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. PMID:21293154
Sample size calculation in metabolic phenotyping studies.
Billoir, Elise; Navratil, Vincent; Blaise, Benjamin J
2015-09-01
The number of samples needed to identify significant effects is a key question in biomedical studies, with consequences on experimental designs, costs and potential discoveries. In metabolic phenotyping studies, sample size determination remains a complex step. This is due particularly to the multiple hypothesis-testing framework and the top-down hypothesis-free approach, with no a priori known metabolic target. Until now, there was no standard procedure available to address this purpose. In this review, we discuss sample size estimation procedures for metabolic phenotyping studies. We release an automated implementation of the Data-driven Sample size Determination (DSD) algorithm for MATLAB and GNU Octave. Original research concerning DSD was published elsewhere. DSD allows the determination of an optimized sample size in metabolic phenotyping studies. The procedure uses analytical data only from a small pilot cohort to generate an expanded data set. The statistical recoupling of variables procedure is used to identify metabolic variables, and their intensity distributions are estimated by Kernel smoothing or log-normal density fitting. Statistically significant metabolic variations are evaluated using the Benjamini-Yekutieli correction and processed for data sets of various sizes. Optimal sample size determination is achieved in a context of biomarker discovery (at least one statistically significant variation) or metabolic exploration (a maximum of statistically significant variations). DSD toolbox is encoded in MATLAB R2008A (Mathworks, Natick, MA) for Kernel and log-normal estimates, and in GNU Octave for log-normal estimates (Kernel density estimates are not robust enough in GNU octave). It is available at http://www.prabi.fr/redmine/projects/dsd/repository, with a tutorial at http://www.prabi.fr/redmine/projects/dsd/wiki. PMID:25600654
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
Sample size calculation for the proportional hazards cure model.
Wang, Songfeng; Zhang, Jiajia; Lu, Wenbin
2012-12-20
In clinical trials with time-to-event endpoints, it is not uncommon to see a significant proportion of patients being cured (or long-term survivors), such as trials for the non-Hodgkins lymphoma disease. The popularly used sample size formula derived under the proportional hazards (PH) model may not be proper to design a survival trial with a cure fraction, because the PH model assumption may be violated. To account for a cure fraction, the PH cure model is widely used in practice, where a PH model is used for survival times of uncured patients and a logistic distribution is used for the probability of patients being cured. In this paper, we develop a sample size formula on the basis of the PH cure model by investigating the asymptotic distributions of the standard weighted log-rank statistics under the null and local alternative hypotheses. The derived sample size formula under the PH cure model is more flexible because it can be used to test the differences in the short-term survival and/or cure fraction. Furthermore, we also investigate as numerical examples the impacts of accrual methods and durations of accrual and follow-up periods on sample size calculation. The results show that ignoring the cure rate in sample size calculation can lead to either underpowered or overpowered studies. We evaluate the performance of the proposed formula by simulation studies and provide an example to illustrate its application with the use of data from a melanoma trial. PMID:22786805
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. PMID:2910062
Statistical identifiability and sample size calculations for serial seroepidemiology
Vinh, Dao Nguyen; Boni, Maciej F.
2015-01-01
Inference on disease dynamics is typically performed using case reporting time series of symptomatic disease. The inferred dynamics will vary depending on the reporting patterns and surveillance system for the disease in question, and the inference will miss mild or underreported epidemics. To eliminate the variation introduced by differing reporting patterns and to capture asymptomatic or subclinical infection, inferential methods can be applied to serological data sets instead of case reporting data. To reconstruct complete disease dynamics, one would need to collect a serological time series. In the statistical analysis presented here, we consider a particular kind of serological time series with repeated, periodic collections of population-representative serum. We refer to this study design as a serial seroepidemiology (SSE) design, and we base the analysis on our epidemiological knowledge of influenza. We consider a study duration of three to four years, during which a single antigenic type of influenza would be circulating, and we evaluate our ability to reconstruct disease dynamics based on serological data alone. We show that the processes of reinfection, antibody generation, and antibody waning confound each other and are not always statistically identifiable, especially when dynamics resemble a non-oscillating endemic equilibrium behavior. We introduce some constraints to partially resolve this confounding, and we show that transmission rates and basic reproduction numbers can be accurately estimated in SSE study designs. Seasonal forcing is more difficult to identify as serology-based studies only detect oscillations in antibody titers of recovered individuals, and these oscillations are typically weaker than those observed for infected individuals. To accurately estimate the magnitude and timing of seasonal forcing, serum samples should be collected every two months and 200 or more samples should be included in each collection; this sample size estimate
Basic concepts for sample size calculation: Critical step for any clinical trials!
Gupta, KK; Attri, JP; Singh, A; Kaur, H; Kaur, G
2016-01-01
Quality of clinical trials has improved steadily over last two decades, but certain areas in trial methodology still require special attention like in sample size calculation. The sample size is one of the basic steps in planning any clinical trial and any negligence in its calculation may lead to rejection of true findings and false results may get approval. Although statisticians play a major role in sample size estimation basic knowledge regarding sample size calculation is very sparse among most of the anesthesiologists related to research including under trainee doctors. In this review, we will discuss how important sample size calculation is for research studies and the effects of underestimation or overestimation of sample size on project's results. We have highlighted the basic concepts regarding various parameters needed to calculate the sample size along with examples. PMID:27375390
A Comparative Study of Power and Sample Size Calculations for Multivariate General Linear Models
ERIC Educational Resources Information Center
Shieh, Gwowen
2003-01-01
Repeated measures and longitudinal studies arise often in social and behavioral science research. During the planning stage of such studies, the calculations of sample size are of particular interest to the investigators and should be an integral part of the research projects. In this article, we consider the power and sample size calculations for…
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…
Effects of Sample Size on Estimates of Population Growth Rates Calculated with Matrix Models
Fiske, Ian J.; Bruna, Emilio M.; Bolker, Benjamin M.
2008-01-01
Background Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (λ) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of λ–Jensen's Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of λ due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of λ. Methodology/Principal Findings Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating λ for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of λ with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography. Conclusions/Significance We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities. PMID:18769483
Manju, Md Abu; Candel, Math J J M; Berger, Martijn P F
2014-07-10
In this paper, the optimal sample sizes at the cluster and person levels for each of two treatment arms are obtained for cluster randomized trials where the cost-effectiveness of treatments on a continuous scale is studied. The optimal sample sizes maximize the efficiency or power for a given budget or minimize the budget for a given efficiency or power. Optimal sample sizes require information on the intra-cluster correlations (ICCs) for effects and costs, the correlations between costs and effects at individual and cluster levels, the ratio of the variance of effects translated into costs to the variance of the costs (the variance ratio), sampling and measuring costs, and the budget. When planning, a study information on the model parameters usually is not available. To overcome this local optimality problem, the current paper also presents maximin sample sizes. The maximin sample sizes turn out to be rather robust against misspecifying the correlation between costs and effects at the cluster and individual levels but may lose much efficiency when misspecifying the variance ratio. The robustness of the maximin sample sizes against misspecifying the ICCs depends on the variance ratio. The maximin sample sizes are robust under misspecification of the ICC for costs for realistic values of the variance ratio greater than one but not robust under misspecification of the ICC for effects. Finally, we show how to calculate optimal or maximin sample sizes that yield sufficient power for a test on the cost-effectiveness of an intervention. PMID:25019136
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. PMID:23934314
Sample size calculations for surveys to substantiate freedom of populations from infectious agents.
Johnson, Wesley O; Su, Chun-Lung; Gardner, Ian A; Christensen, Ronald
2004-03-01
We develop a Bayesian approach to sample size computations for surveys designed to provide evidence of freedom from a disease or from an infectious agent. A population is considered "disease-free" when the prevalence or probability of disease is less than some threshold value. Prior distributions are specified for diagnostic test sensitivity and specificity and we test the null hypothesis that the prevalence is below the threshold. Sample size computations are developed using hypergeometric sampling for finite populations and binomial sampling for infinite populations. A normal approximation is also developed. Our procedures are compared with the frequentist methods of Cameron and Baldock (1998a, Preventive Veterinary Medicine34, 1-17.) using an example of foot-and-mouth disease. User-friendly programs for sample size calculation and analysis of survey data are available at http://www.epi.ucdavis.edu/diagnostictests/. PMID:15032786
A Unified Approach to Power Calculation and Sample Size Determination for Random Regression Models
ERIC Educational Resources Information Center
Shieh, Gwowen
2007-01-01
The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all…
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. PMID:22292397
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.…
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
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
Anand, Suraj P; Murray, Sharon C; Koch, Gary G
2010-05-01
The cost for conducting a "thorough QT/QTc study" is substantial and an unsuccessful outcome of the study can be detrimental to the safety profile of the drug, so sample size calculations play a very important role in ensuring adequate power for a thorough QT study. Current literature offers some help in designing such studies, but these methods have limitations and mostly apply only in the context of linear mixed models with compound symmetry covariance structure. It is not evident that such models can satisfactorily be employed to represent all kinds of QTc data, and the existing literature inadequately addresses whether there is a change in sample size and power for more general covariance structures for the linear mixed models. We assess the use of some of the existing methods to design a thorough QT study through data arising from a GlaxoSmithKline (GSK)-conducted thorough QT study, and explore newer models for sample size calculation. We also provide a new method to calculate the sample size required to detect assay sensitivity with adequate power. PMID:20358438
Sabharwal, Sanjeeve; Patel, Nirav K; Holloway, Ian; Athanasiou, Thanos
2015-03-01
The purpose of this study was to identify how often sample size calculations were reported in recent orthopaedic randomized controlled trials (RCTs) and to determine what proportion of studies that failed to find a significant treatment effect were at risk of type II error. A pre-defined computerized search was performed in MEDLINE to identify RCTs published in 2012 in the 20 highest ranked orthopaedic journals based on impact factor. Data from these studies was used to perform post hoc analysis to determine whether each study was sufficiently powered to detect a small (0.2), medium (0.5) and large (0.8) effect size as defined by Cohen. Sufficient power (1-β) was considered to be 80% and a two-tailed test was performed with an alpha value of 0.05. 120 RCTs were identified using our stated search protocol and just 73 studies (60.80%) described an appropriate sample size calculation. Examination of studies with negative primary outcome revealed that 68 (93.15%) were at risk of type II error for a small treatment effect and only 4 (5.48%) were at risk of type II error for a medium sized treatment effect. Although comparison of the results with existing data from over 10 years ago infers improved practice in sample size calculations within orthopaedic surgery, there remains an ongoing need for improvement of practice. Orthopaedic researchers, as well as journal reviewers and editors have a responsibility to ensure that RCTs conform to standardized methodological guidelines and perform appropriate sample size calculations. PMID:26280864
Sample size calculation for the Wilcoxon-Mann-Whitney test adjusting for ties.
Zhao, Yan D; Rahardja, Dewi; Qu, Yongming
2008-02-10
In this paper we study sample size calculation methods for the asymptotic Wilcoxon-Mann-Whitney test for data with or without ties. The existing methods are applicable either to data with ties or to data without ties but not to both cases. While the existing methods developed for data without ties perform well, the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties. We propose a new method which has a closed-form formula and therefore is very easy to calculate. In addition, the new method can be applied to both data with or without ties. Simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers. PMID:17487941
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. PMID:23024035
Power/sample size calculations for assessing correlates of risk in clinical efficacy trials.
Gilbert, Peter B; Janes, Holly E; Huang, Yunda
2016-09-20
In a randomized controlled clinical trial that assesses treatment efficacy, a common objective is to assess the association of a measured biomarker response endpoint with the primary study endpoint in the active treatment group, using a case-cohort, case-control, or two-phase sampling design. Methods for power and sample size calculations for such biomarker association analyses typically do not account for the level of treatment efficacy, precluding interpretation of the biomarker association results in terms of biomarker effect modification of treatment efficacy, with detriment that the power calculations may tacitly and inadvertently assume that the treatment harms some study participants. We develop power and sample size methods accounting for this issue, and the methods also account for inter-individual variability of the biomarker that is not biologically relevant (e.g., due to technical measurement error). We focus on a binary study endpoint and on a biomarker subject to measurement error that is normally distributed or categorical with two or three levels. We illustrate the methods with preventive HIV vaccine efficacy trials and include an R package implementing the methods. Copyright © 2016 John Wiley & Sons, Ltd. PMID:27037797
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…
Sample size calculations for micro-randomized trials in mHealth.
Liao, Peng; Klasnja, Predrag; Tewari, Ambuj; Murphy, Susan A
2016-05-30
The use and development of mobile interventions are experiencing rapid growth. In "just-in-time" mobile interventions, treatments are provided via a mobile device, and they are intended to help an individual make healthy decisions 'in the moment,' and thus have a proximal, near future impact. Currently, the development of mobile interventions is proceeding at a much faster pace than that of associated data science methods. A first step toward developing data-based methods is to provide an experimental design for testing the proximal effects of these just-in-time treatments. In this paper, we propose a 'micro-randomized' trial design for this purpose. In a micro-randomized trial, treatments are sequentially randomized throughout the conduct of the study, with the result that each participant may be randomized at the 100s or 1000s of occasions at which a treatment might be provided. Further, we develop a test statistic for assessing the proximal effect of a treatment as well as an associated sample size calculator. We conduct simulation evaluations of the sample size calculator in various settings. Rules of thumb that might be used in designing a micro-randomized trial are discussed. This work is motivated by our collaboration on the HeartSteps mobile application designed to increase physical activity. Copyright © 2015 John Wiley & Sons, Ltd. PMID:26707831
Determination of reference limits: statistical concepts and tools for sample size calculation.
Wellek, Stefan; Lackner, Karl J; Jennen-Steinmetz, Christine; Reinhard, Iris; Hoffmann, Isabell; Blettner, Maria
2014-12-01
Reference limits are estimators for 'extreme' percentiles of the distribution of a quantitative diagnostic marker in the healthy population. In most cases, interest will be in the 90% or 95% reference intervals. The standard parametric method of determining reference limits consists of computing quantities of the form X̅±c·S. The proportion of covered values in the underlying population coincides with the specificity obtained when a measurement value falling outside the corresponding reference region is classified as diagnostically suspect. Nonparametrically, reference limits are estimated by means of so-called order statistics. In both approaches, the precision of the estimate depends on the sample size. We present computational procedures for calculating minimally required numbers of subjects to be enrolled in a reference study. The much more sophisticated concept of reference bands replacing statistical reference intervals in case of age-dependent diagnostic markers is also discussed. PMID:25029084
Reliable calculation in probabilistic logic: Accounting for small sample size and model uncertainty
Ferson, S.
1996-12-31
A variety of practical computational problems arise in risk and safety assessments, forensic statistics and decision analyses in which the probability of some event or proposition E is to be estimated from the probabilities of a finite list of related subevents or propositions F,G,H,.... In practice, the analyst`s knowledge may be incomplete in two ways. First, the probabilities of the subevents may be imprecisely known from statistical estimations, perhaps based on very small sample sizes. Second, relationships among the subevents may be known imprecisely. For instance, there may be only limited information about their stochastic dependencies. Representing probability estimates as interval ranges on has been suggested as a way to address the first source of imprecision. A suite of AND, OR and NOT operators defined with reference to the classical Frochet inequalities permit these probability intervals to be used in calculations that address the second source of imprecision, in many cases, in a best possible way. Using statistical confidence intervals as inputs unravels the closure properties of this approach however, requiring that probability estimates be characterized by a nested stack of intervals for all possible levels of statistical confidence, from a point estimate (0% confidence) to the entire unit interval (100% confidence). The corresponding logical operations implied by convolutive application of the logical operators for every possible pair of confidence intervals reduces by symmetry to a manageably simple level-wise iteration. The resulting calculus can be implemented in software that allows users to compute comprehensive and often level-wise best possible bounds on probabilities for logical functions of events.
Tavernier, Elsa; Giraudeau, Bruno
2015-01-01
We aimed to examine the extent to which inaccurate assumptions for nuisance parameters used to calculate sample size can affect the power of a randomized controlled trial (RCT). In a simulation study, we separately considered an RCT with continuous, dichotomous or time-to-event outcomes, with associated nuisance parameters of standard deviation, success rate in the control group and survival rate in the control group at some time point, respectively. For each type of outcome, we calculated a required sample size N for a hypothesized treatment effect, an assumed nuisance parameter and a nominal power of 80%. We then assumed a nuisance parameter associated with a relative error at the design stage. For each type of outcome, we randomly drew 10,000 relative errors of the associated nuisance parameter (from empirical distributions derived from a previously published review). Then, retro-fitting the sample size formula, we derived, for the pre-calculated sample size N, the real power of the RCT, taking into account the relative error for the nuisance parameter. In total, 23%, 0% and 18% of RCTs with continuous, binary and time-to-event outcomes, respectively, were underpowered (i.e., the real power was < 60%, as compared with the 80% nominal power); 41%, 16% and 6%, respectively, were overpowered (i.e., with real power > 90%). Even with proper calculation of sample size, a substantial number of trials are underpowered or overpowered because of imprecise knowledge of nuisance parameters. Such findings raise questions about how sample size for RCTs should be determined. PMID:26173007
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. PMID:22415870
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, 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...
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, 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, 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...
Power and Sample Size Calculation for Log-rank Test with a Time Lag in Treatment Effect
Zhang, Daowen; Quan, Hui
2009-01-01
Summary The log-rank test is the most powerful nonparametric test for detecting a proportional hazards alternative and thus is the most commonly used testing procedure for comparing time-to-event distributions between different treatments in clinical trials. When the log-rank test is used for the primary data analysis, the sample size calculation should also be based on the test to ensure the desired power for the study. In some clinical trials, the treatment effect may not manifest itself right after patients receive the treatment. Therefore, the proportional hazards assumption may not hold. Furthermore, patients may discontinue the study treatment prematurely and thus may have diluted treatment effect after treatment discontinuation. If a patient’s treatment termination time is independent of his/her time-to-event of interest, the termination time can be treated as a censoring time in the final data analysis. Alternatively, we may keep collecting time-to-event data until study termination from those patients who discontinued the treatment and conduct an intent-to-treat (ITT) analysis by including them in the original treatment groups. We derive formulas necessary to calculate the asymptotic power of the log-rank test under this non-proportional hazards alternative for the two data analysis strategies. Simulation studies indicate that the formulas provide accurate power for a variety of trial settings. A clinical trial example is used to illustrate the application of the proposed methods. PMID:19152230
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…
Neumann, Christoph; Taub, Margaret A.; Younkin, Samuel G.; Beaty, Terri H.; Ruczinski, Ingo; Schwender, Holger
2014-01-01
Case-parent trio studies considering genotype data from children affected by a disease and from their parents are frequently used to detect single nucleotide polymorphisms (SNPs) associated with disease. The most popular statistical tests in this study design are transmission/disequlibrium tests (TDTs). Several types of these tests have been developed, e.g., 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, it, however, 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 that 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 the tests have almost the same power, with the score test being slightly more powerful. PMID:25123830
Calculating body frame size (image)
... a person's wrist circumference in relation to his height. For example, a man whose height is over 5' 5" and wrist is 6" ... person is small, medium, or large boned. Women: Height under 5'2" Small = wrist size less than ...
Sample sizes for confidence limits for reliability.
Darby, John L.
2010-02-01
We recently performed an evaluation of the implications of a reduced stockpile of nuclear weapons for surveillance to support estimates of reliability. We found that one technique developed at Sandia National Laboratories (SNL) under-estimates the required sample size for systems-level testing. For a large population the discrepancy is not important, but for a small population it is important. We found that another technique used by SNL provides the correct required sample size. For systems-level testing of nuclear weapons, samples are selected without replacement, and the hypergeometric probability distribution applies. Both of the SNL techniques focus on samples without defects from sampling without replacement. We generalized the second SNL technique to cases with defects in the sample. We created a computer program in Mathematica to automate the calculation of confidence for reliability. We also evaluated sampling with replacement where the binomial probability distribution applies.
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 requirements for evaluating population size structure
Vokoun, J.C.; Rabeni, C.F.; Stanovick, J.S.
2001-01-01
A method with an accompanying computer program is described to estimate the number of individuals needed to construct a sample length-frequency with a given accuracy and precision. First, a reference length-frequency assumed to be accurate for a particular sampling gear and collection strategy was constructed. Bootstrap procedures created length-frequencies with increasing sample size that were randomly chosen from the reference data and then were compared with the reference length-frequency by calculating the mean squared difference. Outputs from two species collected with different gears and an artificial even length-frequency are used to describe the characteristics of the method. The relations between the number of individuals used to construct a length-frequency and the similarity to the reference length-frequency followed a negative exponential distribution and showed the importance of using 300-400 individuals whenever possible.
ERIC Educational Resources Information Center
Mendoza, Jorge L.; Stafford, Karen L.
2001-01-01
Introduces a computer package written for Mathematica, the purpose of which is to perform a number of difficult iterative functions with respect to the squared multiple correlation coefficient under the fixed and random models. These functions include computation of the confidence interval upper and lower bounds, power calculation, calculation of…
Sample Size and Correlational Inference
ERIC Educational Resources Information Center
Anderson, Richard B.; Doherty, Michael E.; Friedrich, Jeff C.
2008-01-01
In 4 studies, the authors examined the hypothesis that the structure of the informational environment makes small samples more informative than large ones for drawing inferences about population correlations. The specific purpose of the studies was to test predictions arising from the signal detection simulations of R. B. Anderson, M. E. Doherty,…
Methods for sample size determination in cluster randomized trials
Rutterford, Clare; Copas, Andrew; Eldridge, Sandra
2015-01-01
Background: The use of cluster randomized trials (CRTs) is increasing, along with the variety in their design and analysis. The simplest approach for their sample size calculation is to calculate the sample size assuming individual randomization and inflate this by a design effect to account for randomization by cluster. The assumptions of a simple design effect may not always be met; alternative or more complicated approaches are required. Methods: We summarise a wide range of sample size methods available for cluster randomized trials. For those familiar with sample size calculations for individually randomized trials but with less experience in the clustered case, this manuscript provides formulae for a wide range of scenarios with associated explanation and recommendations. For those with more experience, comprehensive summaries are provided that allow quick identification of methods for a given design, outcome and analysis method. Results: We present first those methods applicable to the simplest two-arm, parallel group, completely randomized design followed by methods that incorporate deviations from this design such as: variability in cluster sizes; attrition; non-compliance; or the inclusion of baseline covariates or repeated measures. The paper concludes with methods for alternative designs. Conclusions: There is a large amount of methodology available for sample size calculations in CRTs. This paper gives the most comprehensive description of published methodology for sample size calculation and provides an important resource for those designing these trials. PMID:26174515
How to Show that Sample Size Matters
ERIC Educational Resources Information Center
Kozak, Marcin
2009-01-01
This article suggests how to explain a problem of small sample size when considering correlation between two Normal variables. Two techniques are shown: one based on graphs and the other on simulation. (Contains 3 figures and 1 table.)
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.
Finite sample size effects in transformation kinetics
NASA Technical Reports Server (NTRS)
Weinberg, M. C.
1985-01-01
The effect of finite sample size on the kinetic law of phase transformations is considered. The case where the second phase develops by a nucleation and growth mechanism is treated under the assumption of isothermal conditions and constant and uniform nucleation rate. It is demonstrated that for spherical particle growth, a thin sample transformation formula given previously is an approximate version of a more general transformation law. The thin sample approximation is shown to be reliable when a certain dimensionless thickness is small. The latter quantity, rather than the actual sample thickness, determines when the usual law of transformation kinetics valid for bulk (large dimension) samples must be modified.
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
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
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…
A New Sample Size Formula for Regression.
ERIC Educational Resources Information Center
Brooks, Gordon P.; Barcikowski, Robert S.
The focus of this research was to determine the efficacy of a new method of selecting sample sizes for multiple linear regression. A Monte Carlo simulation was used to study both empirical predictive power rates and empirical statistical power rates of the new method and seven other methods: those of C. N. Park and A. L. Dudycha (1974); J. Cohen…
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.
Planning sample sizes when effect sizes are uncertain: The power-calibrated effect size approach.
McShane, Blakeley B; Böckenholt, Ulf
2016-03-01
Statistical power and thus the sample size required to achieve some desired level of power depend on the size of the effect of interest. However, effect sizes are seldom known exactly in psychological research. Instead, researchers often possess an estimate of an effect size as well as a measure of its uncertainty (e.g., a standard error or confidence interval). Previous proposals for planning sample sizes either ignore this uncertainty thereby resulting in sample sizes that are too small and thus power that is lower than the desired level or overstate the impact of this uncertainty thereby resulting in sample sizes that are too large and thus power that is higher than the desired level. We propose a power-calibrated effect size (PCES) approach to sample size planning that accounts for the uncertainty associated with an effect size estimate in a properly calibrated manner: sample sizes determined on the basis of the PCES are neither too small nor too large and thus provide the desired level of power. We derive the PCES for comparisons of independent and dependent means, comparisons of independent and dependent proportions, and tests of correlation coefficients. We also provide a tutorial on setting sample sizes for a replication study using data from prior studies and discuss an easy-to-use website and code that implement our PCES approach to sample size planning. PMID:26651984
Sample size re-estimation in a breast cancer trial
Hade, Erinn; Jarjoura, David; Wei, Lai
2016-01-01
Background During the recruitment phase of a randomized breast cancer trial, investigating the time to recurrence, we found evidence that the failure probabilities used at the design stage were too high. Since most of the methodological research involving sample size re-estimation has focused on normal or binary outcomes, we developed a method which preserves blinding to re-estimate sample size in our time to event trial. Purpose A mistakenly high estimate of the failure rate at the design stage may reduce the power unacceptably for a clinically important hazard ratio. We describe an ongoing trial and an application of a sample size re-estimation method that combines current trial data with prior trial data or assumes a parametric model to re-estimate failure probabilities in a blinded fashion. Methods Using our current blinded trial data and additional information from prior studies, we re-estimate the failure probabilities to be used in sample size re-calculation. We employ bootstrap resampling to quantify uncertainty in the re-estimated sample sizes. Results At the time of re-estimation data from 278 patients was available, averaging 1.2 years of follow up. Using either method, we estimated an increase of 0 for the hazard ratio proposed at the design stage. We show that our method of blinded sample size re-estimation preserves the Type I error rate. We show that when the initial guess of the failure probabilities are correct; the median increase in sample size is zero. Limitations Either some prior knowledge of an appropriate survival distribution shape or prior data is needed for re-estimation. Conclusions In trials when the accrual period is lengthy, blinded sample size re-estimation near the end of the planned accrual period should be considered. In our examples, when assumptions about failure probabilities and HRs are correct the methods usually do not increase sample size or otherwise increase it by very little. PMID:20392786
Determination and calculation of combustion heats of 20 lignite samples
Demirbas, A.; Dincer, K.; Topaloglu, N.
2008-07-01
In this study, the proximate analyses, such as volatile matter (VM), fixed carbon (FC), and higher heating value (HHV), were determined for 20 lignite samples from different areas of Turkey. The lignite samples have been tested with particle size of 0-0.05 mm. Combustion heats (higher heating values, HHVs) of 20 lignite samples obtained from different Turkish sources were determined experimentally and calculated from both ultimate and proximate analyses. The HHVs (MJ/kg) of the lignite samples as a function of fixed carbon (FC, wt%) or volatile materials (VM, %) was calculated from the following equations: HHV = 0.2997FC + 11.1170 (1) HHV = -0.3225VM + 42.223 (2). The correlation coefficients for Eqs. (1) and (2) were 0.9820 and 0.9686, respectively. The combustion heats calculated from Eqs. (1) and (2) showed mean differences of +0.4% and +0.4%, respectively.
The Fisher-Yates Exact Test and Unequal Sample Sizes
ERIC Educational Resources Information Center
Johnson, Edgar M.
1972-01-01
A computational short cut suggested by Feldman and Klinger for the one-sided Fisher-Yates exact test is clarified and is extended to the calculation of probability values for certain two-sided tests when sample sizes are unequal. (Author)
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.
Fast RPA and GW calculations: cubic system size scaling
NASA Astrophysics Data System (ADS)
Kresse, Georg
The random phase approximation (RPA) to the correlation energy and the related GW approximation are among the most promising methods to obtain accurate correlation energy differences and QP energies from diagrammatic perturbation theory at reasonable computational cost. The calculations are, however, usually one to two orders of magnitude more demanding than conventional density functional theory calculations. Here, we show that a cubic system size scaling can be readily obtained reducing the computation time by one to two orders of magnitude for large systems. Furthermore, the scaling with respect to the number of k points used to sample the Brillouin zone can be reduced to linear order. In combination, this allows accurate and very well-converged single-point RPA and GW calculations, with a time complexity that is roughly on par or better than for self-consistent Hartree-Fock and hybrid-functional calculations. Furthermore, the talk discusses the relation between the RPA correlation energy and the GW approximation: the self-energy is the derivative of the RPA correlation energy with respect to the Green's function. The calculated self-energy can be used to compute QP-energies in the GW approximation, any first derivative of the total energy, as well as corrections to the correlation energy from the changes of the charge density when switching from DFT to a many-body body description (GW singles energy contribution).
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
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 52.803 - Sample unit size.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Sample unit size. 52.803 Section 52.803 Agriculture... 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...
Disk calculator indicates legible lettering size for slide projection
NASA Technical Reports Server (NTRS)
Hultberg, R. R.
1965-01-01
Hand-operated disk calculator indicates the minimum size of letters and numbers in relation to the width and height of a working drawing. The lettering is legible when a slide of the drawing is projected.
Hand calculations for transport of radioactive aerosols through sampling systems.
Hogue, Mark; Thompson, Martha; Farfan, Eduardo; Hadlock, Dennis
2014-05-01
Workplace air monitoring programs for sampling radioactive aerosols in nuclear facilities sometimes must rely on sampling systems to move the air to a sample filter in a safe and convenient location. These systems may consist of probes, straight tubing, bends, contractions and other components. Evaluation of these systems for potential loss of radioactive aerosols is important because significant losses can occur. However, it can be very difficult to find fully described equations to model a system manually for a single particle size and even more difficult to evaluate total system efficiency for a polydispersed particle distribution. Some software methods are available, but they may not be directly applicable to the components being evaluated and they may not be completely documented or validated per current software quality assurance requirements. This paper offers a method to model radioactive aerosol transport in sampling systems that is transparent and easily updated with the most applicable models. Calculations are shown with the R Programming Language, but the method is adaptable to other scripting languages. The method has the advantage of transparency and easy verifiability. This paper shows how a set of equations from published aerosol science models may be applied to aspiration and transport efficiency of aerosols in common air sampling system components. An example application using R calculation scripts is demonstrated. The R scripts are provided as electronic attachments. PMID:24667389
40 CFR 600.208-77 - Sample calculation.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 29 2010-07-01 2010-07-01 false Sample calculation. 600.208-77 Section... Model Year Automobiles-Procedures for Calculating Fuel Economy Values § 600.208-77 Sample calculation. An example of the calculation required in this subpart appears in appendix III....
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)...
Sample Size Requirements for Discrete-Choice Experiments in Healthcare: a Practical Guide.
de Bekker-Grob, Esther W; Donkers, Bas; Jonker, Marcel F; Stolk, Elly A
2015-10-01
Discrete-choice experiments (DCEs) have become a commonly used instrument in health economics and patient-preference analysis, addressing a wide range of policy questions. An important question when setting up a DCE is the size of the sample needed to answer the research question of interest. Although theory exists as to the calculation of sample size requirements for stated choice data, it does not address the issue of minimum sample size requirements in terms of the statistical power of hypothesis tests on the estimated coefficients. The purpose of this paper is threefold: (1) to provide insight into whether and how researchers have dealt with sample size calculations for healthcare-related DCE studies; (2) to introduce and explain the required sample size for parameter estimates in DCEs; and (3) to provide a step-by-step guide for the calculation of the minimum sample size requirements for DCEs in health care. PMID:25726010
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. PMID:21823805
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…
Bouman, A. C.; ten Cate-Hoek, A. J.; Ramaekers, B. L. T.; Joore, M. A.
2015-01-01
Background Non-inferiority trials are performed when the main therapeutic effect of the new therapy is expected to be not unacceptably worse than that of the standard therapy, and the new therapy is expected to have advantages over the standard therapy in costs or other (health) consequences. These advantages however are not included in the classic frequentist approach of sample size calculation for non-inferiority trials. In contrast, the decision theory approach of sample size calculation does include these factors. The objective of this study is to compare the conceptual and practical aspects of the frequentist approach and decision theory approach of sample size calculation for non-inferiority trials, thereby demonstrating that the decision theory approach is more appropriate for sample size calculation of non-inferiority trials. Methods The frequentist approach and decision theory approach of sample size calculation for non-inferiority trials are compared and applied to a case of a non-inferiority trial on individually tailored duration of elastic compression stocking therapy compared to two years elastic compression stocking therapy for the prevention of post thrombotic syndrome after deep vein thrombosis. Results The two approaches differ substantially in conceptual background, analytical approach, and input requirements. The sample size calculated according to the frequentist approach yielded 788 patients, using a power of 80% and a one-sided significance level of 5%. The decision theory approach indicated that the optimal sample size was 500 patients, with a net value of €92 million. Conclusions This study demonstrates and explains the differences between the classic frequentist approach and the decision theory approach of sample size calculation for non-inferiority trials. We argue that the decision theory approach of sample size estimation is most suitable for sample size calculation of non-inferiority trials. PMID:26076354
40 CFR 89.418 - Raw emission sampling calculations.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 20 2010-07-01 2010-07-01 false Raw emission sampling calculations. 89... Test Procedures § 89.418 Raw emission sampling calculations. (a) The final test results shall be... cases where the reference conditions vary from those stated, an error may occur in the calculations....
Strategies for Field Sampling When Large Sample Sizes are Required
Technology Transfer Automated Retrieval System (TEKTRAN)
Estimates of prevalence or incidence of infection with a pathogen endemic in a fish population can be valuable information for development and evaluation of aquatic animal health management strategies. However, hundreds of unbiased samples may be required in order to accurately estimate these parame...
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...
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. PMID:26999385
Simple, Defensible Sample Sizes Based on Cost Efficiency
Bacchetti, Peter; McCulloch, Charles E.; Segal, Mark R.
2009-01-01
Summary The conventional approach of choosing sample size to provide 80% or greater power ignores the cost implications of different sample size choices. Costs, however, are often impossible for investigators and funders to ignore in actual practice. Here, we propose and justify a new approach for choosing sample size based on cost efficiency, the ratio of a study’s projected scientific and/or practical value to its total cost. By showing that a study’s projected value exhibits diminishing marginal returns as a function of increasing sample size for a wide variety of definitions of study value, we are able to develop two simple choices that can be defended as more cost efficient than any larger sample size. The first is to choose the sample size that minimizes the average cost per subject. The second is to choose sample size to minimize total cost divided by the square root of sample size. This latter method is theoretically more justifiable for innovative studies, but also performs reasonably well and has some justification in other cases. For example, if projected study value is assumed to be proportional to power at a specific alternative and total cost is a linear function of sample size, then this approach is guaranteed either to produce more than 90% power or to be more cost efficient than any sample size that does. These methods are easy to implement, based on reliable inputs, and well justified, so they should be regarded as acceptable alternatives to current conventional approaches. PMID:18482055
Julious, Steven A; Cooper, Cindy L; Campbell, Michael J
2015-01-01
Sample size justification is an important consideration when planning a clinical trial, not only for the main trial but also for any preliminary pilot trial. When the outcome is a continuous variable, the sample size calculation requires an accurate estimate of the standard deviation of the outcome measure. A pilot trial can be used to get an estimate of the standard deviation, which could then be used to anticipate what may be observed in the main trial. However, an important consideration is that pilot trials often estimate the standard deviation parameter imprecisely. This paper looks at how we can choose an external pilot trial sample size in order to minimise the sample size of the overall clinical trial programme, that is, the pilot and the main trial together. We produce a method of calculating the optimal solution to the required pilot trial sample size when the standardised effect size for the main trial is known. However, as it may not be possible to know the standardised effect size to be used prior to the pilot trial, approximate rules are also presented. For a main trial designed with 90% power and two-sided 5% significance, we recommend pilot trial sample sizes per treatment arm of 75, 25, 15 and 10 for standardised effect sizes that are extra small (≤0.1), small (0.2), medium (0.5) or large (0.8), respectively. PMID:26092476
7 CFR 51.2341 - Sample size for grade determination.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Sample size for grade determination. 51.2341 Section..., AND STANDARDS) United States Standards for Grades of Kiwifruit § 51.2341 Sample size for grade determination. For fruit place-packed in tray pack containers, the sample shall consist of the contents of...
Defect density: a review on the calculation of size program
NASA Astrophysics Data System (ADS)
Hasim, Nurdatillah; Abd Rahman, Aedah
2011-12-01
Defect density is a measurement conducted in one of Malaysia's ICT leading company. This paper will be discussing on issues of defect density measurement. Regarding defects counted, in order to calculate defect density, we also need to consider the total size of product that is the system size. Generally, defect density is a measure of the number of total defect found divided by the size of the system measured. Therefore, the system size is measured by lines of code. Selected projects in the company have been identified and GeroneSoft Code Counter Pro V1.32 is used as tool to count the lines of code. To this end, the paper presents method used. Analyzed defect density data are represented using control chart because shows the capability of the process so that the achievable goal can be set.
A computer program for sample size computations for banding studies
Wilson, K.R.; Nichols, J.D.; Hines, J.E.
1989-01-01
Sample sizes necessary for estimating survival rates of banded birds, adults and young, are derived based on specified levels of precision. The banding study can be new or ongoing. The desired coefficient of variation (CV) for annual survival estimates, the CV for mean annual survival estimates, and the length of the study must be specified to compute sample sizes. A computer program is available for computation of the sample sizes, and a description of the input and output is provided.
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.
A review of software for sample size determination.
Dattalo, Patrick
2009-09-01
The size of a sample is an important element in determining the statistical precision with which population values can be estimated. This article identifies and describes free and commercial programs for sample size determination. Programs are categorized as follows: (a) multiple procedure for sample size determination; (b) single procedure for sample size determination; and (c) Web-based. Programs are described in terms of (a) cost; (b) ease of use, including interface, operating system and hardware requirements, and availability of documentation and technical support; (c) file management, including input and output formats; and (d) analytical and graphical capabilities. PMID:19696082
40 CFR 80.127 - Sample size guidelines.
Code of Federal Regulations, 2013 CFR
2013-07-01
...) 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...
40 CFR 80.127 - Sample size guidelines.
Code of Federal Regulations, 2014 CFR
2014-07-01
...) 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...
40 CFR 80.127 - Sample size guidelines.
Code of Federal Regulations, 2012 CFR
2012-07-01
...) 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)...
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...
40 CFR 91.419 - Raw emission sampling calculations.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 20 2010-07-01 2010-07-01 false Raw emission sampling calculations. 91... Raw emission sampling calculations. (a) Derive the final test results through the steps described in... following equations are to be used when fuel flow is selected as the basis for mass emission...
40 CFR 91.419 - Raw emission sampling calculations.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 21 2013-07-01 2013-07-01 false Raw emission sampling calculations. 91.419 Section 91.419 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) CONTROL OF EMISSIONS FROM MARINE SPARK-IGNITION ENGINES Gaseous Exhaust Test Procedures § 91.419 Raw emission sampling calculations....
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…
7 CFR 52.775 - Sample unit size.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Sample unit size. 52.775 Section 52.775 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... United States Standards for Grades of Canned Red Tart Pitted Cherries 1 Sample Unit Size § 52.775...
Minimum Sample Size Recommendations for Conducting Factor Analyses
ERIC Educational Resources Information Center
Mundfrom, Daniel J.; Shaw, Dale G.; Ke, Tian Lu
2005-01-01
There is no shortage of recommendations regarding the appropriate sample size to use when conducting a factor analysis. Suggested minimums for sample size include from 3 to 20 times the number of variables and absolute ranges from 100 to over 1,000. For the most part, there is little empirical evidence to support these recommendations. This…
Power Analysis and Sample Size Determination in Metabolic Phenotyping.
Blaise, Benjamin J; Correia, Gonçalo; Tin, Adrienne; Young, J Hunter; Vergnaud, Anne-Claire; Lewis, Matthew; Pearce, Jake T M; Elliott, Paul; Nicholson, Jeremy K; Holmes, Elaine; Ebbels, Timothy M D
2016-05-17
Estimation of statistical power and sample size is a key aspect of experimental design. However, in metabolic phenotyping, there is currently no accepted approach for these tasks, in large part due to the unknown nature of the expected effect. In such hypothesis free science, neither the number or class of important analytes nor the effect size are known a priori. We introduce a new approach, based on multivariate simulation, which deals effectively with the highly correlated structure and high-dimensionality of metabolic phenotyping data. First, a large data set is simulated based on the characteristics of a pilot study investigating a given biomedical issue. An effect of a given size, corresponding either to a discrete (classification) or continuous (regression) outcome is then added. Different sample sizes are modeled by randomly selecting data sets of various sizes from the simulated data. We investigate different methods for effect detection, including univariate and multivariate techniques. Our framework allows us to investigate the complex relationship between sample size, power, and effect size for real multivariate data sets. For instance, we demonstrate for an example pilot data set that certain features achieve a power of 0.8 for a sample size of 20 samples or that a cross-validated predictivity QY(2) of 0.8 is reached with an effect size of 0.2 and 200 samples. We exemplify the approach for both nuclear magnetic resonance and liquid chromatography-mass spectrometry data from humans and the model organism C. elegans. PMID:27116637
Mesh size and code option effects of strength calculations
Kaul, Ann M
2010-12-10
Modern Lagrangian hydrodynamics codes include numerical methods which allow calculations to proceed past the point obtainable by a purely Lagrangian scheme. These options can be employed as the user deems necessary to 'complete' a calculation. While one could argue that any calculation is better than none, to truly understand the calculated results and their relationship to physical reality, the user needs to understand how their runtime choices affect the calculated results. One step toward this goal is to understand the effect of each runtime choice on particular pieces of the code physics. This paper will present simulation results for some experiments typically used for strength model validation. Topics to be covered include effect of mesh size, use of various ALE schemes for mesh detangling, and use of anti-hour-glassing schemes. Experiments to be modeled include the lower strain rate ({approx} 10{sup 4} s{sup -1}) gas gun driven Taylor impact experiments and the higher strain rate ({approx} 10{sup 5}-10{sup 6} s{sup -1}) HE products driven perturbed plate experiments. The necessary mesh resolution and the effect of the code runtime options are highly dependent on the amount of localization of strain and stress in each experiment. In turn, this localization is dependent on the geometry of the experimental setup and the drive conditions.
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...
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 Size Requirements for Comparing Two Alpha Coefficients.
ERIC Educational Resources Information Center
Bonnett, Douglas G.
2003-01-01
Derived general formulas to determine the sample size requirements for hypothesis testing with desired power and interval estimation with desired precision. Illustrated the approach with the example of a screening test for adolescent attention deficit disorder. (SLD)
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…
Hickson, Kevin J; O'Keefe, Graeme J
2014-09-01
The scalable XCAT voxelised phantom was used with the GATE Monte Carlo toolkit to investigate the effect of voxel size on dosimetry estimates of internally distributed radionuclide calculated using direct Monte Carlo simulation. A uniformly distributed Fluorine-18 source was simulated in the Kidneys of the XCAT phantom with the organ self dose (kidney ← kidney) and organ cross dose (liver ← kidney) being calculated for a number of organ and voxel sizes. Patient specific dose factors (DF) from a clinically acquired FDG PET/CT study have also been calculated for kidney self dose and liver ← kidney cross dose. Using the XCAT phantom it was found that significantly small voxel sizes are required to achieve accurate calculation of organ self dose. It has also been used to show that a voxel size of 2 mm or less is suitable for accurate calculations of organ cross dose. To compensate for insufficient voxel sampling a correction factor is proposed. This correction factor is applied to the patient specific dose factors calculated with the native voxel size of the PET/CT study. PMID:24859803
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…
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. PMID:24647821
Sample size requirements for training high-dimensional risk predictors
Dobbin, Kevin K.; Song, Xiao
2013-01-01
A common objective of biomarker studies is to develop a predictor of patient survival outcome. Determining the number of samples required to train a predictor from survival data is important for designing such studies. Existing sample size methods for training studies use parametric models for the high-dimensional data and cannot handle a right-censored dependent variable. We present a new training sample size method that is non-parametric with respect to the high-dimensional vectors, and is developed for a right-censored response. The method can be applied to any prediction algorithm that satisfies a set of conditions. The sample size is chosen so that the expected performance of the predictor is within a user-defined tolerance of optimal. The central method is based on a pilot dataset. To quantify uncertainty, a method to construct a confidence interval for the tolerance is developed. Adequacy of the size of the pilot dataset is discussed. An alternative model-based version of our method for estimating the tolerance when no adequate pilot dataset is available is presented. The model-based method requires a covariance matrix be specified, but we show that the identity covariance matrix provides adequate sample size when the user specifies three key quantities. Application of the sample size method to two microarray datasets is discussed. PMID:23873895
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.
Two-stage chain sampling inspection plans with different sample sizes in the two stages
NASA Technical Reports Server (NTRS)
Stephens, K. S.; Dodge, H. F.
1976-01-01
A further generalization of the family of 'two-stage' chain sampling inspection plans is developed - viz, the use of different sample sizes in the two stages. Evaluation of the operating characteristics is accomplished by the Markov chain approach of the earlier work, modified to account for the different sample sizes. Markov chains for a number of plans are illustrated and several algebraic solutions are developed. Since these plans involve a variable amount of sampling, an evaluation of the average sampling number (ASN) is developed. A number of OC curves and ASN curves are presented. Some comparisons with plans having only one sample size are presented and indicate that improved discrimination is achieved by the two-sample-size plans.
Sample sizes in dosage investigational clinical trials: a systematic evaluation.
Huang, Ji-Han; Su, Qian-Min; Yang, Juan; Lv, Ying-Hua; He, Ying-Chun; Chen, Jun-Chao; Xu, Ling; Wang, Kun; Zheng, Qing-Shan
2015-01-01
The main purpose of investigational phase II clinical trials is to explore indications and effective doses. However, as yet, there is no clear rule and no related published literature about the precise suitable sample sizes to be used in phase II clinical trials. To explore this, we searched for clinical trials in the ClinicalTrials.gov registry using the keywords "dose-finding" or "dose-response" and "Phase II". The time span of the search was September 20, 1999, to December 31, 2013. A total of 2103 clinical trials were finally included in our review. Regarding sample sizes, 1,156 clinical trials had <40 participants in each group, accounting for 55.0% of the studies reviewed, and only 17.2% of the studies reviewed had >100 patient cases in a single group. Sample sizes used in parallel study designs tended to be larger than those of crossover designs (median sample size 151 and 37, respectively). In conclusion, in the earlier phases of drug research and development, there are a variety of designs for dosage investigational studies. The sample size of each trial should be comprehensively considered and selected according to the study design and purpose. PMID:25609916
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.
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 livestock movement network data.
Pfeiffer, Caitlin N; Firestone, Simon M; Campbell, Angus J D; Larsen, John W A; Stevenson, Mark A
2015-12-01
The movement of animals between farms contributes to infectious disease spread in production animal populations, and is increasingly investigated with social network analysis methods. Tangible outcomes of this work include the identification of high-risk premises for targeting surveillance or control programs. However, knowledge of the effect of sampling or incomplete network enumeration on these studies is limited. In this study, a simulation algorithm is presented that provides an estimate of required sampling proportions based on predicted network size, density and degree value distribution. The algorithm may be applied a priori to ensure network analyses based on sampled or incomplete data provide population estimates of known precision. Results demonstrate that, for network degree measures, sample size requirements vary with sampling method. The repeatability of the algorithm output under constant network and sampling criteria was found to be consistent for networks with at least 1000 nodes (in this case, farms). Where simulated networks can be constructed to closely mimic the true network in a target population, this algorithm provides a straightforward approach to determining sample size under a given sampling procedure for a network measure of interest. It can be used to tailor study designs of known precision, for investigating specific livestock movement networks and their impact on disease dissemination within populations. PMID:26276397
Fujita, Masahiro; Yajima, Tomonari; Iijima, Kazuaki; Sato, Kiyoshi
2012-05-01
The uncertainty in pesticide residue levels (UPRL) associated with sampling size was estimated using individual acetamiprid and cypermethrin residue data from preharvested apple, broccoli, cabbage, grape, and sweet pepper samples. The relative standard deviation from the mean of each sampling size (n = 2(x), where x = 1-6) of randomly selected samples was defined as the UPRL for each sampling size. The estimated UPRLs, which were calculated on the basis of the regulatory sampling size recommended by the OECD Guidelines on Crop Field Trials (weights from 1 to 5 kg, and commodity unit numbers from 12 to 24), ranged from 2.1% for cypermethrin in sweet peppers to 14.6% for cypermethrin in cabbage samples. The percentages of commodity exceeding the maximum residue limits (MRLs) specified by the Japanese Food Sanitation Law may be predicted from the equation derived from this study, which was based on samples of various size ranges with mean residue levels below the MRL. The estimated UPRLs have confirmed that sufficient sampling weight and numbers are required for analysis and/or re-examination of subsamples to provide accurate values of pesticide residue levels for the enforcement of MRLs. The equation derived from the present study would aid the estimation of more accurate residue levels even from small sampling sizes. PMID:22475588
Approximate sample sizes required to estimate length distributions
Miranda, L.E.
2007-01-01
The sample sizes required to estimate fish length were determined by bootstrapping from reference length distributions. Depending on population characteristics and species-specific maximum lengths, 1-cm length-frequency histograms required 375-1,200 fish to estimate within 10% with 80% confidence, 2.5-cm histograms required 150-425 fish, proportional stock density required 75-140 fish, and mean length required 75-160 fish. In general, smaller species, smaller populations, populations with higher mortality, and simpler length statistics required fewer samples. Indices that require low sample sizes may be suitable for monitoring population status, and when large changes in length are evident, additional sampling effort may be allocated to more precisely define length status with more informative estimators. ?? Copyright by the American Fisheries Society 2007.
Rubow, K.L.; Marple, V.A.; Cantrell, B.K.
1995-12-31
Researchers are becoming increasingly concerned with airborne particulate matter, not only in the respirable size range, but also in larger size ranges. International Standards Organization (ISO) and the American Conference of Governmental Industrial Hygienist (ACGIH) have developed standards for {open_quotes}inhalable{close_quotes} and {open_quotes}thoracic{close_quotes} particulate matter. These require sampling particles up to approximately 100 {mu}m in diameter. The size distribution and mass concentration of airborne particulate matter have been measured in air quality studies of the working sections of more than 20 underground mines by University of Minnesota and U.S. Bureau of Mines personnel. Measurements have been made in more than 15 coal mines and five metal/nonmetal mines over the past eight years. Although mines using diesel-powered equipment were emphasized, mines using all-electric powered equipment were also included. Particle sampling was conducted at fixed locations, i.e., mine portal, ventilation intake entry, haulageways, ventilation return entry, and near raincars, bolters and load-haul-dump equipment. The primary sampling device used was the MSP Model 100 micro-orifice uniform deposit impactor (MOUDI). The MOUDI samples at a flow rate of 30 LPM and. provides particle size distribution information for particles primarily in the 0.1 to 18 {mu}m size range. Up to five MOUDI samplers were simultaneously deployed at the fixed locations. Sampling times were typically 4 to 6 hrs/shift. Results from these field studies have been summarized to determine the average size distributions and mass concentrations at various locations in the mine section sampled. From these average size distributions, predictions are made regarding the expected levels of respirable and thoracic mass concentrations as defined by various health-based size-selective aerosol-sampling criteria.
A simulation study of sample size for DNA barcoding.
Luo, Arong; Lan, Haiqiang; Ling, Cheng; Zhang, Aibing; Shi, Lei; Ho, Simon Y W; Zhu, Chaodong
2015-12-01
For some groups of organisms, DNA barcoding can provide a useful tool in taxonomy, evolutionary biology, and biodiversity assessment. However, the efficacy of DNA barcoding depends on the degree of sampling per species, because a large enough sample size is needed to provide a reliable estimate of genetic polymorphism and for delimiting species. We used a simulation approach to examine the effects of sample size on four estimators of genetic polymorphism related to DNA barcoding: mismatch distribution, nucleotide diversity, the number of haplotypes, and maximum pairwise distance. Our results showed that mismatch distributions derived from subsamples of ≥20 individuals usually bore a close resemblance to that of the full dataset. Estimates of nucleotide diversity from subsamples of ≥20 individuals tended to be bell-shaped around that of the full dataset, whereas estimates from smaller subsamples were not. As expected, greater sampling generally led to an increase in the number of haplotypes. We also found that subsamples of ≥20 individuals allowed a good estimate of the maximum pairwise distance of the full dataset, while smaller ones were associated with a high probability of underestimation. Overall, our study confirms the expectation that larger samples are beneficial for the efficacy of DNA barcoding and suggests that a minimum sample size of 20 individuals is needed in practice for each population. PMID:26811761
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 error…
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
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,…
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
An Investigation of Sample Size Splitting on ATFIND and DIMTEST
ERIC Educational Resources Information Center
Socha, Alan; DeMars, Christine E.
2013-01-01
Modeling multidimensional test data with a unidimensional model can result in serious statistical errors, such as bias in item parameter estimates. Many methods exist for assessing the dimensionality of a test. The current study focused on DIMTEST. Using simulated data, the effects of sample size splitting for use with the ATFIND procedure for…
Sampling and surface reconstruction with adaptive-size meshes
NASA Astrophysics Data System (ADS)
Huang, Wen-Chen; Goldgof, Dmitry B.
1992-03-01
This paper presents a new approach to sampling and surface reconstruction which uses the physically based models. We introduce adaptive-size meshes which automatically update the size of the meshes as the distance between the nodes changes. We have implemented the adaptive-size algorithm to the following three applications: (1) Sampling of the intensity data. (2) Surface reconstruction of the range data. (3) Surface reconstruction of the 3-D computed tomography left ventricle data. The LV data was acquired by the 3-D computed tomography (CT) scanner. It was provided by Dr. Eric Hoffman at University of Pennsylvania Medical school and consists of 16 volumetric (128 X 128 X 118) images taken through the heart cycle.
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.
ERIC Educational Resources Information Center
Smith, Margaret H.
2004-01-01
Unless the sample encompasses a substantial portion of the population, the standard error of an estimator depends on the size of the sample, but not the size of the population. This is a crucial statistical insight that students find very counterintuitive. After trying several ways of convincing students of the validity of this principle, I have…
The PowerAtlas: a power and sample size atlas for microarray experimental design and research
Page, Grier P; Edwards, Jode W; Gadbury, Gary L; Yelisetti, Prashanth; Wang, Jelai; Trivedi, Prinal; Allison, David B
2006-01-01
Background Microarrays permit biologists to simultaneously measure the mRNA abundance of thousands of genes. An important issue facing investigators planning microarray experiments is how to estimate the sample size required for good statistical power. What is the projected sample size or number of replicate chips needed to address the multiple hypotheses with acceptable accuracy? Statistical methods exist for calculating power based upon a single hypothesis, using estimates of the variability in data from pilot studies. There is, however, a need for methods to estimate power and/or required sample sizes in situations where multiple hypotheses are being tested, such as in microarray experiments. In addition, investigators frequently do not have pilot data to estimate the sample sizes required for microarray studies. Results To address this challenge, we have developed a Microrarray PowerAtlas [1]. The atlas enables estimation of statistical power by allowing investigators to appropriately plan studies by building upon previous studies that have similar experimental characteristics. Currently, there are sample sizes and power estimates based on 632 experiments from Gene Expression Omnibus (GEO). The PowerAtlas also permits investigators to upload their own pilot data and derive power and sample size estimates from these data. This resource will be updated regularly with new datasets from GEO and other databases such as The Nottingham Arabidopsis Stock Center (NASC). Conclusion This resource provides a valuable tool for investigators who are planning efficient microarray studies and estimating required sample sizes. PMID:16504070
Effective Sample Size in Diffuse Reflectance Near-IR Spectrometry.
Berntsson, O; Burger, T; Folestad, S; Danielsson, L G; Kuhn, J; Fricke, J
1999-02-01
Two independent methods for determination of the effectively sampled mass per unit area are presented and compared. The first method combines directional-hemispherical transmittance and reflectance measurements. A three-flux approximation of the equation of radiative transfer is used, to separately determine the specific absorption and scattering coefficients of the powder material, which subsequently are used to determine the effective sample size. The second method uses a number of diffuse reflectance measurements on layers of controlled powder thickness in an empirical approach. The two methods are shown to agree well and thus confirm each other. From the determination of the effective sample size at each measured wavelength in the visible-NIR region for two different model powder materials, large differences was found, both between the two analyzed powders and between different wavelengths. As an example, the effective sample size ranges between 15 and 70 mg/cm(2) for microcrystalline cellulose and between 70 and 300 mg/cm(2) for film-coated pellets. However, the contribution to the spectral information obtained from a certain layer decreases rapidly with increasing distance from the powder surface. With both methods, the extent of contribution from various depths of a powder sample to the visible-NIR diffuse reflection signal is characterized. This information is valuable for validation of analytical applications of diffuse reflectance visible-NIR spectrometry. PMID:21662719
McCain, J.D.; Dawes, S.S.; Farthing, W.E.
1986-05-01
The report is Attachment No. 2 to the Final Report of ARB Contract A3-092-32 and provides a tutorial on the use of Cascade (Series) Cyclones to obtain size-fractionated particulate samples from industrial flue gases at stationary sources. The instrumentation and procedures described are designed to protect the purity of the collected samples so that post-test chemical analysis may be performed for organic and inorganic compounds, including instrumental analysis for trace elements. The instrumentation described collects bulk quantities for each of six size fractions over the range 10 to 0.4 micrometer diameter. The report describes the operating principles, calibration, and empirical modeling of small cyclone performance. It also discusses the preliminary calculations, operation, sample retrieval, and data analysis associated with the use of cyclones to obtain size-segregated samples and to measure particle-size distributions.
Computing Confidence Bounds for Power and Sample Size of the General Linear Univariate Model
Taylor, Douglas J.; Muller, Keith E.
2013-01-01
The power of a test, the probability of rejecting the null hypothesis in favor of an alternative, may be computed using estimates of one or more distributional parameters. Statisticians frequently fix mean values and calculate power or sample size using a variance estimate from an existing study. Hence computed power becomes a random variable for a fixed sample size. Likewise, the sample size necessary to achieve a fixed power varies randomly. Standard statistical practice requires reporting uncertainty associated with such point estimates. Previous authors studied an asymptotically unbiased method of obtaining confidence intervals for noncentrality and power of the general linear univariate model in this setting. We provide exact confidence intervals for noncentrality, power, and sample size. Such confidence intervals, particularly one-sided intervals, help in planning a future study and in evaluating existing studies. PMID:24039272
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
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
Surprise Calculator: Estimating relative entropy and Surprise between samples
NASA Astrophysics Data System (ADS)
Seehars, Sebastian
2016-05-01
The Surprise is a measure for consistency between posterior distributions and operates in parameter space. It can be used to analyze either the compatibility of separately analyzed posteriors from two datasets, or the posteriors from a Bayesian update. The Surprise Calculator estimates relative entropy and Surprise between two samples, assuming they are Gaussian. The software requires the R package CompQuadForm to estimate the significance of the Surprise, and rpy2 to interface R with Python.
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.
(Sample) Size Matters: Defining Error in Planktic Foraminiferal Isotope Measurement
NASA Astrophysics Data System (ADS)
Lowery, C.; Fraass, A. J.
2015-12-01
Planktic foraminifera have been used as carriers of stable isotopic signals since the pioneering work of Urey and Emiliani. In those heady days, instrumental limitations required hundreds of individual foraminiferal tests to return a usable value. This had the fortunate side-effect of smoothing any seasonal to decadal changes within the planktic foram population, which generally turns over monthly, removing that potential noise from each sample. With the advent of more sensitive mass spectrometers, smaller sample sizes have now become standard. This has been a tremendous advantage, allowing longer time series with the same investment of time and energy. Unfortunately, the use of smaller numbers of individuals to generate a data point has lessened the amount of time averaging in the isotopic analysis and decreased precision in paleoceanographic datasets. With fewer individuals per sample, the differences between individual specimens will result in larger variation, and therefore error, and less precise values for each sample. Unfortunately, most workers (the authors included) do not make a habit of reporting the error associated with their sample size. We have created an open-source model in R to quantify the effect of sample sizes under various realistic and highly modifiable parameters (calcification depth, diagenesis in a subset of the population, improper identification, vital effects, mass, etc.). For example, a sample in which only 1 in 10 specimens is diagenetically altered can be off by >0.3‰ δ18O VPDB or ~1°C. Additionally, and perhaps more importantly, we show that under unrealistically ideal conditions (perfect preservation, etc.) it takes ~5 individuals from the mixed-layer to achieve an error of less than 0.1‰. Including just the unavoidable vital effects inflates that number to ~10 individuals to achieve ~0.1‰. Combining these errors with the typical machine error inherent in mass spectrometers make this a vital consideration moving forward.
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.
Chaibub Neto, Elias
2015-01-01
In this paper we propose a vectorized implementation of the non-parametric bootstrap for statistics based on sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of sample moment statistics by simply weighting the observed data according to multinomial counts instead of evaluating the statistic on a resampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights and compute the entire vector of bootstrap replications with a few matrix multiplications. Vectorization is particularly important for matrix-oriented programming languages such as R, where matrix/vector calculations tend to be faster than scalar operations implemented in a loop. We illustrate the application of the vectorized implementation in real and simulated data sets, when bootstrapping Pearson’s sample correlation coefficient, and compared its performance against two state-of-the-art R implementations of the non-parametric bootstrap, as well as a straightforward one based on a for loop. Our investigations spanned varying sample sizes and number of bootstrap replications. The vectorized bootstrap compared favorably against the state-of-the-art implementations in all cases tested, and was remarkably/considerably faster for small/moderate sample sizes. The same results were observed in the comparison with the straightforward implementation, except for large sample sizes, where the vectorized bootstrap was slightly slower than the straightforward implementation due to increased time expenditures in the generation of weight matrices via multinomial sampling. PMID:26125965
Air sampling filtration media: Collection efficiency for respirable size-selective sampling
Soo, Jhy-Charm; Monaghan, Keenan; Lee, Taekhee; Kashon, Mike; Harper, Martin
2016-01-01
The collection efficiencies of commonly used membrane air sampling filters in the ultrafine particle size range were investigated. Mixed cellulose ester (MCE; 0.45, 0.8, 1.2, and 5 μm pore sizes), polycarbonate (0.4, 0.8, 2, and 5 μm pore sizes), polytetrafluoroethylene (PTFE; 0.45, 1, 2, and 5 μm pore sizes), polyvinyl chloride (PVC; 0.8 and 5 μm pore sizes), and silver membrane (0.45, 0.8, 1.2, and 5 μm pore sizes) filters were exposed to polydisperse sodium chloride (NaCl) particles in the size range of 10–400 nm. Test aerosols were nebulized and introduced into a calm air chamber through a diffusion dryer and aerosol neutralizer. The testing filters (37 mm diameter) were mounted in a conductive polypropylene filter-holder (cassette) within a metal testing tube. The experiments were conducted at flow rates between 1.7 and 11.2 l min−1. The particle size distributions of NaCl challenge aerosol were measured upstream and downstream of the test filters by a scanning mobility particle sizer (SMPS). Three different filters of each type with at least three repetitions for each pore size were tested. In general, the collection efficiency varied with airflow, pore size, and sampling duration. In addition, both collection efficiency and pressure drop increased with decreased pore size and increased sampling flow rate, but they differed among filter types and manufacturer. The present study confirmed that the MCE, PTFE, and PVC filters have a relatively high collection efficiency for challenge particles much smaller than their nominal pore size and are considerably more efficient than polycarbonate and silver membrane filters, especially at larger nominal pore sizes. PMID:26834310
Sample size determination for longitudinal designs with binary response.
Kapur, Kush; Bhaumik, Runa; Tang, X Charlene; Hur, Kwan; Reda, Domenic J; Bhaumik, Dulal K
2014-09-28
In this article, we develop appropriate statistical methods for determining the required sample size while comparing the efficacy of an intervention to a control with repeated binary response outcomes. Our proposed methodology incorporates the complexity of the hierarchical nature of underlying designs and provides solutions when varying attrition rates are present over time. We explore how the between-subject variability and attrition rates jointly influence the computation of sample size formula. Our procedure also shows how efficient estimation methods play a crucial role in power analysis. A practical guideline is provided when information regarding individual variance component is unavailable. The validity of our methods is established by extensive simulation studies. Results are illustrated with the help of two randomized clinical trials in the areas of contraception and insomnia. PMID:24820424
Effect of sample size on deformation in amorphous metals
NASA Astrophysics Data System (ADS)
Volkert, C. A.; Donohue, A.; Spaepen, F.
2008-04-01
Uniaxial compression tests were performed on micron-sized columns of amorphous PdSi to investigate the effect of sample size on deformation behavior. Cylindrical columns with diameters between 8μm and 140nm were fabricated from sputtered amorphous Pd77Si23 films on Si substrates by focused ion beam machining and compression tests were performed with a nanoindenter outfitted with a flat diamond punch. The columns exhibited elastic behavior until they yielded by either shear band formation on a plane at 50° to the loading axis or by homogenous deformation. Shear band formation occurred only in columns with diameters larger than 400nm. The change in deformation mechanism from shear band formation to homogeneous deformation with decreasing column size is attributed to a required critical strained volume for shear band formation.
Sample size determination for testing equality in a cluster randomized trial with noncompliance.
Lui, Kung-Jong; Chang, Kuang-Chao
2011-01-01
For administrative convenience or cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients rather than individual patients. Furthermore, because of ethical reasons or patient's decision, it is not uncommon to encounter data in which there are patients not complying with their assigned treatments. Thus, the development of a sample size calculation procedure for a CRT with noncompliance is important and useful in practice. Under the exclusion restriction model, we have developed an asymptotic test procedure using a tanh(-1)(x) transformation for testing equality between two treatments among compliers for a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 - β at a nominal α level. We have employed Monte Carlo simulation to evaluate the finite-sample performance of the proposed test procedure with respect to type I error and the accuracy of the derived sample size calculation formula with respect to power in a variety of situations. Finally, we use the data taken from a CRT studying vitamin A supplementation to reduce mortality among preschool children to illustrate the use of sample size calculation proposed here. PMID:21191850
Tooth Wear Prevalence and Sample Size Determination : A Pilot Study
Abd. Karim, Nama Bibi Saerah; Ismail, Noorliza Mastura; Naing, Lin; Ismail, Abdul Rashid
2008-01-01
Tooth wear is the non-carious loss of tooth tissue, which results from three processes namely attrition, erosion and abrasion. These can occur in isolation or simultaneously. Very mild tooth wear is a physiological effect of aging. This study aims to estimate the prevalence of tooth wear among 16-year old Malay school children and determine a feasible sample size for further study. Fifty-five subjects were examined clinically, followed by the completion of self-administered questionnaires. Questionnaires consisted of socio-demographic and associated variables for tooth wear obtained from the literature. The Smith and Knight tooth wear index was used to chart tooth wear. Other oral findings were recorded using the WHO criteria. A software programme was used to determine pathological tooth wear. About equal ratio of male to female were involved. It was found that 18.2% of subjects have no tooth wear, 63.6% had very mild tooth wear, 10.9% mild tooth wear, 5.5% moderate tooth wear and 1.8 % severe tooth wear. In conclusion 18.2% of subjects were deemed to have pathological tooth wear (mild, moderate & severe). Exploration with all associated variables gave a sample size ranging from 560 – 1715. The final sample size for further study greatly depends on available time and resources. PMID:22589636
Improving Microarray Sample Size Using Bootstrap Data Combination
Phan, John H.; Moffitt, Richard A.; Barrett, Andrea B.; Wang, May D.
2016-01-01
Microarray technology has enabled us to simultaneously measure the expression of thousands of genes. Using this high-throughput technology, we can examine subtle genetic changes between biological samples and build predictive models for clinical applications. Although microarrays have dramatically increased the rate of data collection, sample size is still a major issue when selecting features. Previous methods show that combining multiple microarray datasets improves feature selection using simple methods such as fold change. We propose a wrapper-based gene selection technique that combines bootstrap estimated classification errors for individual genes across multiple datasets and reduces the contribution of datasets with high variance. We use the bootstrap because it is an unbiased estimator of classification error that is also effective for small sample data. Coupled with data combination across multiple datasets, we show that our meta-analytic approach improves the biological relevance of gene selection using prostate and renal cancer microarray data. PMID:19164001
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
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
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…
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.
ERIC Educational Resources Information Center
Lawson, Chris A.; Fisher, Anna V.
2011-01-01
Developmental studies have provided mixed evidence with regard to the question of whether children consider sample size and sample diversity in their inductive generalizations. Results from four experiments with 105 undergraduates, 105 school-age children (M = 7.2 years), and 105 preschoolers (M = 4.9 years) showed that preschoolers made a higher…
Decadal predictive skill assessment - ensemble and hindcast sample size impact
NASA Astrophysics Data System (ADS)
Sienz, Frank; Müller, Wolfgang; Pohlmann, Holger
2015-04-01
Hindcast, respectively retrospective prediction experiments have to be performed to validate decadal prediction systems. These are necessarily restricted in the number due to the computational constrains. From weather and seasonal prediction it is known that, the ensemble size is crucial. A similar dependency is likely for decadal predictions but, differences are expected due to the differing time-scales of the involved processes and the longer prediction horizon. It is shown here, that the ensemble and hindcast sample size have a large impact on the uncertainty assessment of the ensemble mean, as well as for the detection of prediction skill. For that purpose a conceptual model is developed, which enables the systematic analysis of statistical properties and its dependencies in a framework close to that of real decadal predictions. In addition, a set of extended range hindcast experiments have been undertaken, covering the entire 20th century.
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)
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.
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
Automated sampling assessment for molecular simulations using the effective sample size
Zhang, Xin; Bhatt, Divesh; Zuckerman, Daniel M.
2010-01-01
To quantify the progress in the development of algorithms and forcefields used in molecular simulations, a general method for the assessment of the sampling quality is needed. Statistical mechanics principles suggest the populations of physical states characterize equilibrium sampling in a fundamental way. We therefore develop an approach for analyzing the variances in state populations, which quantifies the degree of sampling in terms of the effective sample size (ESS). The ESS estimates the number of statistically independent configurations contained in a simulated ensemble. The method is applicable to both traditional dynamics simulations as well as more modern (e.g., multi–canonical) approaches. Our procedure is tested in a variety of systems from toy models to atomistic protein simulations. We also introduce a simple automated procedure to obtain approximate physical states from dynamic trajectories: this allows sample–size estimation in systems for which physical states are not known in advance. PMID:21221418
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.
Gough, E J; Gough, N M
1984-01-11
In order to facilitate the direct computation of the sizes of DNA fragments separated by gel electrophoresis, we have written and evaluated programmes for the Hewlett-Packard 41C programmable calculator. The sizes estimated for DNA fragments of known length using some of these programmes were found to be more accurate than the estimates obtained by conventional graphical procedures. These programmes should be adaptable to other programmable calculators. PMID:6320110
Calculation of a fluctuating entropic force by phase space sampling.
Waters, James T; Kim, Harold D
2015-07-01
A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system. PMID:26274308
NASA Astrophysics Data System (ADS)
Cienciala, Piotr; Hassan, Marwan A.
2016-03-01
Adequate description of hydraulic variables based on a sample of field measurements is challenging in coarse-bed streams, a consequence of high spatial heterogeneity in flow properties that arises due to the complexity of channel boundary. By applying a resampling procedure based on bootstrapping to an extensive field data set, we have estimated sampling variability and its relationship with sample size in relation to two common methods of representing flow characteristics, spatially averaged velocity profiles and fitted probability distributions. The coefficient of variation in bed shear stress and roughness length estimated from spatially averaged velocity profiles and in shape and scale parameters of gamma distribution fitted to local values of bed shear stress, velocity, and depth was high, reaching 15-20% of the parameter value even at the sample size of 100 (sampling density 1 m-2). We illustrated implications of these findings with two examples. First, sensitivity analysis of a 2-D hydrodynamic model to changes in roughness length parameter showed that the sampling variability range observed in our resampling procedure resulted in substantially different frequency distributions and spatial patterns of modeled hydraulic variables. Second, using a bedload formula, we showed that propagation of uncertainty in the parameters of a gamma distribution used to model bed shear stress led to the coefficient of variation in predicted transport rates exceeding 50%. Overall, our findings underscore the importance of reporting the precision of estimated hydraulic parameters. When such estimates serve as input into models, uncertainty propagation should be explicitly accounted for by running ensemble simulations.
Computing Power and Sample Size for Informational Odds Ratio †
Efird, Jimmy T.
2013-01-01
The informational odds ratio (IOR) measures the post-exposure odds divided by the pre-exposure odds (i.e., information gained after knowing exposure status). A desirable property of an adjusted ratio estimate is collapsibility, wherein the combined crude ratio will not change after adjusting for a variable that is not a confounder. Adjusted traditional odds ratios (TORs) are not collapsible. In contrast, Mantel-Haenszel adjusted IORs, analogous to relative risks (RRs) generally are collapsible. IORs are a useful measure of disease association in case-referent studies, especially when the disease is common in the exposed and/or unexposed groups. This paper outlines how to compute power and sample size in the simple case of unadjusted IORs. PMID:24157518
Son, Dae-Soon; Lee, DongHyuk; Lee, Kyusang; Jung, Sin-Ho; Ahn, Taejin; Lee, Eunjin; Sohn, Insuk; Chung, Jongsuk; Park, Woongyang; Huh, Nam; Lee, Jae Won
2015-02-01
An empirical method of sample size determination for building prediction models was proposed recently. Permutation method which is used in this procedure is a commonly used method to address the problem of overfitting during cross-validation while evaluating the performance of prediction models constructed from microarray data. But major drawback of such methods which include bootstrapping and full permutations is prohibitively high cost of computation required for calculating the sample size. In this paper, we propose that a single representative null distribution can be used instead of a full permutation by using both simulated and real data sets. During simulation, we have used a dataset with zero effect size and confirmed that the empirical type I error approaches to 0.05. Hence this method can be confidently applied to reduce overfitting problem during cross-validation. We have observed that pilot data set generated by random sampling from real data could be successfully used for sample size determination. We present our results using an experiment that was repeated for 300 times while producing results comparable to that of full permutation method. Since we eliminate full permutation, sample size estimation time is not a function of pilot data size. In our experiment we have observed that this process takes around 30min. With the increasing number of clinical studies, developing efficient sample size determination methods for building prediction models is critical. But empirical methods using bootstrap and permutation usually involve high computing costs. In this study, we propose a method that can reduce required computing time drastically by using representative null distribution of permutations. We use data from pilot experiments to apply this method for designing clinical studies efficiently for high throughput data. PMID:25555898
Quantum state discrimination bounds for finite sample size
Audenaert, Koenraad M. R.; Mosonyi, Milan; Verstraete, Frank
2012-12-15
In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of the two given and completely known states, {rho} or {sigma}. In general, it is not possible to decide the identity of the true state with certainty, and the optimal measurement strategy depends on whether the two possible errors (mistaking {rho} for {sigma}, or the other way around) are treated as of equal importance or not. Results on the quantum Chernoff and Hoeffding bounds and the quantum Stein's lemma show that, if several copies of the system are available then the optimal error probabilities decay exponentially in the number of copies, and the decay rate is given by a certain statistical distance between {rho} and {sigma} (the Chernoff distance, the Hoeffding distances, and the relative entropy, respectively). While these results provide a complete solution to the asymptotic problem, they are not completely satisfying from a practical point of view. Indeed, in realistic scenarios one has access only to finitely many copies of a system, and therefore it is desirable to have bounds on the error probabilities for finite sample size. In this paper we provide finite-size bounds on the so-called Stein errors, the Chernoff errors, the Hoeffding errors, and the mixed error probabilities related to the Chernoff and the Hoeffding errors.
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
Sample size estimation for the sorcerer's apprentice. Guide for the uninitiated and intimidated.
Ray, J. G.; Vermeulen, M. J.
1999-01-01
OBJECTIVE: To review the importance of and practical application of sample size determination for clinical studies in the primary care setting. QUALITY OF EVIDENCE: A MEDLINE search was performed from January 1966 to January 1998 using the MeSH headings and text words "sample size," "sample estimation," and "study design." Article references, medical statistics texts, and university colleagues were also consulted for recommended resources. Citations that offered a clear and simple approach to sample size estimation were accepted, specifically those related to statistical analyses commonly applied in primary care research. MAIN MESSAGE: The chance of committing an alpha statistical error, or finding that there is a difference between two groups when there really is none, is usually set at 5%. The probability of finding no difference between two groups, when, in actuality, there is a difference, is commonly accepted at 20%, and is called the beta error. The power of a study, usually set at 80% (i.e., 1 minus beta), defines the probability that a true difference will be observed between two groups. Using these parameters, we provide examples for estimating the required sample size for comparing two means (t test), comparing event rates between two groups, calculating an odds ratio or a correlation coefficient, or performing a meta-analysis. Estimation of sample size needed before initiation of a study enables statistical power to be maximized and bias minimized, increasing the validity of the study. CONCLUSION: Sample size estimation can be done by any novice researcher who wishes to maximize the quality of his or her study. PMID:10424273
7 CFR 51.2838 - Samples for grade and size determination.
Code of Federal Regulations, 2010 CFR
2010-01-01
... or Jumbo size or larger the package shall be the sample. When individual packages contain less than... 7 Agriculture 2 2010-01-01 2010-01-01 false Samples for grade and size determination. 51.2838... Creole Types) Samples for Grade and Size Determination § 51.2838 Samples for grade and size...
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
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.
Martin, James; Taljaard, Monica; Girling, Alan; Hemming, Karla
2016-01-01
Background Stepped-wedge cluster randomised trials (SW-CRT) are increasingly being used in health policy and services research, but unless they are conducted and reported to the highest methodological standards, they are unlikely to be useful to decision-makers. Sample size calculations for these designs require allowance for clustering, time effects and repeated measures. Methods We carried out a methodological review of SW-CRTs up to October 2014. We assessed adherence to reporting each of the 9 sample size calculation items recommended in the 2012 extension of the CONSORT statement to cluster trials. Results We identified 32 completed trials and 28 independent protocols published between 1987 and 2014. Of these, 45 (75%) reported a sample size calculation, with a median of 5.0 (IQR 2.5–6.0) of the 9 CONSORT items reported. Of those that reported a sample size calculation, the majority, 33 (73%), allowed for clustering, but just 15 (33%) allowed for time effects. There was a small increase in the proportions reporting a sample size calculation (from 64% before to 84% after publication of the CONSORT extension, p=0.07). The type of design (cohort or cross-sectional) was not reported clearly in the majority of studies, but cohort designs seemed to be most prevalent. Sample size calculations in cohort designs were particularly poor with only 3 out of 24 (13%) of these studies allowing for repeated measures. Discussion The quality of reporting of sample size items in stepped-wedge trials is suboptimal. There is an urgent need for dissemination of the appropriate guidelines for reporting and methodological development to match the proliferation of the use of this design in practice. Time effects and repeated measures should be considered in all SW-CRT power calculations, and there should be clarity in reporting trials as cohort or cross-sectional designs. PMID:26846897
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, 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....
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....
Threshold-dependent sample sizes for selenium assessment with stream fish tissue
Hitt, Nathaniel P.; Smith, David
2013-01-01
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 4-8 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 8 fish could detect an increase of ∼ 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 ∼ 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 ∼ 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 by increased precision of composites for estimating mean
Enhanced ligand sampling for relative protein-ligand binding free energy calculations.
Kaus, Joseph W; McCammon, J Andrew
2015-05-21
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
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
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... Part 600—Sample Fuel Economy Calculations (a) This sample fuel economy calculation is applicable to... Highway Fuel Economy Test Procedure and calculation similar to that shown in paragraph (a) by...
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.
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.
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.
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
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
7 CFR 51.3200 - Samples for grade and size determination.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Samples for grade and size determination. 51.3200... Grade and Size Determination § 51.3200 Samples for grade and size determination. Individual samples.... When individual packages contain 20 pounds or more and the onions are packed for Large or Jumbo size...
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
Lakens, Daniël
2013-01-01
Effect sizes are the most important outcome of empirical studies. Most articles on effect sizes highlight their importance to communicate the practical significance of results. For scientists themselves, effect sizes are most useful because they facilitate cumulative science. Effect sizes can be used to determine the sample size for follow-up studies, or examining effects across studies. This article aims to provide a practical primer on how to calculate and report effect sizes for t-tests and ANOVA's such that effect sizes can be used in a-priori power analyses and meta-analyses. Whereas many articles about effect sizes focus on between-subjects designs and address within-subjects designs only briefly, I provide a detailed overview of the similarities and differences between within- and between-subjects designs. I suggest that some research questions in experimental psychology examine inherently intra-individual effects, which makes effect sizes that incorporate the correlation between measures the best summary of the results. Finally, a supplementary spreadsheet is provided to make it as easy as possible for researchers to incorporate effect size calculations into their workflow. PMID:24324449
7 CFR 51.1548 - Samples for grade and size determination.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Samples for grade and size determination. 51.1548..., AND STANDARDS) United States Standards for Grades of Potatoes 1 Samples for Grade and Size Determination § 51.1548 Samples for grade and size determination. Individual samples shall consist of at...
7 CFR 51.629 - Sample for grade or size determination.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Sample for grade or size determination. 51.629 Section..., California, and Arizona) Sample for Grade Or Size Determination § 51.629 Sample for grade or size determination. Each sample shall consist of 33 grapefruit. When individual packages contain at least...
7 CFR 51.690 - Sample for grade or size determination.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Sample for grade or size determination. 51.690 Section..., California, and Arizona) Sample for Grade Or Size Determination § 51.690 Sample for grade or size determination. Each sample shall consist of 50 oranges. When individual packages contain at least 50...
Sample sizes for brain atrophy outcomes in trials for secondary progressive multiple sclerosis
Altmann, D R.; Jasperse, B; Barkhof, F; Beckmann, K; Filippi, M; Kappos, L D.; Molyneux, P; Polman, C H.; Pozzilli, C; Thompson, A J.; Wagner, K; Yousry, T A.; Miller, D H.
2009-01-01
Background: Progressive brain atrophy in multiple sclerosis (MS) may reflect neuroaxonal and myelin loss and MRI measures of brain tissue loss are used as outcome measures in MS treatment trials. This study investigated sample sizes required to demonstrate reduction of brain atrophy using three outcome measures in a parallel group, placebo-controlled trial for secondary progressive MS (SPMS). Methods: Data were taken from a cohort of 43 patients with SPMS who had been followed up with 6-monthly T1-weighted MRI for up to 3 years within the placebo arm of a therapeutic trial. Central cerebral volumes (CCVs) were measured using a semiautomated segmentation approach, and brain volume normalized for skull size (NBV) was measured using automated segmentation (SIENAX). Change in CCV and NBV was measured by subtraction of baseline from serial CCV and SIENAX images; in addition, percentage brain volume change relative to baseline was measured directly using a registration-based method (SIENA). Sample sizes for given treatment effects and power were calculated for standard analyses using parameters estimated from the sample. Results: For a 2-year trial duration, minimum sample sizes per arm required to detect a 50% treatment effect at 80% power were 32 for SIENA, 69 for CCV, and 273 for SIENAX. Two-year minimum sample sizes were smaller than 1-year by 71% for SIENAX, 55% for CCV, and 44% for SIENA. Conclusion: SIENA and central cerebral volume are feasible outcome measures for inclusion in placebo-controlled trials in secondary progressive multiple sclerosis. GLOSSARY ANCOVA = analysis of covariance; CCV = central cerebral volume; FSL = FMRIB Software Library; MNI = Montreal Neurological Institute; MS = multiple sclerosis; NBV = normalized brain volume; PBVC = percent brain volume change; RRMS = relapsing–remitting multiple sclerosis; SPMS = secondary progressive multiple sclerosis. PMID:19005170
On the validity of the Poisson assumption in sampling nanometer-sized aerosols
Damit, Brian E; Wu, Dr. Chang-Yu; Cheng, Mengdawn
2014-01-01
A Poisson process is traditionally believed to apply to the sampling of aerosols. For a constant aerosol concentration, it is assumed that a Poisson process describes the fluctuation in the measured concentration because aerosols are stochastically distributed in space. Recent studies, however, have shown that sampling of micrometer-sized aerosols has non-Poissonian behavior with positive correlations. The validity of the Poisson assumption for nanometer-sized aerosols has not been examined and thus was tested in this study. Its validity was tested for four particle sizes - 10 nm, 25 nm, 50 nm and 100 nm - by sampling from indoor air with a DMA- CPC setup to obtain a time series of particle counts. Five metrics were calculated from the data: pair-correlation function (PCF), time-averaged PCF, coefficient of variation, probability of measuring a concentration at least 25% greater than average, and posterior distributions from Bayesian inference. To identify departures from Poissonian behavior, these metrics were also calculated for 1,000 computer-generated Poisson time series with the same mean as the experimental data. For nearly all comparisons, the experimental data fell within the range of 80% of the Poisson-simulation values. Essentially, the metrics for the experimental data were indistinguishable from a simulated Poisson process. The greater influence of Brownian motion for nanometer-sized aerosols may explain the Poissonian behavior observed for smaller aerosols. Although the Poisson assumption was found to be valid in this study, it must be carefully applied as the results here do not definitively prove applicability in all sampling situations.
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…
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
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
Alternative sample sizes for verification dose experiments and dose audits
NASA Astrophysics Data System (ADS)
Taylor, W. A.; Hansen, J. M.
1999-01-01
ISO 11137 (1995), "Sterilization of Health Care Products—Requirements for Validation and Routine Control—Radiation Sterilization", provides sampling plans for performing initial verification dose experiments and quarterly dose audits. Alternative sampling plans are presented which provide equivalent protection. These sampling plans can significantly reduce the cost of testing. These alternative sampling plans have been included in a draft ISO Technical Report (type 2). This paper examines the rational behind the proposed alternative sampling plans. The protection provided by the current verification and audit sampling plans is first examined. Then methods for identifying equivalent plans are highlighted. Finally, methods for comparing the cost associated with the different plans are provided. This paper includes additional guidance for selecting between the original and alternative sampling plans not included in the technical report.
40 CFR 91.419 - Raw emission sampling calculations.
Code of Federal Regulations, 2012 CFR
2012-07-01
... mass flow rate , MHCexh = Molecular weight of hydrocarbons in the exhaust; see the following equation: MHCexh = 12.01 + 1.008 × α Where: α=Hydrocarbon/carbon atomic ratio of the fuel. Mexh=Molecular weight of..., calculated from the following equation: ER04OC96.019 WCO = Mass rate of CO in exhaust, MCO = Molecular...
40 CFR 91.419 - Raw emission sampling calculations.
Code of Federal Regulations, 2011 CFR
2011-07-01
... mass flow rate , MHCexh = Molecular weight of hydrocarbons in the exhaust; see the following equation: MHCexh = 12.01 + 1.008 × α Where: α=Hydrocarbon/carbon atomic ratio of the fuel. Mexh=Molecular weight of..., calculated from the following equation: ER04OC96.019 WCO = Mass rate of CO in exhaust, MCO = Molecular...
40 CFR 91.419 - Raw emission sampling calculations.
Code of Federal Regulations, 2014 CFR
2014-07-01
... mass flow rate , MHCexh = Molecular weight of hydrocarbons in the exhaust; see the following equation: MHCexh = 12.01 + 1.008 × α Where: α=Hydrocarbon/carbon atomic ratio of the fuel. Mexh=Molecular weight of..., calculated from the following equation: ER04OC96.019 WCO = Mass rate of CO in exhaust, MCO = Molecular...
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.
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... 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, 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, 2014 CFR
2014-07-01
... 40 Protection of Environment 30 2014-07-01 2014-07-01 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 89.418 - Raw emission sampling calculations.
Code of Federal Regulations, 2014 CFR
2014-07-01
... be determined for each mode. (1) For measurements using the mass flow method, see § 89.416(a). (2... using the mass flow method (see § 89.416(a)): ER23OC98.011 ER23OC98.012 ER23OC98.013 α = H/C mole ratio...) The pollutant mass flow for each mode shall be calculated as follows: Gas mass = u × Gas conc. ×...
40 CFR 89.418 - Raw emission sampling calculations.
Code of Federal Regulations, 2013 CFR
2013-07-01
... be determined for each mode. (1) For measurements using the mass flow method, see § 89.416(a). (2... using the mass flow method (see § 89.416(a)): ER23OC98.011 ER23OC98.012 ER23OC98.013 α = H/C mole ratio...) The pollutant mass flow for each mode shall be calculated as follows: Gas mass = u × Gas conc. ×...
40 CFR 89.418 - Raw emission sampling calculations.
Code of Federal Regulations, 2012 CFR
2012-07-01
... be determined for each mode. (1) For measurements using the mass flow method, see § 89.416(a). (2... using the mass flow method (see § 89.416(a)): ER23OC98.011 ER23OC98.012 ER23OC98.013 α = H/C mole ratio...) The pollutant mass flow for each mode shall be calculated as follows: Gas mass = u × Gas conc. ×...
40 CFR 89.418 - Raw emission sampling calculations.
Code of Federal Regulations, 2011 CFR
2011-07-01
... be determined for each mode. (1) For measurements using the mass flow method, see § 89.416(a). (2... using the mass flow method (see § 89.416(a)): ER23OC98.011 ER23OC98.012 ER23OC98.013 α = H/C mole ratio...) The pollutant mass flow for each mode shall be calculated as follows: Gas mass = u × Gas conc. ×...
A Variational Approach to Enhanced Sampling and Free Energy Calculations
NASA Astrophysics Data System (ADS)
Parrinello, Michele
2015-03-01
The presence of kinetic bottlenecks severely hampers the ability of widely used sampling methods like molecular dynamics or Monte Carlo to explore complex free energy landscapes. One of the most popular methods for addressing this problem is umbrella sampling which is based on the addition of an external bias which helps overcoming the kinetic barriers. The bias potential is usually taken to be a function of a restricted number of collective variables. However constructing the bias is not simple, especially when the number of collective variables increases. Here we introduce a functional of the bias which, when minimized, allows us to recover the free energy. We demonstrate the usefulness and the flexibility of this approach on a number of examples which include the determination of a six dimensional free energy surface. Besides the practical advantages, the existence of such a variational principle allows us to look at the enhanced sampling problem from a rather convenient vantage point.
Variational Approach to Enhanced Sampling and Free Energy Calculations
NASA Astrophysics Data System (ADS)
Valsson, Omar; Parrinello, Michele
2014-08-01
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variables. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient, and flexible sampling method. A number of numerical examples are presented which include the determination of a three-dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.
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…
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.
40 CFR 89.424 - Dilute emission sampling calculations.
Code of Federal Regulations, 2012 CFR
2012-07-01
... as measured, ppm. (Note: If a CO instrument that meets the criteria specified in 40 CFR part 1065, subpart C, is used without a sample dryer according to 40 CFR 1065.145, COem must be substituted directly... following equations: (1) Hydrocarbon mass: HCmass= Vmix × DensityHC × (HCconc/106) (2) Oxides of...
40 CFR 89.424 - Dilute emission sampling calculations.
Code of Federal Regulations, 2013 CFR
2013-07-01
... as measured, ppm. (Note: If a CO instrument that meets the criteria specified in 40 CFR part 1065, subpart C, is used without a sample dryer according to 40 CFR 1065.145, COem must be substituted directly... following equations: (1) Hydrocarbon mass: HCmass= Vmix × DensityHC × (HCconc/106) (2) Oxides of...
40 CFR 89.424 - Dilute emission sampling calculations.
Code of Federal Regulations, 2014 CFR
2014-07-01
... as measured, ppm. (Note: If a CO instrument that meets the criteria specified in 40 CFR part 1065, subpart C, is used without a sample dryer according to 40 CFR 1065.145, COem must be substituted directly... following equations: (1) Hydrocarbon mass: HCmass= Vmix × DensityHC × (HCconc/106) (2) Oxides of...
40 CFR 89.424 - Dilute emission sampling calculations.
Code of Federal Regulations, 2010 CFR
2010-07-01
... as measured, ppm. (Note: If a CO instrument that meets the criteria specified in 40 CFR part 1065, subpart C, is used without a sample dryer according to 40 CFR 1065.145, COem must be substituted directly... following equations: (1) Hydrocarbon mass: HCmass= Vmix × DensityHC × (HCconc/106) (2) Oxides of...
40 CFR 89.424 - Dilute emission sampling calculations.
Code of Federal Regulations, 2011 CFR
2011-07-01
... as measured, ppm. (Note: If a CO instrument that meets the criteria specified in 40 CFR part 1065, subpart C, is used without a sample dryer according to 40 CFR 1065.145, COem must be substituted directly... test results are computed by use of the following formula: ER23OC98.018 Where: Awm = Weighted...
Grain size measurements using the point-sampled intercept technique
Srinivasan, S. ); Russ, J.C.; Scattergood, R.O. . Dept. of Materials Science and Engineering)
1991-01-01
Recent developments in the field of stereology and measurement of three-dimensional size scales from two-dimensional sections have emanated from the medical field, particularly in the area of pathology. Here, the measurement of biological cell sizes and their distribution are critical for diagnosis and treatment of such deadly diseases as cancer. The purpose of this paper is to introduce these new methods to the materials science community and to illustrate their application using a series of typical microstructures found in polycrystalline ceramics. As far as the current authors are aware, these methods have not been applied in materials-science related applications.
Space resection model calculation based on Random Sample Consensus algorithm
NASA Astrophysics Data System (ADS)
Liu, Xinzhu; Kang, Zhizhong
2016-03-01
Resection has been one of the most important content in photogrammetry. It aims at the position and attitude information of camera at the shooting point. However in some cases, the observed values for calculating are with gross errors. This paper presents a robust algorithm that using RANSAC method with DLT model can effectually avoiding the difficulties to determine initial values when using co-linear equation. The results also show that our strategies can exclude crude handicap and lead to an accurate and efficient way to gain elements of exterior orientation.
X-Ray Dose and Spot Size Calculations for the DARHT-II Distributed Target
McCarrick, J
2001-04-05
The baseline DARHT-II converter target consists of foamed tantalum within a solid-density cylindrical tamper. The baseline design has been modified by D. Ho to further optimize the integrated line density of material in the course of multiple beam pulses. LASNEX simulations of the hydrodynamic expansion of the target have been performed by D. Ho (documented elsewhere). The resulting density profiles have been used as inputs in the MCNP radiation transport code to calculate the X-ray dose and spot size assuming a incoming Gaussian electron beam with {sigma} = 0.65mm, and a PIC-generated beam taking into account the ''swept'' spot emerging from the DARHT-II kicker system. A prerequisite to these calculations is the absorption spectrum of air. In order to obtain this, a separate series of MCNP runs was performed for a set of monoenergetic photon sources, tallying the energy deposited in a volume of air. The forced collision feature was used to improve the statistics since the photon mean free path in air is extremely long at the energies of interest. A sample input file is given below. The resulting data for the MCNP DE and DF cards is shown in the beam-pulse input files, one of which is listed below. Note that the DE and DF cards are entered in column format for easy reading.
Estimating the Effective Sample Size of Tree Topologies from Bayesian Phylogenetic Analyses
Lanfear, Robert; Hua, Xia; Warren, Dan L.
2016-01-01
Bayesian phylogenetic analyses estimate posterior distributions of phylogenetic tree topologies and other parameters using Markov chain Monte Carlo (MCMC) methods. Before making inferences from these distributions, it is important to assess their adequacy. To this end, the effective sample size (ESS) estimates how many truly independent samples of a given parameter the output of the MCMC represents. The ESS of a parameter is frequently much lower than the number of samples taken from the MCMC because sequential samples from the chain can be non-independent due to autocorrelation. Typically, phylogeneticists use a rule of thumb that the ESS of all parameters should be greater than 200. However, we have no method to calculate an ESS of tree topology samples, despite the fact that the tree topology is often the parameter of primary interest and is almost always central to the estimation of other parameters. That is, we lack a method to determine whether we have adequately sampled one of the most important parameters in our analyses. In this study, we address this problem by developing methods to estimate the ESS for tree topologies. We combine these methods with two new diagnostic plots for assessing posterior samples of tree topologies, and compare their performance on simulated and empirical data sets. Combined, the methods we present provide new ways to assess the mixing and convergence of phylogenetic tree topologies in Bayesian MCMC analyses. PMID:27435794
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…
Sample size and scene identification (cloud) - Effect on albedo
NASA Technical Reports Server (NTRS)
Vemury, S. K.; Stowe, L.; Jacobowitz, H.
1984-01-01
Scan channels on the Nimbus 7 Earth Radiation Budget instrument sample radiances from underlying earth scenes at a number of incident and scattering angles. A sampling excess toward measurements at large satellite zenith angles is noted. Also, at large satellite zenith angles, the present scheme for scene selection causes many observations to be classified as cloud, resulting in higher flux averages. Thus the combined effect of sampling bias and scene identification errors is to overestimate the computed albedo. It is shown, using a process of successive thresholding, that observations with satellite zenith angles greater than 50-60 deg lead to incorrect cloud identification. Elimination of these observations has reduced the albedo from 32.2 to 28.8 percent. This reduction is very nearly the same and in the right direction as the discrepancy between the albedoes derived from the scanner and the wide-field-of-view channels.
7 CFR 201.43 - Size of sample.
Code of Federal Regulations, 2012 CFR
2012-01-01
... units. Coated seed for germination test only shall consist of at least 1,000 seed units. ..., Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE (CONTINUED) FEDERAL SEED ACT FEDERAL SEED ACT... of samples of agricultural seed, vegetable seed and screenings to be submitted for analysis, test,...
7 CFR 201.43 - Size of sample.
Code of Federal Regulations, 2014 CFR
2014-01-01
... units. Coated seed for germination test only shall consist of at least 1,000 seed units. ..., Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE (CONTINUED) FEDERAL SEED ACT FEDERAL SEED ACT... of samples of agricultural seed, vegetable seed and screenings to be submitted for analysis, test,...
7 CFR 201.43 - Size of sample.
Code of Federal Regulations, 2013 CFR
2013-01-01
... units. Coated seed for germination test only shall consist of at least 1,000 seed units. ..., Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE (CONTINUED) FEDERAL SEED ACT FEDERAL SEED ACT... of samples of agricultural seed, vegetable seed and screenings to be submitted for analysis, test,...
7 CFR 201.43 - Size of sample.
Code of Federal Regulations, 2011 CFR
2011-01-01
..., Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE (CONTINUED) FEDERAL SEED ACT FEDERAL SEED ACT... of samples of agricultural seed, vegetable seed and screenings to be submitted for analysis, test, or examination: (a) Two ounces (57 grams) of grass seed not otherwise mentioned, white or alsike clover, or...
7 CFR 201.43 - Size of sample.
Code of Federal Regulations, 2010 CFR
2010-01-01
..., Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE (CONTINUED) FEDERAL SEED ACT FEDERAL SEED ACT... of samples of agricultural seed, vegetable seed and screenings to be submitted for analysis, test, or examination: (a) Two ounces (57 grams) of grass seed not otherwise mentioned, white or alsike clover, or...
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 score…
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, 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...
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...
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.
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
Xiang, Jianping; Yu, Jihnhee; Snyder, Kenneth V.; Levy, Elad I.; Siddiqui, Adnan H.; Meng, Hui
2016-01-01
Background We previously established three logistic regression models for discriminating intracranial aneurysm rupture status based on morphological and hemodynamic analysis of 119 aneurysms (Stroke. 2011;42:144–152). In this study we tested if these models would remain stable with increasing sample size and investigated sample sizes required for various confidence levels. Methods We augmented our previous dataset of 119 aneurysms into a new dataset of 204 samples by collecting additional 85 consecutive aneurysms, on which we performed flow simulation and calculated morphological and hemodynamic parameters as done previously. We performed univariate significance tests of these parameters, and on the significant parameters we performed multivariate logistic regression. The new regression models were compared against the original models. Receiver operating characteristics analysis was applied to compare the performance of regression models. Furthermore, we performed regression analysis based on bootstrapping resampling statistical simulations to explore how many aneurysm cases were required to generate stable models. Results Univariate tests of the 204 aneurysms generated an identical list of significant morphological and hemodynamic parameters as previously from analysis of 119 cases. Furthermore, multivariate regression analysis produced three parsimonious predictive models that were almost identical to the previous ones; with model coefficients that had narrower confidence intervals than the original ones. Bootstrapping showed that 10%, 5%, 2%, and 1% convergence levels of confidence interval required 120, 200, 500, and 900 aneurysms, respectively. Conclusions Our original hemodynamic-morphological rupture prediction models are stable and improve with increasing sample size. Results from resampling statistical simulations provide guidance for designing future large multi-population studies. PMID:25488922
Geoscience Education Research Methods: Thinking About Sample Size
NASA Astrophysics Data System (ADS)
Slater, S. J.; Slater, T. F.; CenterAstronomy; Physics Education Research
2011-12-01
Geoscience education research is at a critical point in which conditions are sufficient to propel our field forward toward meaningful improvements in geosciences education practices. Our field has now reached a point where the outcomes of our research is deemed important to endusers and funding agencies, and where we now have a large number of scientists who are either formally trained in geosciences education research, or who have dedicated themselves to excellence in this domain. At this point we now must collectively work through our epistemology, our rules of what methodologies will be considered sufficiently rigorous, and what data and analysis techniques will be acceptable for constructing evidence. In particular, we have to work out our answer to that most difficult of research questions: "How big should my 'N' be??" This paper presents a very brief answer to that question, addressing both quantitative and qualitative methodologies. Research question/methodology alignment, effect size and statistical power will be discussed, in addition to a defense of the notion that bigger is not always better.
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,…
Tian, Guo-Liang; Tang, Man-Lai; Zhenqiu Liu; Ming Tan; Tang, Nian-Sheng
2011-06-01
Sample size determination is an essential component in public health survey designs on sensitive topics (e.g. drug abuse, homosexuality, induced abortions and pre or extramarital sex). Recently, non-randomised models have been shown to be an efficient and cost effective design when comparing with randomised response models. However, sample size formulae for such non-randomised designs are not yet available. In this article, we derive sample size formulae for the non-randomised triangular design based on the power analysis approach. We first consider the one-sample problem. Power functions and their corresponding sample size formulae for the one- and two-sided tests based on the large-sample normal approximation are derived. The performance of the sample size formulae is evaluated in terms of (i) the accuracy of the power values based on the estimated sample sizes and (ii) the sample size ratio of the non-randomised triangular design and the design of direct questioning (DDQ). We also numerically compare the sample sizes required for the randomised Warner design with those required for the DDQ and the non-randomised triangular design. Theoretical justification is provided. Furthermore, we extend the one-sample problem to the two-sample problem. An example based on an induced abortion study in Taiwan is presented to illustrate the proposed methods. PMID:19221169
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…
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. PMID:22923253
Ab initio spur size calculation in liquid water at room temperature
NASA Astrophysics Data System (ADS)
Muroya, Yusa; Mozumder, Asokendu
2016-07-01
An attempt was made to calculate the spur size in liquid water at room temperature from fundamental interactions. Electron trapping, elastic scattering, and positive-ion back attraction undergone in sub-excitation and sub-vibrational stages in the 100 fs time scale for thermalization were considered and included in the model. Overall diffusional broadening was estimated to be 41.2 Å, attended by the positive-ion pull back of 24.0 Å, resulting in a calculated spur size of 17.2 Å. Electron trapping is seen in competition with thermalization in the ultimate stage, which results in the trapped electron position distribution as a sum of Gaussians.
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.
Sample size estimation for the van Elteren test--a stratified Wilcoxon-Mann-Whitney test.
Zhao, Yan D
2006-08-15
The van Elteren test is a type of stratified Wilcoxon-Mann-Whitney test for comparing two treatments accounting for strata. In this paper, we study sample size estimation methods for the asymptotic version of the van Elteren test, assuming that the stratum fractions (ratios of each stratum size to the total sample size) and the treatment fractions (ratios of each treatment size to the stratum size) are known in the study design. In particular, we develop three large-sample sample size estimation methods and present a real data example to illustrate the necessary information in the study design phase in order to apply the methods. Simulation studies are conducted to compare the performance of the methods and recommendations are made for method choice. Finally, sample size estimation for the van Elteren test when the stratum fractions are unknown is also discussed. PMID:16372389
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
2010-01-01
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
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
Lange, Oliver F; Baker, David
2012-01-01
Recent work has shown that NMR structures can be determined by integrating sparse NMR data with structure prediction methods such as Rosetta. The experimental data serve to guide the search for the lowest energy state towards the deep minimum at the native state which is frequently missed in Rosetta de novo structure calculations. However, as the protein size increases, sampling again becomes limiting; for example, the standard Rosetta protocol involving Monte Carlo fragment insertion starting from an extended chain fails to converge for proteins over 150 amino acids even with guidance from chemical shifts (CS-Rosetta) and other NMR data. The primary limitation of this protocol—that every folding trajectory is completely independent of every other—was recently overcome with the development of a new approach involving resolution-adapted structural recombination (RASREC). Here we describe the RASREC approach in detail and compare it to standard CS-Rosetta. We show that the improved sampling of RASREC is essential in obtaining accurate structures over a benchmark set of 11 proteins in the 15-25 kDa size range using chemical shifts, backbone RDCs and HN-HN NOE data; in a number of cases the improved sampling methodology makes a larger contribution than incorporation of additional experimental data. Experimental data are invaluable for guiding sampling to the vicinity of the global energy minimum, but for larger proteins, the standard Rosetta fold-from-extended-chain protocol does not converge on the native minimum even with experimental data and the more powerful RASREC approach is necessary to converge to accurate solutions. PMID:22423358
Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems
Azadi, Sam Foulkes, W. M. C.
2015-09-14
We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency, and practical improvements are introduced. In particular, we test a simple but efficient method of finite-size correction based on an accurate combination of twist averaging and density functional theory. Our diffusion quantum Monte Carlo results for lithium and aluminum, as examples of metallic systems, demonstrate excellent agreement between all of the approaches considered.
Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids
NASA Astrophysics Data System (ADS)
Holzmann, Markus; Clay, Raymond C.; Morales, Miguel A.; Tubman, Norm M.; Ceperley, David M.; Pierleoni, Carlo
2016-07-01
Concentrating on zero temperature quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one- and two-body correlation functions. We introduce effective procedures, such as using the potential and wave function split up into long and short range functions to simplify the method, and we discuss how to treat backflow wave functions. Then we explicitly test the accuracy of our method to correct finite size errors on example hydrogen and helium many-body systems and show that the finite size bias can be drastically reduced for even small systems.
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.
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…
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. PMID:26865383
Design and sample size considerations for simultaneous global drug development program.
Huang, Qin; Chen, Gang; Yuan, Zhilong; Lan, K K Gordon
2012-09-01
Due to the potential impact of ethnic factors on clinical outcomes, the global registration of a new treatment is challenging. China and Japan often require local trials in addition to a multiregional clinical trial (MRCT) to support the efficacy and safety claim of the treatment. The impact of ethnic factors on the treatment effect has been intensively investigated and discussed from different perspectives. However, most current methods are focusing on the assessment of the consistency or similarity of the treatment effect between different ethnic groups in exploratory nature. In this article, we propose a new method for the design and sample size consideration for a simultaneous global drug development program (SGDDP) using weighted z-tests. In the proposed method, to test the efficacy of a new treatment for the targeted ethnic (TE) group, a weighted test that combines the information collected from both the TE group and the nontargeted ethnic (NTE) group is used. The influence of ethnic factors and local medical practice on the treatment effect is accounted for by down-weighting the information collected from NTE group in the combined test statistic. This design controls rigorously the overall false positive rate for the program at a given level. The sample sizes needed for the TE group in an SGDDP for three most commonly used efficacy endpoints, continuous, binary, and time-to-event, are then calculated. PMID:22946950
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
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... Appendix III to Part 600—Sample Fuel Economy Label Calculation Suppose that a manufacturer called Mizer Motors has a product line composed of eight car lines. Of these eight, four are available with the...
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... Appendix III to Part 600—Sample Fuel Economy Label Calculation Suppose that a manufacturer called Mizer Motors has a product line composed of eight car lines. Of these eight, four are available with the...
12 CFR Appendix M2 to Part 1026 - Sample Calculations of Repayment Disclosures
Code of Federal Regulations, 2012 CFR
2012-01-01
... 12 Banks and Banking 8 2012-01-01 2012-01-01 false Sample Calculations of Repayment Disclosures M2 Appendix M2 to Part 1026 Banks and Banking BUREAU OF CONSUMER FINANCIAL PROTECTION TRUTH IN LENDING (REGULATION Z) Pt. 1026, App. M2 Appendix M2 to Part 1026—Sample Calculations of Repayment Disclosures...
12 CFR Appendix M2 to Part 1026 - Sample Calculations of Repayment Disclosures
Code of Federal Regulations, 2013 CFR
2013-01-01
... 12 Banks and Banking 8 2013-01-01 2013-01-01 false Sample Calculations of Repayment Disclosures M2 Appendix M2 to Part 1026 Banks and Banking BUREAU OF CONSUMER FINANCIAL PROTECTION TRUTH IN LENDING (REGULATION Z) Pt. 1026, App. M2 Appendix M2 to Part 1026—Sample Calculations of Repayment Disclosures...
EFFECTS OF SAMPLING NOZZLES ON THE PARTICLE COLLECTION CHARACTERISTICS OF INERTIAL SIZING DEVICES
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 s...