:355-363; The Statistician 2000; 49(2):177-187) used a simple form of benefit function and assumed paired comparisons between two medical treatments and that the variance of the treatment effect is known. We generalize this setting, by introducing a logistic benefit function, and by extending the more usual unpaired case, without assuming the variance to be known.
An In Situ Method for Sizing Insoluble Residues in Precipitation and Other Aqueous Samples.
Axson, Jessica L; Creamean, Jessie M; Bondy, Amy L; Capracotta, Sonja S; Warner, Katy Y; Ault, Andrew P
2015-01-01
Particles are frequently incorporated into clouds or precipitation, influencing climate by acting as cloud condensation or ice nuclei, taking up coatings during cloud processing, and removing species through wet deposition. Many of these particles, particularly ice nuclei, can remain suspended within cloud droplets/crystals as insoluble residues. While previous studies have measured the soluble or bulk mass of species within clouds and precipitation, no studies to date have determined the number concentration and size distribution of insoluble residues in precipitation or cloud water using in situ methods. Herein, for the first time we demonstrate that Nanoparticle Tracking Analysis (NTA) is a powerful in situ method for determining the total number concentration, number size distribution, and surface area distribution of insoluble residues in precipitation, both of rain and melted snow. The method uses 500 μL or less of liquid sample and does not require sample modification. Number concentrations for the insoluble residues in aqueous precipitation samples ranged from 2.0-3.0(±0.3)×10(8) particles cm(-3), while surface area ranged from 1.8(±0.7)-3.2(±1.0)×10(7) μm(2) cm(-3). Number size distributions peaked between 133-150 nm, with both single and multi-modal character, while surface area distributions peaked between 173-270 nm. Comparison with electron microscopy of particles up to 10 μm show that, by number, > 97% residues are <1 μm in diameter, the upper limit of the NTA. The range of concentration and distribution properties indicates that insoluble residue properties vary with ambient aerosol concentrations, cloud microphysics, and meteorological dynamics. NTA has great potential for studying the role that insoluble residues play in critical atmospheric processes.
An In Situ Method for Sizing Insoluble Residues in Precipitation and Other Aqueous Samples
Axson, Jessica L.; Creamean, Jessie M.; Bondy, Amy L.; Capracotta, Sonja S.; Warner, Katy Y.; Ault, Andrew P.
2015-01-01
Particles are frequently incorporated into clouds or precipitation, influencing climate by acting as cloud condensation or ice nuclei, taking up coatings during cloud processing, and removing species through wet deposition. Many of these particles, particularly ice nuclei, can remain suspended within cloud droplets/crystals as insoluble residues. While previous studies have measured the soluble or bulk mass of species within clouds and precipitation, no studies to date have determined the number concentration and size distribution of insoluble residues in precipitation or cloud water using in situ methods. Herein, for the first time we demonstrate that Nanoparticle Tracking Analysis (NTA) is a powerful in situ method for determining the total number concentration, number size distribution, and surface area distribution of insoluble residues in precipitation, both of rain and melted snow. The method uses 500 μL or less of liquid sample and does not require sample modification. Number concentrations for the insoluble residues in aqueous precipitation samples ranged from 2.0–3.0(±0.3)×108 particles cm−3, while surface area ranged from 1.8(±0.7)–3.2(±1.0)×107 μm2 cm−3. Number size distributions peaked between 133–150 nm, with both single and multi-modal character, while surface area distributions peaked between 173–270 nm. Comparison with electron microscopy of particles up to 10 μm show that, by number, > 97% residues are <1 μm in diameter, the upper limit of the NTA. The range of concentration and distribution properties indicates that insoluble residue properties vary with ambient aerosol concentrations, cloud microphysics, and meteorological dynamics. NTA has great potential for studying the role that insoluble residues play in critical atmospheric processes. PMID:25705069
Martín Andrés, A; Herranz Tejedor, I; Álvarez Hernández, M
2015-01-01
The Mantel-Haenszel test is the most frequent asymptotic test used for analyzing stratified 2 × 2 tables. Its exact alternative is the test of Birch, which has recently been reconsidered by Jung. Both tests have a conditional origin: Pearson's chi-squared test and Fisher's exact test, respectively. But both tests have the same drawback that the result of global test (the stratified test) may not be compatible with the result of individual tests (the test for each stratum). In this paper, we propose to carry out the global test using a multiple comparisons method (MC method) which does not have this disadvantage. By refining the method (MCB method) an alternative to the Mantel-Haenszel and Birch tests may be obtained. The new MC and MCB methods have the advantage that they may be applied from an unconditional view, a methodology which until now has not been applied to this problem. We also propose some sample size calculation methods.
Silverman, Rachel K; Ivanova, Anastasia
2017-02-06
Sequential parallel comparison design (SPCD) was proposed to reduce placebo response in a randomized trial with placebo comparator. Subjects are randomized between placebo and drug in stage 1 of the trial and then placebo non-responders are re-randomized in stage 2. Efficacy analysis includes all data from stage 1 and all placebo non-responding subjects from stage 2. This article investigates the possibility to re-estimate the sample size and adjust the design parameters, allocation proportion to placebo in stage 1 of SPCD and weight of stage 1 data in the overall efficacy test statistic, during an interim analysis.
Ando, Yuki; Uyama, Yoshiaki
2012-09-01
Multiregional clinical trials including Japanese subjects are playing a key role in new drug development in Japan. In addition to the consideration of differences in intrinsic and extrinsic ethnic factors, deciding the sample size of Japanese subjects is an important issue when a multiregional clinical trial is intended to be used for Japanese submission. Accumulated experience suggests that there are several points to consider, such as the basic principles described in the guidance document, drug development strategy, trial phase, and disease background. The difficulty of interpreting the results of Japanese trials should also be considered.
Coalescence computations for large samples drawn from populations of time-varying sizes
Polanski, Andrzej; Szczesna, Agnieszka; Garbulowski, Mateusz; Kimmel, Marek
2017-01-01
We present new results concerning probability distributions of times in the coalescence tree and expected allele frequencies for coalescent with large sample size. The obtained results are based on computational methodologies, which involve combining coalescence time scale changes with techniques of integral transformations and using analytical formulae for infinite products. We show applications of the proposed methodologies for computing probability distributions of times in the coalescence tree and their limits, for evaluation of accuracy of approximate expressions for times in the coalescence tree and expected allele frequencies, and for analysis of large human mitochondrial DNA dataset. PMID:28170404
Origin of sample size effect: Stochastic dislocation formation in crystalline metals at small scales
Huang, Guan-Rong; Huang, J. C.; Tsai, W. Y.
2016-01-01
In crystalline metals at small scales, the dislocation density will be increased by stochastic events of dislocation network, leading to a universal power law for various material structures. In this work, we develop a model obeyed by a probability distribution of dislocation density to describe the dislocation formation in terms of a chain reaction. The leading order terms of steady-state of probability distribution gives physical and quantitative insight to the scaling exponent n values in the power law of sample size effect. This approach is found to be consistent with experimental n values in a wide range. PMID:27976740
Origin of sample size effect: Stochastic dislocation formation in crystalline metals at small scales
NASA Astrophysics Data System (ADS)
Huang, Guan-Rong; Huang, J. C.; Tsai, W. Y.
2016-12-01
In crystalline metals at small scales, the dislocation density will be increased by stochastic events of dislocation network, leading to a universal power law for various material structures. In this work, we develop a model obeyed by a probability distribution of dislocation density to describe the dislocation formation in terms of a chain reaction. The leading order terms of steady-state of probability distribution gives physical and quantitative insight to the scaling exponent n values in the power law of sample size effect. This approach is found to be consistent with experimental n values in a wide range.
Friede, Tim; Kieser, Meinhard
2013-01-01
The internal pilot study design allows for modifying the sample size during an ongoing study based on a blinded estimate of the variance thus maintaining the trial integrity. Various blinded sample size re-estimation procedures have been proposed in the literature. We compare the blinded sample size re-estimation procedures based on the one-sample variance of the pooled data with a blinded procedure using the randomization block information with respect to bias and variance of the variance estimators, and the distribution of the resulting sample sizes, power, and actual type I error rate. For reference, sample size re-estimation based on the unblinded variance is also included in the comparison. It is shown that using an unbiased variance estimator (such as the one using the randomization block information) for sample size re-estimation does not guarantee that the desired power is achieved. Moreover, in situations that are common in clinical trials, the variance estimator that employs the randomization block length shows a higher variability than the simple one-sample estimator and in turn the sample size resulting from the related re-estimation procedure. This higher variability can lead to a lower power as was demonstrated in the setting of noninferiority trials. In summary, the one-sample estimator obtained from the pooled data is extremely simple to apply, shows good performance, and is therefore recommended for application.
Garamszegi, László Z; Møller, Anders P
2010-11-01
Comparative analyses aim to explain interspecific variation in phenotype among taxa. In this context, phylogenetic approaches are generally applied to control for similarity due to common descent, because such phylogenetic relationships can produce spurious similarity in phenotypes (known as phylogenetic inertia or bias). On the other hand, these analyses largely ignore potential biases due to within-species variation. Phylogenetic comparative studies inherently assume that species-specific means from intraspecific samples of modest sample size are biologically meaningful. However, within-species variation is often significant, because measurement errors, within- and between-individual variation, seasonal fluctuations, and differences among populations can all reduce the repeatability of a trait. Although simulations revealed that low repeatability can increase the type I error in a phylogenetic study, researchers only exercise great care in accounting for similarity in phenotype due to common phylogenetic descent, while problems posed by intraspecific variation are usually neglected. A meta-analysis of 194 comparative analyses all adjusting for similarity due to common phylogenetic descent revealed that only a few studies reported intraspecific repeatabilities, and hardly any considered or partially dealt with errors arising from intraspecific variation. This is intriguing, because the meta-analytic data suggest that the effect of heterogeneous sampling can be as important as phylogenetic bias, and thus they should be equally controlled in comparative studies. We provide recommendations about how to handle such effects of heterogeneous sampling.
Bolton tooth size ratio among qatari population sample: An odontometric study
Hashim, Hayder A; AL-Sayed, Najah; AL-Hussain, Hashim
2017-01-01
Objectives: To establish the overall and anterior Bolton ratio among a sample of Qatari population and to investigate whether there is a difference between males and females, as well as to compare the result obtained by Bolton. Materials and Methods: The current study consisted of 100 orthodontic study participants (50 males and 50 females) with different malocclusions and age ranging between 15 and 20 years. An electronic digital caliper was used to measure the mesiodistal tooth width of all maxillary and mandibular permanent teeth except second and third molars. The Student's t-test was used to compare tooth-size ratios between males and females and between the results of the present study and Bolton's result. Results: The anterior and overall ratio in Qatari individuals were 78.6 ± 3.4 and 91.8 ± 3.1, respectively. The tooth size ratios were slightly greater in males than that in females, however, the differences were not statistically significant (P > 0.05). There were no significant differences in the overall ratio between Qatari individuals and Bolton's results (P > 0.05), whereas statistical significant differences were observed in anterior ratio (P = 0.007). Conclusions: Within the limitation of the limitations of the present study, definite conclusion was difficult to establish. Thus, a further study with a large sample in each malocclusion group is required. PMID:28197399
On the Question of Effective Sample Size in Network Modeling: An Asymptotic Inquiry.
Kolaczyk, Eric D; Krivitsky, Pavel N
2015-05-01
The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this area to date by researchers from various disciplines, however, there remain many questions of a decidedly foundational nature - natural analogues of standard questions already posed and addressed in more classical areas of statistics - that have yet to even be posed, much less addressed. Here we raise and consider one such question in connection with network modeling. Specifically, we ask, "Given an observed network, what is the sample size?" Using simple, illustrative examples from the class of exponential random graph models, we show that the answer to this question can very much depend on basic properties of the networks expected under the model, as the number of vertices nV in the network grows. In particular, adopting the (asymptotic) scaling of the variance of the maximum likelihood parameter estimates as a notion of effective sample size, say neff, we show that whether the networks are sparse or not under our model (i.e., having relatively few or many edges between vertices, respectively) is sufficient to yield an order of magnitude difference in neff, from O(nV ) to [Formula: see text]. We then explore some practical implications of this result, using both simulation and data on food-sharing from Lamalera, Indonesia.
DRME: Count-based differential RNA methylation analysis at small sample size scenario.
Liu, Lian; Zhang, Shao-Wu; Gao, Fan; Zhang, Yixin; Huang, Yufei; Chen, Runsheng; Meng, Jia
2016-04-15
Differential methylation, which concerns difference in the degree of epigenetic regulation via methylation between two conditions, has been formulated as a beta or beta-binomial distribution to address the within-group biological variability in sequencing data. However, a beta or beta-binomial model is usually difficult to infer at small sample size scenario with discrete reads count in sequencing data. On the other hand, as an emerging research field, RNA methylation has drawn more and more attention recently, and the differential analysis of RNA methylation is significantly different from that of DNA methylation due to the impact of transcriptional regulation. We developed DRME to better address the differential RNA methylation problem. The proposed model can effectively describe within-group biological variability at small sample size scenario and handles the impact of transcriptional regulation on RNA methylation. We tested the newly developed DRME algorithm on simulated and 4 MeRIP-Seq case-control studies and compared it with Fisher's exact test. It is in principle widely applicable to several other RNA-related data types as well, including RNA Bisulfite sequencing and PAR-CLIP. The code together with an MeRIP-Seq dataset is available online (https://github.com/lzcyzm/DRME) for evaluation and reproduction of the figures shown in this article.
Sample size planning for phase II trials based on success probabilities for phase III.
Götte, Heiko; Schüler, Armin; Kirchner, Marietta; Kieser, Meinhard
2015-01-01
In recent years, high failure rates in phase III trials were observed. One of the main reasons is overoptimistic assumptions for the planning of phase III resulting from limited phase II information and/or unawareness of realistic success probabilities. We present an approach for planning a phase II trial in a time-to-event setting that considers the whole phase II/III clinical development programme. We derive stopping boundaries after phase II that minimise the number of events under side conditions for the conditional probabilities of correct go/no-go decision after phase II as well as the conditional success probabilities for phase III. In addition, we give general recommendations for the choice of phase II sample size. Our simulations show that unconditional probabilities of go/no-go decision as well as the unconditional success probabilities for phase III are influenced by the number of events observed in phase II. However, choosing more than 150 events in phase II seems not necessary as the impact on these probabilities then becomes quite small. We recommend considering aspects like the number of compounds in phase II and the resources available when determining the sample size. The lower the number of compounds and the lower the resources are for phase III, the higher the investment for phase II should be.
Multivariate multidistance tests for high-dimensional low sample size case-control studies.
Marozzi, Marco
2015-04-30
A class of multivariate tests for case-control studies with high-dimensional low sample size data and with complex dependence structure, which are common in medical imaging and molecular biology, is proposed. The tests can be applied when the number of variables is much larger than the number of subjects and when the underlying population distributions are heavy-tailed or skewed. As a motivating application, we consider a case-control study where phase-contrast cinematic cardiovascular magnetic resonance imaging has been used to compare many cardiovascular characteristics of young healthy smokers and young healthy non-smokers. The tests are based on the combination of tests on interpoint distances. It is theoretically proved that the tests are exact, unbiased and consistent. It is shown that the tests are very powerful under normal, heavy-tailed and skewed distributions. The tests can also be applied to case-control studies with high-dimensional low sample size data from other medical imaging techniques (like computed tomography or X-ray radiography), chemometrics and microarray data (proteomics and transcriptomics).
On Two-Stage Multiple Comparison Procedures When There Are Unequal Sample Sizes in the First Stage.
ERIC Educational Resources Information Center
Wilcox, Rand R.
1984-01-01
Two stage multiple-comparison procedures give an exact solution to problems of power and Type I errors, but require equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes. (Author/BW)
ERIC Educational Resources Information Center
Shieh, Gwowen; Jan, Show-Li
2013-01-01
The authors examined 2 approaches for determining the required sample size of Welch's test for detecting equality of means when the greatest difference between any 2 group means is given. It is shown that the actual power obtained with the sample size of the suggested approach is consistently at least as great as the nominal power. However, the…
ERIC Educational Resources Information Center
Guo, Jiin-Huarng; Luh, Wei-Ming
2008-01-01
This study proposes an approach for determining appropriate sample size for Welch's F test when unequal variances are expected. Given a certain maximum deviation in population means and using the quantile of F and t distributions, there is no need to specify a noncentrality parameter and it is easy to estimate the approximate sample size needed…
ERIC Educational Resources Information Center
In'nami, Yo; Koizumi, Rie
2013-01-01
The importance of sample size, although widely discussed in the literature on structural equation modeling (SEM), has not been widely recognized among applied SEM researchers. To narrow this gap, we focus on second language testing and learning studies and examine the following: (a) Is the sample size sufficient in terms of precision and power of…
Wang, Jixian
2010-09-01
Sample size reestimation (SSRE) provides a useful tool to change the sample size when an interim look reveals that the original sample size is inadequate. To control the overall type I error, for testing one hypothesis, several approaches have been proposed to construct a statistic so that its distribution is independent to the SSRE under the null hypothesis. We considered a similar approach for comparisons between multiple treatment arms and placebo, allowing the change of sample sizes in all arms depending on interim information. A construction of statistics similar to that for a single hypothesis test is proposed. When the changes of sample sizes in different arms are proportional, we show that one-step and stepwise Dunnett tests can be used directly on statistics constructed in the proposed way. The approach can also be applied to clinical trials with SSRE and treatment selection at interim. The proposed approach is evaluated with simulations under different situations.
A cold finger cooling system for the efficient graphitisation of microgram-sized carbon samples
NASA Astrophysics Data System (ADS)
Yang, Bin; Smith, A. M.; Hua, Quan
2013-01-01
At ANSTO, we use the Bosch reaction to convert sample CO2 to graphite for production of our radiocarbon AMS targets. Key to the efficient graphitisation of ultra-small samples are the type of iron catalyst used and the effective trapping of water vapour during the reaction. Here we report a simple liquid nitrogen cooling system that enables us to rapidly adjust the temperature of the cold finger in our laser-heated microfurnace. This has led to an improvement in the graphitisation of microgram-sized carbon samples. This simple system uses modest amounts of liquid nitrogen (typically <200 mL/h during graphitisation) and is compact and reliable. We have used it to produce over 120 AMS targets containing between 5 and 20 μg of carbon, with conversion efficiencies for 5 μg targets ranging from 80% to 100%. In addition, this cooling system has been adapted for use with our conventional graphitisation reactors and has also improved their performance.
Mörlein, Daniel; Christensen, Rune Haubo Bojesen; Gertheiss, Jan
2015-02-01
To prevent impaired consumer acceptance due to insensitive sensory quality control, it is of primary importance to periodically validate the performance of the assessors. This communication show cases how the uncertainty of sensitivity and specificity estimates is influenced by the total number of assessed samples and the prevalence of positive (here: boar tainted) samples. Furthermore, a statistically sound approach to determining the sample size that is necessary for performance validation is provided. Results show that a small sample size is associated with large uncertainty, i.e., confidence intervals and thus compromising the point estimates for assessor sensitivity. In turn, to reliably identify sensitive assessors with sufficient test power, a large sample size is needed given a certain level of confidence. Easy-to-use tables for sample size estimations are provided.
NASA Astrophysics Data System (ADS)
Mori, Taizo; Hegmann, Torsten
2016-10-01
Size, shape, overall composition, and surface functionality largely determine the properties and applications of metal nanoparticles. Aside from well-defined metal clusters, their composition is often estimated assuming a quasi-spherical shape of the nanoparticle core. With decreasing diameter of the assumed circumscribed sphere, particularly in the range of only a few nanometers, the estimated nanoparticle composition increasingly deviates from the real composition, leading to significant discrepancies between anticipated and experimentally observed composition, properties, and characteristics. We here assembled a compendium of tables, models, and equations for thiol-protected gold nanoparticles that will allow experimental scientists to more accurately estimate the composition of their gold nanoparticles using TEM image analysis data. The estimates obtained from following the routines described here will then serve as a guide for further analytical characterization of as-synthesized gold nanoparticles by other bulk (thermal, structural, chemical, and compositional) and surface characterization techniques. While the tables, models, and equations are dedicated to gold nanoparticles, the composition of other metal nanoparticle cores with face-centered cubic lattices can easily be estimated simply by substituting the value for the radius of the metal atom of interest.
Analyzing insulin samples by size-exclusion chromatography: a column degradation study.
Teska, Brandon M; Kumar, Amit; Carpenter, John F; Wempe, Michael F
2015-04-01
Investigating insulin analogs and probing their intrinsic stability at physiological temperature, we observed significant degradation in the size-exclusion chromatography (SEC) signal over a moderate number of insulin sample injections, which generated concerns about the quality of the separations. Therefore, our research goal was to identify the cause(s) for the observed signal degradation and attempt to mitigate the degradation in order to extend SEC column lifespan. In these studies, we used multiangle light scattering, nuclear magnetic resonance, and gas chromatography-mass spectrometry methods to evaluate column degradation. The results from these studies illustrate: (1) that zinc ions introduced by the insulin product produced the observed column performance issues; and (2) that including ethylenediaminetetraacetic acid, a zinc chelator, in the mobile phase helped to maintain column performance.
Thrane, Susan; Cohen, Susan M.
2013-01-01
Objective To calculate the effect of Reiki therapy for pain and anxiety in randomized clinical trials. Data Sources A systematic search of PubMed, ProQuest, Cochrane, PsychInfo, CINAHL, Web of Science, Global Health, and Medline databases was conducted using the search terms pain, anxiety, and Reiki. The Center for Reiki Research was also examined for articles. Study Selection Studies that used randomization and a control or usual care group, used Reiki therapy in one arm of the study, published in 2000 or later in peer-reviewed journals in English, and measured pain or anxiety were included. Results After removing duplicates, 49 articles were examined and 12 articles received full review. Seven studies met the inclusion criteria: four articles studied cancer patients; one examined post-surgical patients; and two analyzed community dwelling older adults. Effect sizes were calculated for all studies using Cohen’s d statistic. Effect sizes for within group differences ranged from d=0.24 for decrease in anxiety in women undergoing breast biopsy to d=2.08 for decreased pain in community dwelling adults. The between group differences ranged from d=0.32 for decrease of pain in a Reiki versus rest intervention for cancer patients to d=4.5 for decrease in pain in community dwelling adults. Conclusions While the number of studies is limited, based on the size Cohen’s d statistics calculated in this review, there is evidence to suggest that Reiki therapy may be effective for pain and anxiety. Continued research using Reiki therapy with larger sample sizes, consistently randomized groups, and standardized treatment protocols is recommended. PMID:24582620
Results of an indoor size fractionated PM school sampling program in Libby, Montana.
Ward, Tony J; Noonan, Curtis W; Hooper, Kathi
2007-07-01
Libby, Montana is the only PM(2.5) non-attainment area in the western United States with the exceptions of parts of southern California. During January through March 2005, a particulate matter (PM) sampling program was conducted within Libby's elementary and middle schools to establish baseline indoor PM concentrations before a wood stove change-out program is implemented over the next several years. As part of this program, indoor concentrations of PM mass, organic carbon (OC), and elemental carbon (EC) in five different size fractions (>2.5, 1.0-2.5, 0.5-1.0, 0.25-0.5, and <0.25 microm) were measured. Total measured PM mass concentrations were much higher inside the elementary school, with particle size fraction (>2.5, 0.5-1.0, 0.25-0.5, and <0.25 microm) concentrations between 2 and 5 times higher when compared to the middle school. The 1.0-2.5 microm fraction had the largest difference between the two sites, with elementary school concentrations nearly 10 times higher than the middle school values. The carbon component for the schools' indoor PM was found to be predominantly composed of OC. Measured total OC and EC concentrations, as well as concentrations within individual size fractions, were an average of two to five times higher at the elementary school when compared to the middle school. For the ultrafine fraction (<0.25), EC concentrations were similar between each of the schools. Despite the differences in concentrations between the schools at the various fraction levels, the OC/EC ratio was determined to be similar.
Sediment grain size estimation using airborne remote sensing, field sampling, and robust statistic.
Castillo, Elena; Pereda, Raúl; Luis, Julio Manuel de; Medina, Raúl; Viguri, Javier
2011-10-01
Remote sensing has been used since the 1980s to study parameters in relation with coastal zones. It was not until the beginning of the twenty-first century that it started to acquire imagery with good temporal and spectral resolution. This has encouraged the development of reliable imagery acquisition systems that consider remote sensing as a water management tool. Nevertheless, the spatial resolution that it provides is not adapted to carry out coastal studies. This article introduces a new methodology for estimating the most fundamental physical property of intertidal sediment, the grain size, in coastal zones. The study combines hyperspectral information (CASI-2 flight), robust statistic, and simultaneous field work (chemical and radiometric sampling), performed over Santander Bay, Spain. Field data acquisition was used to build a spectral library in order to study different atmospheric correction algorithms for CASI-2 data and to develop algorithms to estimate grain size in an estuary. Two robust estimation techniques (MVE and MCD multivariate M-estimators of location and scale) were applied to CASI-2 imagery, and the results showed that robust adjustments give acceptable and meaningful algorithms. These adjustments have given the following R(2) estimated results: 0.93 in the case of sandy loam contribution, 0.94 for the silty loam, and 0.67 for clay loam. The robust statistic is a powerful tool for large dataset.
Tian, Zhen; Li, Yongbao; Hassan-Rezaeian, Nima; Jiang, Steve B; Jia, Xun
2017-03-01
We have previously developed a GPU-based Monte Carlo (MC) dose engine on the OpenCL platform, named goMC, with a built-in analytical linear accelerator (linac) beam model. In this paper, we report our recent improvement on goMC to move it toward clinical use. First, we have adapted a previously developed automatic beam commissioning approach to our beam model. The commissioning was conducted through an optimization process, minimizing the discrepancies between calculated dose and measurement. We successfully commissioned six beam models built for Varian TrueBeam linac photon beams, including four beams of different energies (6 MV, 10 MV, 15 MV, and 18 MV) and two flattening-filter-free (FFF) beams of 6 MV and 10 MV. Second, to facilitate the use of goMC for treatment plan dose calculations, we have developed an efficient source particle sampling strategy. It uses the pre-generated fluence maps (FMs) to bias the sampling of the control point for source particles already sampled from our beam model. It could effectively reduce the number of source particles required to reach a statistical uncertainty level in the calculated dose, as compared to the conventional FM weighting method. For a head-and-neck patient treated with volumetric modulated arc therapy (VMAT), a reduction factor of ~2.8 was achieved, accelerating dose calculation from 150.9 s to 51.5 s. The overall accuracy of goMC was investigated on a VMAT prostate patient case treated with 10 MV FFF beam. 3D gamma index test was conducted to evaluate the discrepancy between our calculated dose and the dose calculated in Varian Eclipse treatment planning system. The passing rate was 99.82% for 2%/2 mm criterion and 95.71% for 1%/1 mm criterion. Our studies have demonstrated the effectiveness and feasibility of our auto-commissioning approach and new source sampling strategy for fast and accurate MC dose calculations for treatment plans.
Atterton, Thomas; De Groote, Isabelle; Eliopoulos, Constantine
2016-10-01
The construction of the biological profile from human skeletal remains is the foundation of anthropological examination. However, remains may be fragmentary and the elements usually employed, such as the pelvis and skull, are not available. The clavicle has been successfully used for sex estimation in samples from Iran and Greece. In the present study, the aim was to test the suitability of the measurements used in those previous studies on a British Medieval population. In addition, the project tested whether discrimination between sexes was due to size or clavicular strength. The sample consisted of 23 females and 25 males of pre-determined sex from two medieval collections: Poulton and Gloucester. Six measurements were taken using an osteometric board, sliding calipers and graduated tape. In addition, putty rings and bi-planar radiographs were made and robusticity measures calculated. The resulting variables were used in stepwise discriminant analyses. The linear measurements allowed correct sex classification in 89.6% of all individuals. This demonstrates the applicability of the clavicle for sex estimation in British populations. The most powerful discriminant factor was maximum clavicular length and the best combination of factors was maximum clavicular length and circumference. This result is similar to that obtained by other studies. To further investigate the extent of sexual dimorphism of the clavicle, the biomechanical properties of the polar second moment of area J and the ratio of maximum to minimum bending rigidity are included in the analysis. These were found to have little influence when entered into the discriminant function analysis.
Matzke, Melissa M; Allan, Sarah E; Anderson, Kim A; Waters, Katrina M
2012-12-01
The use of passive sampling devices (PSDs) for monitoring hydrophobic organic contaminants in aquatic environments can entail logistical constraints that often limit a comprehensive statistical sampling plan, thus resulting in a restricted number of samples. The present study demonstrates an approach for using the results of a pilot study designed to estimate sampling variability, which in turn can be used as variance estimates for confidence intervals for future n = 1 PSD samples of the same aquatic system. Sets of three to five PSDs were deployed in the Portland Harbor Superfund site for three sampling periods over the course of two years. The PSD filters were extracted and, as a composite sample, analyzed for 33 polycyclic aromatic hydrocarbon compounds. The between-sample and within-sample variances were calculated to characterize sources of variability in the environment and sampling methodology. A method for calculating a statistically reliable and defensible confidence interval for the mean of a single aquatic passive sampler observation (i.e., n = 1) using an estimate of sample variance derived from a pilot study is presented. Coverage probabilities are explored over a range of variance values using a Monte Carlo simulation.
McCarthy, K.
2008-01-01
Semipermeable membrane devices (SPMDs) were deployed in the Columbia Slough, near Portland, Oregon, on three separate occasions to measure the spatial and seasonal distribution of dissolved polycyclic aromatic hydrocarbons (PAHs) and organochlorine compounds (OCs) in the slough. Concentrations of PAHs and OCs in SPMDs showed spatial and seasonal differences among sites and indicated that unusually high flows in the spring of 2006 diluted the concentrations of many of the target contaminants. However, the same PAHs - pyrene, fluoranthene, and the alkylated homologues of phenanthrene, anthracene, and fluorene - and OCs - polychlorinated biphenyls, pentachloroanisole, chlorpyrifos, dieldrin, and the metabolites of dichlorodiphenyltrichloroethane (DDT) - predominated throughout the system during all three deployment periods. The data suggest that storm washoff may be a predominant source of PAHs in the slough but that OCs are ubiquitous, entering the slough by a variety of pathways. Comparison of SPMDs deployed on the stream bed with SPMDs deployed in the overlying water column suggests that even for the very hydrophobic compounds investigated, bed sediments may not be a predominant source in this system. Perdeuterated phenanthrene (phenanthrene-d10). spiked at a rate of 2 ??g per SPMD, was shown to be a reliable performance reference compound (PRC) under the conditions of these deployments. Post-deployment concentrations of the PRC revealed differences in sampling conditions among sites and between seasons, but indicate that for SPMDs deployed throughout the main slough channel, differences in sampling rates were small enough to make site-to-site comparisons of SPMD concentrations straightforward. ?? Springer Science+Business Media B.V. 2007.
Xiong, Xiaoping; Wu, Jianrong
2017-01-01
The treatment of cancer has progressed dramatically in recent decades, such that it is no longer uncommon to see a cure or log-term survival in a significant proportion of patients with various types of cancer. To adequately account for the cure fraction when designing clinical trials, the cure models should be used. In this article, a sample size formula for the weighted log-rank test is derived under the fixed alternative hypothesis for the proportional hazards cure models. Simulation showed that the proposed sample size formula provides an accurate estimation of sample size for designing clinical trials under the proportional hazards cure models.
Standardization of bulb and root sample sizes for the Allium cepa test.
Barbério, A; Voltolini, J C; Mello, M L S
2011-06-01
Although the Allium cepa test has been widely used to identify potentially cytotoxic and genotoxic pollutants in aquatic environments, variable non-standardized choices have been made regarding the number of plant bulbs and roots analyzed. We propose numbers for bulbs and roots per bulb when comparing the frequencies of micronuclei, mitotic anomalies and mitotic index with this test. Roots that had been treated with aqueous solutions, such as water samples collected in August 2007 from the Paraíba do Sul River at the Brazilian cities of Tremembé and Aparecida; negative and positive controls were used for bioassays. The presence of pollutants in the river water had been presumed based on our previous cytological data and an official report by the São Paulo State Environmental Agency (Brazil) on presence of fecal contaminants (Tremembé and Aparecida) and elevated dissolved aluminium (Aparecida) in the water under study. The sampling of ten bulbs and five roots per bulb was found adequate for comparative studies to evaluate with the A. cepa test the potential damage inflicted by pollutants in aquatic environments. Furthermore, even one bulb and one root per bulb was sufficient in discerning this damage, thereby shortening the time required to attain a statistically confident comparative evaluation. However, to allow for the use of statistical programs based on the evaluation of average values, and to avoid criticism based on genetic variability, we propose that three bulbs and three roots per bulb be considered as standard sample sizes for the A. cepa test.
Oh, Suk Yung; Bae, Young Chan
2010-07-15
The method presented in this paper was developed to predict liquid-liquid equilibria in ternary liquid mixtures by using a combination of a thermodynamic model and molecular dynamics simulations. In general, common classical thermodynamic models have many parameters which are determined by fitting a model with experimental data. This proposed method, however, provides a simple procedure for calculating liquid-liquid equilibria utilizing binary interaction parameters and molecular size parameters determined from molecular dynamics simulations. This method was applied to mixtures containing water, hydrocarbons, alcohols, chlorides, ketones, acids, and other organic liquids over various temperature ranges. The predicted results agree well with the experimental data without the use of adjustable parameters.
Tsukakoshi, Yoshiki; Yasui, Akemi
2011-11-01
To give a quantitative guide to sample size allocation for developing sampling designs for a food composition survey, we discuss sampling strategies that consider the importance of each food; namely, consumption or production, variability of composition, and the restrictions within the available resources for sample collection and analysis are considered., Here we consider two strategies: 'proportional' and 'Neyman' are discussed. Both of these incorporate consumed quantity of foods, and we review some available statistics for allocation issues. The Neyman optimal strategy allocates less sample size for starch than proportional, because the former incorporates variability in the composition. Those strategies improved accuracy in dietary nutrient intake more than equal sample size allocation. Those strategies will be useful as we often face sample size allocation problems, wherein we decide whether to sample 'five white potatoes and five taros or nine white and one taros'. Allocating sufficient sample size for important foodstuffs is essential in assuring data quality. Nevertheless, the food composition table should be as comprehensive as possible.
Optimizing Stream Water Mercury Sampling for Calculation of Fish Bioaccumulation Factors
Mercury (Hg) bioaccumulation factors (BAFs) for game fishes are widely employed for monitoring, assessment, and regulatory purposes. Mercury BAFs are calculated as the fish Hg concentration (Hgfish) divided by the water Hg concentration (Hgwater) and, consequently, are sensitive ...
Methods for calculating dietary energy density in a nationally representative sample.
Vernarelli, Jacqueline A; Mitchell, Diane C; Rolls, Barbara J; Hartman, Terryl J
2013-01-01
There has been a growing interest in examining dietary energy density (ED, kcal/g) as it relates to various health outcomes. Consuming a diet low in ED has been recommended in the 2010 Dietary Guidelines, as well as by other agencies, as a dietary approach for disease prevention. Translating this recommendation into practice; however, is difficult. Currently there is no standardized method for calculating dietary ED; as dietary ED can be calculated with foods alone, or with a combination of foods and beverages. Certain items may be defined as either a food or a beverage (e.g., meal replacement shakes) and require special attention. National survey data are an excellent resource for evaluating factors that are important to dietary ED calculation. The National Health and Nutrition Examination Survey (NHANES) nutrient and food database does not include an ED variable, thus researchers must independently calculate ED. The objective of this study was to provide information that will inform the selection of a standardized ED calculation method by comparing and contrasting methods for ED calculation. The present study evaluates all consumed items and defines foods and beverages based on both USDA food codes and how the item was consumed. Results are presented as mean EDs for the different calculation methods stratified by population demographics (e.g. age, sex). Using United State Department of Agriculture (USDA) food codes in the 2005-2008 NHANES, a standardized method for calculating dietary ED can be derived. This method can then be adapted by other researchers for consistency across studies.
Treaftis, H.N.; Kacsmar, P.; Suppers, K., Tomb, T.F.
1986-02-01
The paper discusses the results of a study conducted to evaluate two different methods used to measure the particle size distribution of an aerosol. Comparative samples were collected in the laboratory with Sierra's Models 260 and 298 cascade impaction samplers and a sampler consisting of a pump and filter using coal and limestone aerosols of varying particle size distributions. The particle size distributions determined from each of the impaction samples were compared to each other as well as to the particle size distribution determined from data obtained from a Coulter Counter analysis of the total dust sample collected on the filter. The results of the laboratory study are discussed and compared to a limited amount of similar data obtained from samples collected with the impaction samplers in underground coal mines.
Park, Justin C.; Li, Jonathan G.; Arhjoul, Lahcen; Yan, Guanghua; Lu, Bo; Fan, Qiyong; Liu, Chihray
2015-04-15
Purpose: The use of sophisticated dose calculation procedure in modern radiation therapy treatment planning is inevitable in order to account for complex treatment fields created by multileaf collimators (MLCs). As a consequence, independent volumetric dose verification is time consuming, which affects the efficiency of clinical workflow. In this study, the authors present an efficient adaptive beamlet-based finite-size pencil beam (AB-FSPB) dose calculation algorithm that minimizes the computational procedure while preserving the accuracy. Methods: The computational time of finite-size pencil beam (FSPB) algorithm is proportional to the number of infinitesimal and identical beamlets that constitute an arbitrary field shape. In AB-FSPB, dose distribution from each beamlet is mathematically modeled such that the sizes of beamlets to represent an arbitrary field shape no longer need to be infinitesimal nor identical. As a result, it is possible to represent an arbitrary field shape with combinations of different sized and minimal number of beamlets. In addition, the authors included the model parameters to consider MLC for its rounded edge and transmission. Results: Root mean square error (RMSE) between treatment planning system and conventional FSPB on a 10 × 10 cm{sup 2} square field using 10 × 10, 2.5 × 2.5, and 0.5 × 0.5 cm{sup 2} beamlet sizes were 4.90%, 3.19%, and 2.87%, respectively, compared with RMSE of 1.10%, 1.11%, and 1.14% for AB-FSPB. This finding holds true for a larger square field size of 25 × 25 cm{sup 2}, where RMSE for 25 × 25, 2.5 × 2.5, and 0.5 × 0.5 cm{sup 2} beamlet sizes were 5.41%, 4.76%, and 3.54% in FSPB, respectively, compared with RMSE of 0.86%, 0.83%, and 0.88% for AB-FSPB. It was found that AB-FSPB could successfully account for the MLC transmissions without major discrepancy. The algorithm was also graphical processing unit (GPU) compatible to maximize its computational speed. For an intensity modulated radiation therapy (
NASA Astrophysics Data System (ADS)
Grohmann, Carlos H.; Sawakuchi, André O.
2013-01-01
In this work, we analyze how variation in cell size influences the volume calculated from digital terrain models (DTMs) derived from a LiDAR (light detection and ranging) survey in two coastal Late Holocene dune fields in southern Brazil. Cell size varied from 1 to 100 m. RMSE (root mean square error) of the resampled DTMs from the original LiDAR (with 0.5 m resolution) increases linearly with cell size, while R2 (coefficient of determination) decreases following a second-order trend. The volume does not show simple linear or exponential behavior, but fluctuates with positive and negative deviations from the original DTM. This can be explained by a random factor in the position of the cell with regard to landforms and a relationship between cell and landform size, wherein a small change in cell size can lead to an under- or overestimation of volume. The ASTER GDEM (global digital elevation model) and X-SAR SRTM (Shuttle Radar Topography Mission) 1″ digital elevation models (DEMs) were not considered viable volume sources due to large deviations from the reference data, either as a consequence of noise in the SRTM X-SAR data or lack of bias elevation correction to a common reference base in the GDEM processing chain. Volumes from a 3-arcsec SIR-C SRTM deviated around ± 5% from the reference data and are considered suitable input for numerical simulations of Quaternary dune field evolution models because these values should be within the expected range of sediment volume changes over hundreds to millions of years.
Oba, Yurika; Yamada, Toshihiro
2017-05-01
We estimated the sample size (the number of samples) required to evaluate the concentration of radiocesium ((137)Cs) in Japanese fir (Abies firma Sieb. & Zucc.), 5 years after the outbreak of the Fukushima Daiichi Nuclear Power Plant accident. We investigated the spatial structure of the contamination levels in this species growing in a mixed deciduous broadleaf and evergreen coniferous forest stand. We sampled 40 saplings with a tree height of 150 cm-250 cm in a Fukushima forest community. The results showed that: (1) there was no correlation between the (137)Cs concentration in needles and soil, and (2) the difference in the spatial distribution pattern of (137)Cs concentration between needles and soil suggest that the contribution of root uptake to (137)Cs in new needles of this species may be minor in the 5 years after the radionuclides were released into the atmosphere. The concentration of (137)Cs in needles showed a strong positive spatial autocorrelation in the distance class from 0 to 2.5 m, suggesting that the statistical analysis of data should consider spatial autocorrelation in the case of an assessment of the radioactive contamination of forest trees. According to our sample size analysis, a sample size of seven trees was required to determine the mean contamination level within an error in the means of no more than 10%. This required sample size may be feasible for most sites.
ERIC Educational Resources Information Center
Burton, Megan; Mims, Patricia
2012-01-01
Learning through meaningful problem solving is integral in any successful mathematics program (Carpenter et al. 1999). The National Council of Teachers of Mathematics (NCTM) promotes the use of problem solving as a means to deepen understanding of all content areas within mathematics (NCTM 2000). This article describes a first-grade lesson that…
NASA Technical Reports Server (NTRS)
Clanton, U. S.; Fletcher, C. R.
1976-01-01
The paper describes a Monte Carlo model for simulation of two-dimensional representations of thin sections of some of the more common igneous rock textures. These representations are extrapolated to three dimensions to develop a volume of 'rock'. The model (here applied to a medium-grained high-Ti basalt) can be used to determine a statistically significant sample for a lunar rock or to predict the probable errors in the oxide contents that can occur during the analysis of a sample that is not representative of the parent rock.
Efficient free energy calculations by combining two complementary tempering sampling methods.
Xie, Liangxu; Shen, Lin; Chen, Zhe-Ning; Yang, Mingjun
2017-01-14
Although energy barriers can be efficiently crossed in the reaction coordinate (RC) guided sampling, this type of method suffers from identification of the correct RCs or requirements of high dimensionality of the defined RCs for a given system. If only the approximate RCs with significant barriers are used in the simulations, hidden energy barriers with small to medium height would exist in other degrees of freedom (DOFs) relevant to the target process and consequently cause the problem of insufficient sampling. To address the sampling in this so-called hidden barrier situation, here we propose an effective approach to combine temperature accelerated molecular dynamics (TAMD), an efficient RC-guided sampling method, with the integrated tempering sampling (ITS), a generalized ensemble sampling method. In this combined ITS-TAMD method, the sampling along the major RCs with high energy barriers is guided by TAMD and the sampling of the rest of the DOFs with lower but not negligible barriers is enhanced by ITS. The performance of ITS-TAMD to three systems in the processes with hidden barriers has been examined. In comparison to the standalone TAMD or ITS approach, the present hybrid method shows three main improvements. (1) Sampling efficiency can be improved at least five times even if in the presence of hidden energy barriers. (2) The canonical distribution can be more accurately recovered, from which the thermodynamic properties along other collective variables can be computed correctly. (3) The robustness of the selection of major RCs suggests that the dimensionality of necessary RCs can be reduced. Our work shows more potential applications of the ITS-TAMD method as the efficient and powerful tool for the investigation of a broad range of interesting cases.
12 CFR Appendix M2 to Part 226 - Sample Calculations of Repayment Disclosures
Code of Federal Regulations, 2012 CFR
2012-01-01
... total balance if making only minimum payments pmt = minimum monthly payment fc = monthly finance charge...=month+1; * increment month counter; pmt=round(pmin*tbal,0.01); * calculate payment as percentage of balance; if month ge expm and expm ne 0 then perrate1=(rrate/365)*days; if pmt lt dmin then...