Effects of sample size on estimates of population growth rates calculated with matrix models.

PubMed

Fiske, Ian J; Bruna, Emilio M; Bolker, Benjamin M

2008-08-28

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 (lambda) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of lambda-Jensen's Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of lambda 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 lambda. Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating lambda for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of lambda 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. 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.

A note on sample size calculation for mean comparisons based on noncentral t-statistics.

PubMed

Chow, Shein-Chung; Shao, Jun; Wang, Hansheng

2002-11-01

One-sample and two-sample t-tests are commonly used in analyzing data from clinical trials in comparing mean responses from two drug products. During the planning stage of a clinical study, a crucial step is the sample size calculation, i.e., the determination of the number of subjects (patients) needed to achieve a desired power (e.g., 80%) for detecting a clinically meaningful difference in the mean drug responses. Based on noncentral t-distributions, we derive some sample size calculation formulas for testing equality, testing therapeutic noninferiority/superiority, and testing therapeutic equivalence, under the popular one-sample design, two-sample parallel design, and two-sample crossover design. Useful tables are constructed and some examples are given for illustration.

45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations

Code of Federal Regulations, 2013 CFR

2013-10-01

... 45 Public Welfare 4 2013-10-01 2013-10-01 false Calculating Sample Size for NYTD Follow-Up Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... REQUIREMENTS APPLICABLE TO TITLE IV-E Pt. 1356, App. C Appendix C to Part 1356—Calculating Sample Size for NYTD...

Sample size calculation for studies with grouped survival data.

PubMed

Li, Zhiguo; Wang, Xiaofei; Wu, Yuan; Owzar, Kouros

2018-06-10

Grouped survival data arise often in studies where the disease status is assessed at regular visits to clinic. The time to the event of interest can only be determined to be between two adjacent visits or is right censored at one visit. In data analysis, replacing the survival time with the endpoint or midpoint of the grouping interval leads to biased estimators of the effect size in group comparisons. Prentice and Gloeckler developed a maximum likelihood estimator for the proportional hazards model with grouped survival data and the method has been widely applied. Previous work on sample size calculation for designing studies with grouped data is based on either the exponential distribution assumption or the approximation of variance under the alternative with variance under the null. Motivated by studies in HIV trials, cancer trials and in vitro experiments to study drug toxicity, we develop a sample size formula for studies with grouped survival endpoints that use the method of Prentice and Gloeckler for comparing two arms under the proportional hazards assumption. We do not impose any distributional assumptions, nor do we use any approximation of variance of the test statistic. The sample size formula only requires estimates of the hazard ratio and survival probabilities of the event time of interest and the censoring time at the endpoints of the grouping intervals for one of the two arms. The formula is shown to perform well in a simulation study and its application is illustrated in the three motivating examples. Copyright © 2018 John Wiley & Sons, Ltd.

Sample size calculation in cost-effectiveness cluster randomized trials: optimal and maximin approaches.

PubMed

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.

Bayesian sample size calculations in phase II clinical trials using a mixture of informative priors.

PubMed

Gajewski, Byron J; Mayo, Matthew S

2006-08-15

A number of researchers have discussed phase II clinical trials from a Bayesian perspective. A recent article by Mayo and Gajewski focuses on sample size calculations, which they determine by specifying an informative prior distribution and then calculating a posterior probability that the true response will exceed a prespecified target. In this article, we extend these sample size calculations to include a mixture of informative prior distributions. The mixture comes from several sources of information. For example consider information from two (or more) clinicians. The first clinician is pessimistic about the drug and the second clinician is optimistic. We tabulate the results for sample size design using the fact that the simple mixture of Betas is a conjugate family for the Beta- Binomial model. We discuss the theoretical framework for these types of Bayesian designs and show that the Bayesian designs in this paper approximate this theoretical framework. Copyright 2006 John Wiley & Sons, Ltd.

GLIMMPSE Lite: Calculating Power and Sample Size on Smartphone Devices

PubMed Central

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

Sample Size Calculations for Micro-randomized Trials in mHealth

PubMed Central

Liao, Peng; Klasnja, Predrag; Tewari, Ambuj; Murphy, Susan A.

2015-01-01

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. PMID:26707831

Power/Sample Size Calculations for Assessing Correlates of Risk in Clinical Efficacy Trials

PubMed Central

Gilbert, Peter B.; Janes, Holly E.; Huang, Yunda

2016-01-01

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. PMID:27037797

Power and Sample Size Calculations for Logistic Regression Tests for Differential Item Functioning

ERIC Educational Resources Information Center

Li, Zhushan

2014-01-01

Logistic regression is a popular method for detecting uniform and nonuniform differential item functioning (DIF) effects. Theoretical formulas for the power and sample size calculations are derived for likelihood ratio tests and Wald tests based on the asymptotic distribution of the maximum likelihood estimators for the logistic regression model.…

Sample Size Calculation for Estimating or Testing a Nonzero Squared Multiple Correlation Coefficient

ERIC Educational Resources Information Center

Krishnamoorthy, K.; Xia, Yanping

2008-01-01

The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to…

The effect of clustering on lot quality assurance sampling: a probabilistic model to calculate sample sizes for quality assessments

PubMed Central

2013-01-01

Background Traditional Lot Quality Assurance Sampling (LQAS) designs assume observations are collected using simple random sampling. Alternatively, randomly sampling clusters of observations and then individuals within clusters reduces costs but decreases the precision of the classifications. In this paper, we develop a general framework for designing the cluster(C)-LQAS system and illustrate the method with the design of data quality assessments for the community health worker program in Rwanda. Results To determine sample size and decision rules for C-LQAS, we use the beta-binomial distribution to account for inflated risk of errors introduced by sampling clusters at the first stage. We present general theory and code for sample size calculations. The C-LQAS sample sizes provided in this paper constrain misclassification risks below user-specified limits. Multiple C-LQAS systems meet the specified risk requirements, but numerous considerations, including per-cluster versus per-individual sampling costs, help identify optimal systems for distinct applications. Conclusions We show the utility of C-LQAS for data quality assessments, but the method generalizes to numerous applications. This paper provides the necessary technical detail and supplemental code to support the design of C-LQAS for specific programs. PMID:24160725

The effect of clustering on lot quality assurance sampling: a probabilistic model to calculate sample sizes for quality assessments.

PubMed

Hedt-Gauthier, Bethany L; Mitsunaga, Tisha; Hund, Lauren; Olives, Casey; Pagano, Marcello

2013-10-26

Traditional Lot Quality Assurance Sampling (LQAS) designs assume observations are collected using simple random sampling. Alternatively, randomly sampling clusters of observations and then individuals within clusters reduces costs but decreases the precision of the classifications. In this paper, we develop a general framework for designing the cluster(C)-LQAS system and illustrate the method with the design of data quality assessments for the community health worker program in Rwanda. To determine sample size and decision rules for C-LQAS, we use the beta-binomial distribution to account for inflated risk of errors introduced by sampling clusters at the first stage. We present general theory and code for sample size calculations.The C-LQAS sample sizes provided in this paper constrain misclassification risks below user-specified limits. Multiple C-LQAS systems meet the specified risk requirements, but numerous considerations, including per-cluster versus per-individual sampling costs, help identify optimal systems for distinct applications. We show the utility of C-LQAS for data quality assessments, but the method generalizes to numerous applications. This paper provides the necessary technical detail and supplemental code to support the design of C-LQAS for specific programs.

Sample size calculations for the design of cluster randomized trials: A summary of methodology.

PubMed

Gao, Fei; Earnest, Arul; Matchar, David B; Campbell, Michael J; Machin, David

2015-05-01

Cluster randomized trial designs are growing in popularity in, for example, cardiovascular medicine research and other clinical areas and parallel statistical developments concerned with the design and analysis of these trials have been stimulated. Nevertheless, reviews suggest that design issues associated with cluster randomized trials are often poorly appreciated and there remain inadequacies in, for example, describing how the trial size is determined and the associated results are presented. In this paper, our aim is to provide pragmatic guidance for researchers on the methods of calculating sample sizes. We focus attention on designs with the primary purpose of comparing two interventions with respect to continuous, binary, ordered categorical, incidence rate and time-to-event outcome variables. Issues of aggregate and non-aggregate cluster trials, adjustment for variation in cluster size and the effect size are detailed. The problem of establishing the anticipated magnitude of between- and within-cluster variation to enable planning values of the intra-cluster correlation coefficient and the coefficient of variation are also described. Illustrative examples of calculations of trial sizes for each endpoint type are included. Copyright © 2015 Elsevier Inc. All rights reserved.

A general approach for sample size calculation for the three-arm 'gold standard' non-inferiority design.

PubMed

Stucke, Kathrin; Kieser, Meinhard

2012-12-10

In the three-arm 'gold standard' non-inferiority design, an experimental treatment, an active reference, and a placebo are compared. This design is becoming increasingly popular, and it is, whenever feasible, recommended for use by regulatory guidelines. We provide a general method to calculate the required sample size for clinical trials performed in this design. As special cases, the situations of continuous, binary, and Poisson distributed outcomes are explored. Taking into account the correlation structure of the involved test statistics, the proposed approach leads to considerable savings in sample size as compared with application of ad hoc methods for all three scale levels. Furthermore, optimal sample size allocation ratios are determined that result in markedly smaller total sample sizes as compared with equal assignment. As optimal allocation makes the active treatment groups larger than the placebo group, implementation of the proposed approach is also desirable from an ethical viewpoint. Copyright © 2012 John Wiley & Sons, Ltd.

Reporting and methodological quality of sample size calculations in cluster randomized trials could be improved: a review.

PubMed

Rutterford, Clare; Taljaard, Monica; Dixon, Stephanie; Copas, Andrew; Eldridge, Sandra

2015-06-01

To assess the quality of reporting and accuracy of a priori estimates used in sample size calculations for cluster randomized trials (CRTs). We reviewed 300 CRTs published between 2000 and 2008. The prevalence of reporting sample size elements from the 2004 CONSORT recommendations was evaluated and a priori estimates compared with those observed in the trial. Of the 300 trials, 166 (55%) reported a sample size calculation. Only 36 of 166 (22%) reported all recommended descriptive elements. Elements specific to CRTs were the worst reported: a measure of within-cluster correlation was specified in only 58 of 166 (35%). Only 18 of 166 articles (11%) reported both a priori and observed within-cluster correlation values. Except in two cases, observed within-cluster correlation values were either close to or less than a priori values. Even with the CONSORT extension for cluster randomization, the reporting of sample size elements specific to these trials remains below that necessary for transparent reporting. Journal editors and peer reviewers should implement stricter requirements for authors to follow CONSORT recommendations. Authors should report observed and a priori within-cluster correlation values to enable comparisons between these over a wider range of trials. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Sample size calculations for stepped wedge and cluster randomised trials: a unified approach

PubMed Central

Hemming, Karla; Taljaard, Monica

2016-01-01

Objectives To clarify and illustrate sample size calculations for the cross-sectional stepped wedge cluster randomized trial (SW-CRT) and to present a simple approach for comparing the efficiencies of competing designs within a unified framework. Study Design and Setting We summarize design effects for the SW-CRT, the parallel cluster randomized trial (CRT), and the parallel cluster randomized trial with before and after observations (CRT-BA), assuming cross-sectional samples are selected over time. We present new formulas that enable trialists to determine the required cluster size for a given number of clusters. We illustrate by example how to implement the presented design effects and give practical guidance on the design of stepped wedge studies. Results For a fixed total cluster size, the choice of study design that provides the greatest power depends on the intracluster correlation coefficient (ICC) and the cluster size. When the ICC is small, the CRT tends to be more efficient; when the ICC is large, the SW-CRT tends to be more efficient and can serve as an alternative design when the CRT is an infeasible design. Conclusion Our unified approach allows trialists to easily compare the efficiencies of three competing designs to inform the decision about the most efficient design in a given scenario. PMID:26344808

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…

Inference and sample size calculation for clinical trials with incomplete observations of paired binary outcomes.

PubMed

Zhang, Song; Cao, Jing; Ahn, Chul

2017-02-20

We investigate the estimation of intervention effect and sample size determination for experiments where subjects are supposed to contribute paired binary outcomes with some incomplete observations. We propose a hybrid estimator to appropriately account for the mixed nature of observed data: paired outcomes from those who contribute complete pairs of observations and unpaired outcomes from those who contribute either pre-intervention or post-intervention outcomes. We theoretically prove that if incomplete data are evenly distributed between the pre-intervention and post-intervention periods, the proposed estimator will always be more efficient than the traditional estimator. A numerical research shows that when the distribution of incomplete data is unbalanced, the proposed estimator will be superior when there is moderate-to-strong positive within-subject correlation. We further derive a closed-form sample size formula to help researchers determine how many subjects need to be enrolled in such studies. Simulation results suggest that the calculated sample size maintains the empirical power and type I error under various design configurations. We demonstrate the proposed method using a real application example. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Methods for sample size determination in cluster randomized trials

PubMed Central

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

Relative efficiency and sample size for cluster randomized trials with variable cluster sizes.

PubMed

You, Zhiying; Williams, O Dale; Aban, Inmaculada; Kabagambe, Edmond Kato; Tiwari, Hemant K; Cutter, Gary

2011-02-01

The statistical power of cluster randomized trials depends on two sample size components, the number of clusters per group and the numbers of individuals within clusters (cluster size). Variable cluster sizes are common and this variation alone may have significant impact on study power. Previous approaches have taken this into account by either adjusting total sample size using a designated design effect or adjusting the number of clusters according to an assessment of the relative efficiency of unequal versus equal cluster sizes. This article defines a relative efficiency of unequal versus equal cluster sizes using noncentrality parameters, investigates properties of this measure, and proposes an approach for adjusting the required sample size accordingly. We focus on comparing two groups with normally distributed outcomes using t-test, and use the noncentrality parameter to define the relative efficiency of unequal versus equal cluster sizes and show that statistical power depends only on this parameter for a given number of clusters. We calculate the sample size required for an unequal cluster sizes trial to have the same power as one with equal cluster sizes. Relative efficiency based on the noncentrality parameter is straightforward to calculate and easy to interpret. It connects the required mean cluster size directly to the required sample size with equal cluster sizes. Consequently, our approach first determines the sample size requirements with equal cluster sizes for a pre-specified study power and then calculates the required mean cluster size while keeping the number of clusters unchanged. Our approach allows adjustment in mean cluster size alone or simultaneous adjustment in mean cluster size and number of clusters, and is a flexible alternative to and a useful complement to existing methods. Comparison indicated that we have defined a relative efficiency that is greater than the relative efficiency in the literature under some conditions. Our measure

Requirements for Minimum Sample Size for Sensitivity and Specificity Analysis

PubMed Central

Adnan, Tassha Hilda

2016-01-01

Sensitivity and specificity analysis is commonly used for screening and diagnostic tests. The main issue researchers face is to determine the sufficient sample sizes that are related with screening and diagnostic studies. Although the formula for sample size calculation is available but concerning majority of the researchers are not mathematicians or statisticians, hence, sample size calculation might not be easy for them. This review paper provides sample size tables with regards to sensitivity and specificity analysis. These tables were derived from formulation of sensitivity and specificity test using Power Analysis and Sample Size (PASS) software based on desired type I error, power and effect size. The approaches on how to use the tables were also discussed. PMID:27891446

The large sample size fallacy.

PubMed

Lantz, Björn

2013-06-01

Significance in the statistical sense has little to do with significance in the common practical sense. Statistical significance is a necessary but not a sufficient condition for practical significance. Hence, results that are extremely statistically significant may be highly nonsignificant in practice. The degree of practical significance is generally determined by the size of the observed effect, not the p-value. The results of studies based on large samples are often characterized by extreme statistical significance despite small or even trivial effect sizes. Interpreting such results as significant in practice without further analysis is referred to as the large sample size fallacy in this article. The aim of this article is to explore the relevance of the large sample size fallacy in contemporary nursing research. Relatively few nursing articles display explicit measures of observed effect sizes or include a qualitative discussion of observed effect sizes. Statistical significance is often treated as an end in itself. Effect sizes should generally be calculated and presented along with p-values for statistically significant results, and observed effect sizes should be discussed qualitatively through direct and explicit comparisons with the effects in related literature. © 2012 Nordic College of Caring Science.

[Effect sizes, statistical power and sample sizes in "the Japanese Journal of Psychology"].

PubMed

Suzukawa, Yumi; Toyoda, Hideki

2012-04-01

This study analyzed the statistical power of research studies published in the "Japanese Journal of Psychology" in 2008 and 2009. Sample effect sizes and sample statistical powers were calculated for each statistical test and analyzed with respect to the analytical methods and the fields of the studies. The results show that in the fields like perception, cognition or learning, the effect sizes were relatively large, although the sample sizes were small. At the same time, because of the small sample sizes, some meaningful effects could not be detected. In the other fields, because of the large sample sizes, meaningless effects could be detected. This implies that researchers who could not get large enough effect sizes would use larger samples to obtain significant results.

A simple approach to power and sample size calculations in logistic regression and Cox regression models.

PubMed

Vaeth, Michael; Skovlund, Eva

2004-06-15

For a given regression problem it is possible to identify a suitably defined equivalent two-sample problem such that the power or sample size obtained for the two-sample problem also applies to the regression problem. For a standard linear regression model the equivalent two-sample problem is easily identified, but for generalized linear models and for Cox regression models the situation is more complicated. An approximately equivalent two-sample problem may, however, also be identified here. In particular, we show that for logistic regression and Cox regression models the equivalent two-sample problem is obtained by selecting two equally sized samples for which the parameters differ by a value equal to the slope times twice the standard deviation of the independent variable and further requiring that the overall expected number of events is unchanged. In a simulation study we examine the validity of this approach to power calculations in logistic regression and Cox regression models. Several different covariate distributions are considered for selected values of the overall response probability and a range of alternatives. For the Cox regression model we consider both constant and non-constant hazard rates. The results show that in general the approach is remarkably accurate even in relatively small samples. Some discrepancies are, however, found in small samples with few events and a highly skewed covariate distribution. Comparison with results based on alternative methods for logistic regression models with a single continuous covariate indicates that the proposed method is at least as good as its competitors. The method is easy to implement and therefore provides a simple way to extend the range of problems that can be covered by the usual formulas for power and sample size determination. Copyright 2004 John Wiley & Sons, Ltd.

Sample size considerations for clinical research studies in nuclear cardiology.

PubMed

Chiuzan, Cody; West, Erin A; Duong, Jimmy; Cheung, Ken Y K; Einstein, Andrew J

2015-12-01

Sample size calculation is an important element of research design that investigators need to consider in the planning stage of the study. Funding agencies and research review panels request a power analysis, for example, to determine the minimum number of subjects needed for an experiment to be informative. Calculating the right sample size is crucial to gaining accurate information and ensures that research resources are used efficiently and ethically. The simple question "How many subjects do I need?" does not always have a simple answer. Before calculating the sample size requirements, a researcher must address several aspects, such as purpose of the research (descriptive or comparative), type of samples (one or more groups), and data being collected (continuous or categorical). In this article, we describe some of the most frequent methods for calculating the sample size with examples from nuclear cardiology research, including for t tests, analysis of variance (ANOVA), non-parametric tests, correlation, Chi-squared tests, and survival analysis. For the ease of implementation, several examples are also illustrated via user-friendly free statistical software.

Sample size and power for cost-effectiveness analysis (part 1).

PubMed

Glick, Henry A

2011-03-01

Basic sample size and power formulae for cost-effectiveness analysis have been established in the literature. These formulae are reviewed and the similarities and differences between sample size and power for cost-effectiveness analysis and for the analysis of other continuous variables such as changes in blood pressure or weight are described. The types of sample size and power tables that are commonly calculated for cost-effectiveness analysis are also described and the impact of varying the assumed parameter values on the resulting sample size and power estimates is discussed. Finally, the way in which the data for these calculations may be derived are discussed.

Causality in Statistical Power: Isomorphic Properties of Measurement, Research Design, Effect Size, and Sample Size.

PubMed

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.

Sample size in studies on diagnostic accuracy in ophthalmology: a literature survey.

PubMed

Bochmann, Frank; Johnson, Zoe; Azuara-Blanco, Augusto

2007-07-01

To assess the sample sizes used in studies on diagnostic accuracy in ophthalmology. Design and sources: A survey literature published in 2005. The frequency of reporting calculations of sample sizes and the samples' sizes were extracted from the published literature. A manual search of five leading clinical journals in ophthalmology with the highest impact (Investigative Ophthalmology and Visual Science, Ophthalmology, Archives of Ophthalmology, American Journal of Ophthalmology and British Journal of Ophthalmology) was conducted by two independent investigators. A total of 1698 articles were identified, of which 40 studies were on diagnostic accuracy. One study reported that sample size was calculated before initiating the study. Another study reported consideration of sample size without calculation. The mean (SD) sample size of all diagnostic studies was 172.6 (218.9). The median prevalence of the target condition was 50.5%. Only a few studies consider sample size in their methods. Inadequate sample sizes in diagnostic accuracy studies may result in misleading estimates of test accuracy. An improvement over the current standards on the design and reporting of diagnostic studies is warranted.

Developing the Noncentrality Parameter for Calculating Group Sample Sizes in Heterogeneous Analysis of Variance

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…

Biostatistics Series Module 5: Determining Sample Size

PubMed Central

Hazra, Avijit; Gogtay, Nithya

2016-01-01

Determining the appropriate sample size for a study, whatever be its type, is a fundamental aspect of biomedical research. An adequate sample ensures that the study will yield reliable information, regardless of whether the data ultimately suggests a clinically important difference between the interventions or elements being studied. The probability of Type 1 and Type 2 errors, the expected variance in the sample and the effect size are the essential determinants of sample size in interventional studies. Any method for deriving a conclusion from experimental data carries with it some risk of drawing a false conclusion. Two types of false conclusion may occur, called Type 1 and Type 2 errors, whose probabilities are denoted by the symbols σ and β. A Type 1 error occurs when one concludes that a difference exists between the groups being compared when, in reality, it does not. This is akin to a false positive result. A Type 2 error occurs when one concludes that difference does not exist when, in reality, a difference does exist, and it is equal to or larger than the effect size defined by the alternative to the null hypothesis. This may be viewed as a false negative result. When considering the risk of Type 2 error, it is more intuitive to think in terms of power of the study or (1 − β). Power denotes the probability of detecting a difference when a difference does exist between the groups being compared. Smaller α or larger power will increase sample size. Conventional acceptable values for power and α are 80% or above and 5% or below, respectively, when calculating sample size. Increasing variance in the sample tends to increase the sample size required to achieve a given power level. The effect size is the smallest clinically important difference that is sought to be detected and, rather than statistical convention, is a matter of past experience and clinical judgment. Larger samples are required if smaller differences are to be detected. Although the

Sample size of the reference sample in a case-augmented study.

PubMed

Ghosh, Palash; Dewanji, Anup

2017-05-01

The case-augmented study, in which a case sample is augmented with a reference (random) sample from the source population with only covariates information known, is becoming popular in different areas of applied science such as pharmacovigilance, ecology, and econometrics. In general, the case sample is available from some source (for example, hospital database, case registry, etc.); however, the reference sample is required to be drawn from the corresponding source population. The required minimum size of the reference sample is an important issue in this regard. In this work, we address the minimum sample size calculation and discuss related issues. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Approximate sample size formulas for the two-sample trimmed mean test with unequal variances.

PubMed

Luh, Wei-Ming; Guo, Jiin-Huarng

2007-05-01

Yuen's two-sample trimmed mean test statistic is one of the most robust methods to apply when variances are heterogeneous. The present study develops formulas for the sample size required for the test. The formulas are applicable for the cases of unequal variances, non-normality and unequal sample sizes. Given the specified alpha and the power (1-beta), the minimum sample size needed by the proposed formulas under various conditions is less than is given by the conventional formulas. Moreover, given a specified size of sample calculated by the proposed formulas, simulation results show that Yuen's test can achieve statistical power which is generally superior to that of the approximate t test. A numerical example is provided.

Sample size considerations when groups are the appropriate unit of analyses

PubMed Central

Sadler, Georgia Robins; Ko, Celine Marie; Alisangco, Jennifer; Rosbrook, Bradley P.; Miller, Eric; Fullerton, Judith

2007-01-01

This paper discusses issues to be considered by nurse researchers when groups should be used as a unit of randomization. Advantages and disadvantages are presented, with statistical calculations needed to determine effective sample size. Examples of these concepts are presented using data from the Black Cosmetologists Promoting Health Program. Different hypothetical scenarios and their impact on sample size are presented. Given the complexity of calculating sample size when using groups as a unit of randomization, it’s advantageous for researchers to work closely with statisticians when designing and implementing studies that anticipate the use of groups as the unit of randomization. PMID:17693219

Sample size determination for estimating antibody seroconversion rate under stable malaria transmission intensity.

PubMed

Sepúlveda, Nuno; Drakeley, Chris

2015-04-03

In the last decade, several epidemiological studies have demonstrated the potential of using seroprevalence (SP) and seroconversion rate (SCR) as informative indicators of malaria burden in low transmission settings or in populations on the cusp of elimination. However, most of studies are designed to control ensuing statistical inference over parasite rates and not on these alternative malaria burden measures. SP is in essence a proportion and, thus, many methods exist for the respective sample size determination. In contrast, designing a study where SCR is the primary endpoint, is not an easy task because precision and statistical power are affected by the age distribution of a given population. Two sample size calculators for SCR estimation are proposed. The first one consists of transforming the confidence interval for SP into the corresponding one for SCR given a known seroreversion rate (SRR). The second calculator extends the previous one to the most common situation where SRR is unknown. In this situation, data simulation was used together with linear regression in order to study the expected relationship between sample size and precision. The performance of the first sample size calculator was studied in terms of the coverage of the confidence intervals for SCR. The results pointed out to eventual problems of under or over coverage for sample sizes ≤250 in very low and high malaria transmission settings (SCR ≤ 0.0036 and SCR ≥ 0.29, respectively). The correct coverage was obtained for the remaining transmission intensities with sample sizes ≥ 50. Sample size determination was then carried out for cross-sectional surveys using realistic SCRs from past sero-epidemiological studies and typical age distributions from African and non-African populations. For SCR < 0.058, African studies require a larger sample size than their non-African counterparts in order to obtain the same precision. The opposite happens for the remaining transmission

Neuromuscular dose-response studies: determining sample size.

PubMed

Kopman, A F; Lien, C A; Naguib, M

2011-02-01

Investigators planning dose-response studies of neuromuscular blockers have rarely used a priori power analysis to determine the minimal sample size their protocols require. Institutional Review Boards and peer-reviewed journals now generally ask for this information. This study outlines a proposed method for meeting these requirements. The slopes of the dose-response relationships of eight neuromuscular blocking agents were determined using regression analysis. These values were substituted for γ in the Hill equation. When this is done, the coefficient of variation (COV) around the mean value of the ED₅₀ for each drug is easily calculated. Using these values, we performed an a priori one-sample two-tailed t-test of the means to determine the required sample size when the allowable error in the ED₅₀ was varied from ±10-20%. The COV averaged 22% (range 15-27%). We used a COV value of 25% in determining the sample size. If the allowable error in finding the mean ED₅₀ is ±15%, a sample size of 24 is needed to achieve a power of 80%. Increasing 'accuracy' beyond this point requires increasing greater sample sizes (e.g. an 'n' of 37 for a ±12% error). On the basis of the results of this retrospective analysis, a total sample size of not less than 24 subjects should be adequate for determining a neuromuscular blocking drug's clinical potency with a reasonable degree of assurance.

Publication Bias in Psychology: A Diagnosis Based on the Correlation between Effect Size and Sample Size

PubMed Central

Kühberger, Anton; Fritz, Astrid; Scherndl, Thomas

2014-01-01

Background The p value obtained from a significance test provides no information about the magnitude or importance of the underlying phenomenon. Therefore, additional reporting of effect size is often recommended. Effect sizes are theoretically independent from sample size. Yet this may not hold true empirically: non-independence could indicate publication bias. Methods We investigate whether effect size is independent from sample size in psychological research. We randomly sampled 1,000 psychological articles from all areas of psychological research. We extracted p values, effect sizes, and sample sizes of all empirical papers, and calculated the correlation between effect size and sample size, and investigated the distribution of p values. Results We found a negative correlation of r = −.45 [95% CI: −.53; −.35] between effect size and sample size. In addition, we found an inordinately high number of p values just passing the boundary of significance. Additional data showed that neither implicit nor explicit power analysis could account for this pattern of findings. Conclusion The negative correlation between effect size and samples size, and the biased distribution of p values indicate pervasive publication bias in the entire field of psychology. PMID:25192357

Publication bias in psychology: a diagnosis based on the correlation between effect size and sample size.

PubMed

Kühberger, Anton; Fritz, Astrid; Scherndl, Thomas

2014-01-01

The p value obtained from a significance test provides no information about the magnitude or importance of the underlying phenomenon. Therefore, additional reporting of effect size is often recommended. Effect sizes are theoretically independent from sample size. Yet this may not hold true empirically: non-independence could indicate publication bias. We investigate whether effect size is independent from sample size in psychological research. We randomly sampled 1,000 psychological articles from all areas of psychological research. We extracted p values, effect sizes, and sample sizes of all empirical papers, and calculated the correlation between effect size and sample size, and investigated the distribution of p values. We found a negative correlation of r = -.45 [95% CI: -.53; -.35] between effect size and sample size. In addition, we found an inordinately high number of p values just passing the boundary of significance. Additional data showed that neither implicit nor explicit power analysis could account for this pattern of findings. The negative correlation between effect size and samples size, and the biased distribution of p values indicate pervasive publication bias in the entire field of psychology.

Quantification of errors in ordinal outcome scales using shannon entropy: effect on sample size calculations.

PubMed

Mandava, Pitchaiah; Krumpelman, Chase S; Shah, Jharna N; White, Donna L; Kent, Thomas A

2013-01-01

Clinical trial outcomes often involve an ordinal scale of subjective functional assessments but the optimal way to quantify results is not clear. In stroke, the most commonly used scale, the modified Rankin Score (mRS), a range of scores ("Shift") is proposed as superior to dichotomization because of greater information transfer. The influence of known uncertainties in mRS assessment has not been quantified. We hypothesized that errors caused by uncertainties could be quantified by applying information theory. Using Shannon's model, we quantified errors of the "Shift" compared to dichotomized outcomes using published distributions of mRS uncertainties and applied this model to clinical trials. We identified 35 randomized stroke trials that met inclusion criteria. Each trial's mRS distribution was multiplied with the noise distribution from published mRS inter-rater variability to generate an error percentage for "shift" and dichotomized cut-points. For the SAINT I neuroprotectant trial, considered positive by "shift" mRS while the larger follow-up SAINT II trial was negative, we recalculated sample size required if classification uncertainty was taken into account. Considering the full mRS range, error rate was 26.1%±5.31 (Mean±SD). Error rates were lower for all dichotomizations tested using cut-points (e.g. mRS 1; 6.8%±2.89; overall p<0.001). Taking errors into account, SAINT I would have required 24% more subjects than were randomized. We show when uncertainty in assessments is considered, the lowest error rates are with dichotomization. While using the full range of mRS is conceptually appealing, a gain of information is counter-balanced by a decrease in reliability. The resultant errors need to be considered since sample size may otherwise be underestimated. In principle, we have outlined an approach to error estimation for any condition in which there are uncertainties in outcome assessment. We provide the user with programs to calculate and incorporate

Conservative Sample Size Determination for Repeated Measures Analysis of Covariance.

PubMed

Morgan, Timothy M; Case, L Douglas

2013-07-05

In the design of a randomized clinical trial with one pre and multiple post randomized assessments of the outcome variable, one needs to account for the repeated measures in determining the appropriate sample size. Unfortunately, one seldom has a good estimate of the variance of the outcome measure, let alone the correlations among the measurements over time. We show how sample sizes can be calculated by making conservative assumptions regarding the correlations for a variety of covariance structures. The most conservative choice for the correlation depends on the covariance structure and the number of repeated measures. In the absence of good estimates of the correlations, the sample size is often based on a two-sample t-test, making the 'ultra' conservative and unrealistic assumption that there are zero correlations between the baseline and follow-up measures while at the same time assuming there are perfect correlations between the follow-up measures. Compared to the case of taking a single measurement, substantial savings in sample size can be realized by accounting for the repeated measures, even with very conservative assumptions regarding the parameters of the assumed correlation matrix. Assuming compound symmetry, the sample size from the two-sample t-test calculation can be reduced at least 44%, 56%, and 61% for repeated measures analysis of covariance by taking 2, 3, and 4 follow-up measures, respectively. The results offer a rational basis for determining a fairly conservative, yet efficient, sample size for clinical trials with repeated measures and a baseline value.

Phylogenetic effective sample size.

PubMed

Bartoszek, Krzysztof

2016-10-21

In this paper I address the question-how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes-the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Sample size determination for mediation analysis of longitudinal data.

PubMed

Pan, Haitao; Liu, Suyu; Miao, Danmin; Yuan, Ying

2018-03-27

Sample size planning for longitudinal data is crucial when designing mediation studies because sufficient statistical power is not only required in grant applications and peer-reviewed publications, but is essential to reliable research results. However, sample size determination is not straightforward for mediation analysis of longitudinal design. To facilitate planning the sample size for longitudinal mediation studies with a multilevel mediation model, this article provides the sample size required to achieve 80% power by simulations under various sizes of the mediation effect, within-subject correlations and numbers of repeated measures. The sample size calculation is based on three commonly used mediation tests: Sobel's method, distribution of product method and the bootstrap method. Among the three methods of testing the mediation effects, Sobel's method required the largest sample size to achieve 80% power. Bootstrapping and the distribution of the product method performed similarly and were more powerful than Sobel's method, as reflected by the relatively smaller sample sizes. For all three methods, the sample size required to achieve 80% power depended on the value of the ICC (i.e., within-subject correlation). A larger value of ICC typically required a larger sample size to achieve 80% power. Simulation results also illustrated the advantage of the longitudinal study design. The sample size tables for most encountered scenarios in practice have also been published for convenient use. Extensive simulations study showed that the distribution of the product method and bootstrapping method have superior performance to the Sobel's method, but the product method was recommended to use in practice in terms of less computation time load compared to the bootstrapping method. A R package has been developed for the product method of sample size determination in mediation longitudinal study design.

RnaSeqSampleSize: real data based sample size estimation for RNA sequencing.

PubMed

Zhao, Shilin; Li, Chung-I; Guo, Yan; Sheng, Quanhu; Shyr, Yu

2018-05-30

One of the most important and often neglected components of a successful RNA sequencing (RNA-Seq) experiment is sample size estimation. A few negative binomial model-based methods have been developed to estimate sample size based on the parameters of a single gene. However, thousands of genes are quantified and tested for differential expression simultaneously in RNA-Seq experiments. Thus, additional issues should be carefully addressed, including the false discovery rate for multiple statistic tests, widely distributed read counts and dispersions for different genes. To solve these issues, we developed a sample size and power estimation method named RnaSeqSampleSize, based on the distributions of gene average read counts and dispersions estimated from real RNA-seq data. Datasets from previous, similar experiments such as the Cancer Genome Atlas (TCGA) can be used as a point of reference. Read counts and their dispersions were estimated from the reference's distribution; using that information, we estimated and summarized the power and sample size. RnaSeqSampleSize is implemented in R language and can be installed from Bioconductor website. A user friendly web graphic interface is provided at http://cqs.mc.vanderbilt.edu/shiny/RnaSeqSampleSize/ . RnaSeqSampleSize provides a convenient and powerful way for power and sample size estimation for an RNAseq experiment. It is also equipped with several unique features, including estimation for interested genes or pathway, power curve visualization, and parameter optimization.

The cost of large numbers of hypothesis tests on power, effect size and sample size.

PubMed

Lazzeroni, L C; Ray, A

2012-01-01

Advances in high-throughput biology and computer science are driving an exponential increase in the number of hypothesis tests in genomics and other scientific disciplines. Studies using current genotyping platforms frequently include a million or more tests. In addition to the monetary cost, this increase imposes a statistical cost owing to the multiple testing corrections needed to avoid large numbers of false-positive results. To safeguard against the resulting loss of power, some have suggested sample sizes on the order of tens of thousands that can be impractical for many diseases or may lower the quality of phenotypic measurements. This study examines the relationship between the number of tests on the one hand and power, detectable effect size or required sample size on the other. We show that once the number of tests is large, power can be maintained at a constant level, with comparatively small increases in the effect size or sample size. For example at the 0.05 significance level, a 13% increase in sample size is needed to maintain 80% power for ten million tests compared with one million tests, whereas a 70% increase in sample size is needed for 10 tests compared with a single test. Relative costs are less when measured by increases in the detectable effect size. We provide an interactive Excel calculator to compute power, effect size or sample size when comparing study designs or genome platforms involving different numbers of hypothesis tests. The results are reassuring in an era of extreme multiple testing.

Comparison of Sample Size by Bootstrap and by Formulas Based on Normal Distribution Assumption.

PubMed

Wang, Zuozhen

2018-01-01

Bootstrapping technique is distribution-independent, which provides an indirect way to estimate the sample size for a clinical trial based on a relatively smaller sample. In this paper, sample size estimation to compare two parallel-design arms for continuous data by bootstrap procedure are presented for various test types (inequality, non-inferiority, superiority, and equivalence), respectively. Meanwhile, sample size calculation by mathematical formulas (normal distribution assumption) for the identical data are also carried out. Consequently, power difference between the two calculation methods is acceptably small for all the test types. It shows that the bootstrap procedure is a credible technique for sample size estimation. After that, we compared the powers determined using the two methods based on data that violate the normal distribution assumption. To accommodate the feature of the data, the nonparametric statistical method of Wilcoxon test was applied to compare the two groups in the data during the process of bootstrap power estimation. As a result, the power estimated by normal distribution-based formula is far larger than that by bootstrap for each specific sample size per group. Hence, for this type of data, it is preferable that the bootstrap method be applied for sample size calculation at the beginning, and that the same statistical method as used in the subsequent statistical analysis is employed for each bootstrap sample during the course of bootstrap sample size estimation, provided there is historical true data available that can be well representative of the population to which the proposed trial is planning to extrapolate.

Sample size, power calculations, and their implications for the cost of thorough studies of drug induced QT interval prolongation.

PubMed

Malik, Marek; Hnatkova, Katerina; Batchvarov, Velislav; Gang, Yi; Smetana, Peter; Camm, A John

2004-12-01

Regulatory authorities require new drugs to be investigated using a so-called "thorough QT/QTc study" to identify compounds with a potential of influencing cardiac repolarization in man. Presently drafted regulatory consensus requires these studies to be powered for the statistical detection of QTc interval changes as small as 5 ms. Since this translates into a noticeable drug development burden, strategies need to be identified allowing the size and thus the cost of thorough QT/QTc studies to be minimized. This study investigated the influence of QT and RR interval data quality and the precision of heart rate correction on the sample sizes of thorough QT/QTc studies. In 57 healthy subjects (26 women, age range 19-42 years), a total of 4,195 drug-free digital electrocardiograms (ECG) were obtained (65-84 ECGs per subject). All ECG parameters were measured manually using the most accurate approach with reconciliation of measurement differences between different cardiologists and aligning the measurements of corresponding ECG patterns. From the data derived in this measurement process, seven different levels of QT/RR data quality were obtained, ranging from the simplest approach of measuring 3 beats in one ECG lead to the most exact approach. Each of these QT/RR data-sets was processed with eight different heart rate corrections ranging from Bazett and Fridericia corrections to the individual QT/RR regression modelling with optimization of QT/RR curvature. For each combination of data quality and heart rate correction, standard deviation of individual mean QTc values and mean of individual standard deviations of QTc values were calculated and used to derive the size of thorough QT/QTc studies with an 80% power to detect 5 ms QTc changes at the significance level of 0.05. Irrespective of data quality and heart rate corrections, the necessary sample sizes of studies based on between-subject comparisons (e.g., parallel studies) are very substantial requiring >140

Systematic review finds major deficiencies in sample size methodology and reporting for stepped-wedge cluster randomised trials

PubMed Central

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

A note on power and sample size calculations for the Kruskal-Wallis test for ordered categorical data.

PubMed

Fan, Chunpeng; Zhang, Donghui

2012-01-01

Although the Kruskal-Wallis test has been widely used to analyze ordered categorical data, power and sample size methods for this test have been investigated to a much lesser extent when the underlying multinomial distributions are unknown. This article generalizes the power and sample size procedures proposed by Fan et al. ( 2011 ) for continuous data to ordered categorical data, when estimates from a pilot study are used in the place of knowledge of the true underlying distribution. Simulations show that the proposed power and sample size formulas perform well. A myelin oligodendrocyte glycoprotein (MOG) induced experimental autoimmunce encephalomyelitis (EAE) mouse study is used to demonstrate the application of the methods.

On the repeated measures designs and sample sizes for randomized controlled trials.

PubMed

Tango, Toshiro

2016-04-01

For the analysis of longitudinal or repeated measures data, generalized linear mixed-effects models provide a flexible and powerful tool to deal with heterogeneity among subject response profiles. However, the typical statistical design adopted in usual randomized controlled trials is an analysis of covariance type analysis using a pre-defined pair of "pre-post" data, in which pre-(baseline) data are used as a covariate for adjustment together with other covariates. Then, the major design issue is to calculate the sample size or the number of subjects allocated to each treatment group. In this paper, we propose a new repeated measures design and sample size calculations combined with generalized linear mixed-effects models that depend not only on the number of subjects but on the number of repeated measures before and after randomization per subject used for the analysis. The main advantages of the proposed design combined with the generalized linear mixed-effects models are (1) it can easily handle missing data by applying the likelihood-based ignorable analyses under the missing at random assumption and (2) it may lead to a reduction in sample size, compared with the simple pre-post design. The proposed designs and the sample size calculations are illustrated with real data arising from randomized controlled trials. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Sample size determination for logistic regression on a logit-normal distribution.

PubMed

Kim, Seongho; Heath, Elisabeth; Heilbrun, Lance

2017-06-01

Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination ([Formula: see text]) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for [Formula: see text] for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size.

The endothelial sample size analysis in corneal specular microscopy clinical examinations.

PubMed

Abib, Fernando C; Holzchuh, Ricardo; Schaefer, Artur; Schaefer, Tania; Godois, Ronialci

2012-05-01

To evaluate endothelial cell sample size and statistical error in corneal specular microscopy (CSM) examinations. One hundred twenty examinations were conducted with 4 types of corneal specular microscopes: 30 with each BioOptics, CSO, Konan, and Topcon corneal specular microscopes. All endothelial image data were analyzed by respective instrument software and also by the Cells Analyzer software with a method developed in our lab. A reliability degree (RD) of 95% and a relative error (RE) of 0.05 were used as cut-off values to analyze images of the counted endothelial cells called samples. The sample size mean was the number of cells evaluated on the images obtained with each device. Only examinations with RE < 0.05 were considered statistically correct and suitable for comparisons with future examinations. The Cells Analyzer software was used to calculate the RE and customized sample size for all examinations. Bio-Optics: sample size, 97 ± 22 cells; RE, 6.52 ± 0.86; only 10% of the examinations had sufficient endothelial cell quantity (RE < 0.05); customized sample size, 162 ± 34 cells. CSO: sample size, 110 ± 20 cells; RE, 5.98 ± 0.98; only 16.6% of the examinations had sufficient endothelial cell quantity (RE < 0.05); customized sample size, 157 ± 45 cells. Konan: sample size, 80 ± 27 cells; RE, 10.6 ± 3.67; none of the examinations had sufficient endothelial cell quantity (RE > 0.05); customized sample size, 336 ± 131 cells. Topcon: sample size, 87 ± 17 cells; RE, 10.1 ± 2.52; none of the examinations had sufficient endothelial cell quantity (RE > 0.05); customized sample size, 382 ± 159 cells. A very high number of CSM examinations had sample errors based on Cells Analyzer software. The endothelial sample size (examinations) needs to include more cells to be reliable and reproducible. The Cells Analyzer tutorial routine will be useful for CSM examination reliability and reproducibility.

"PowerUp"!: A Tool for Calculating Minimum Detectable Effect Sizes and Minimum Required Sample Sizes for Experimental and Quasi-Experimental Design Studies

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…

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

PubMed

Herzog, Sereina A; Low, Nicola; Berghold, Andrea

2015-06-19

The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Sample Size Estimation: The Easy Way

ERIC Educational Resources Information Center

Weller, Susan C.

2015-01-01

This article presents a simple approach to making quick sample size estimates for basic hypothesis tests. Although there are many sources available for estimating sample sizes, methods are not often integrated across statistical tests, levels of measurement of variables, or effect sizes. A few parameters are required to estimate sample sizes and…

Experimental design, power and sample size for animal reproduction experiments.

PubMed

Chapman, Phillip L; Seidel, George E

2008-01-01

The present paper concerns statistical issues in the design of animal reproduction experiments, with emphasis on the problems of sample size determination and power calculations. We include examples and non-technical discussions aimed at helping researchers avoid serious errors that may invalidate or seriously impair the validity of conclusions from experiments. Screen shots from interactive power calculation programs and basic SAS power calculation programs are presented to aid in understanding statistical power and computing power in some common experimental situations. Practical issues that are common to most statistical design problems are briefly discussed. These include one-sided hypothesis tests, power level criteria, equality of within-group variances, transformations of response variables to achieve variance equality, optimal specification of treatment group sizes, 'post hoc' power analysis and arguments for the increased use of confidence intervals in place of hypothesis tests.

Acceleration of intensity-modulated radiotherapy dose calculation by importance sampling of the calculation matrices.

PubMed

Thieke, Christian; Nill, Simeon; Oelfke, Uwe; Bortfeld, Thomas

2002-05-01

In inverse planning for intensity-modulated radiotherapy, the dose calculation is a crucial element limiting both the maximum achievable plan quality and the speed of the optimization process. One way to integrate accurate dose calculation algorithms into inverse planning is to precalculate the dose contribution of each beam element to each voxel for unit fluence. These precalculated values are stored in a big dose calculation matrix. Then the dose calculation during the iterative optimization process consists merely of matrix look-up and multiplication with the actual fluence values. However, because the dose calculation matrix can become very large, this ansatz requires a lot of computer memory and is still very time consuming, making it not practical for clinical routine without further modifications. In this work we present a new method to significantly reduce the number of entries in the dose calculation matrix. The method utilizes the fact that a photon pencil beam has a rapid radial dose falloff, and has very small dose values for the most part. In this low-dose part of the pencil beam, the dose contribution to a voxel is only integrated into the dose calculation matrix with a certain probability. Normalization with the reciprocal of this probability preserves the total energy, even though many matrix elements are omitted. Three probability distributions were tested to find the most accurate one for a given memory size. The sampling method is compared with the use of a fully filled matrix and with the well-known method of just cutting off the pencil beam at a certain lateral distance. A clinical example of a head and neck case is presented. It turns out that a sampled dose calculation matrix with only 1/3 of the entries of the fully filled matrix does not sacrifice the quality of the resulting plans, whereby the cutoff method results in a suboptimal treatment plan.

Use of methods for specifying the target difference in randomised controlled trial sample size calculations: Two surveys of trialists' practice.

PubMed

Cook, Jonathan A; Hislop, Jennifer M; Altman, Doug G; Briggs, Andrew H; Fayers, Peter M; Norrie, John D; Ramsay, Craig R; Harvey, Ian M; Vale, Luke D

2014-06-01

the most recent trial, the target difference was usually one viewed as important by a stakeholder group, mostly also viewed as a realistic difference given the interventions under evaluation, and sometimes one that led to an achievable sample size. The response rates achieved were relatively low despite the surveys being short, well presented, and having utilised reminders. Substantial variations in practice exist with awareness, use, and willingness to recommend methods varying substantially. The findings support the view that sample size calculation is a more complex process than would appear to be the case from trial reports and protocols. Guidance on approaches for sample size estimation may increase both awareness and use of appropriate formal methods. © The Author(s), 2014.

Sample Size for Tablet Compression and Capsule Filling Events During Process Validation.

PubMed

Charoo, Naseem Ahmad; Durivage, Mark; Rahman, Ziyaur; Ayad, Mohamad Haitham

2017-12-01

During solid dosage form manufacturing, the uniformity of dosage units (UDU) is ensured by testing samples at 2 stages, that is, blend stage and tablet compression or capsule/powder filling stage. The aim of this work is to propose a sample size selection approach based on quality risk management principles for process performance qualification (PPQ) and continued process verification (CPV) stages by linking UDU to potential formulation and process risk factors. Bayes success run theorem appeared to be the most appropriate approach among various methods considered in this work for computing sample size for PPQ. The sample sizes for high-risk (reliability level of 99%), medium-risk (reliability level of 95%), and low-risk factors (reliability level of 90%) were estimated to be 299, 59, and 29, respectively. Risk-based assignment of reliability levels was supported by the fact that at low defect rate, the confidence to detect out-of-specification units would decrease which must be supplemented with an increase in sample size to enhance the confidence in estimation. Based on level of knowledge acquired during PPQ and the level of knowledge further required to comprehend process, sample size for CPV was calculated using Bayesian statistics to accomplish reduced sampling design for CPV. Copyright © 2017 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

Sample size allocation for food item radiation monitoring and safety inspection.

PubMed

Seto, Mayumi; Uriu, Koichiro

2015-03-01

The objective of this study is to identify a procedure for determining sample size allocation for food radiation inspections of more than one food item to minimize the potential risk to consumers of internal radiation exposure. We consider a simplified case of food radiation monitoring and safety inspection in which a risk manager is required to monitor two food items, milk and spinach, in a contaminated area. Three protocols for food radiation monitoring with different sample size allocations were assessed by simulating random sampling and inspections of milk and spinach in a conceptual monitoring site. Distributions of (131)I and radiocesium concentrations were determined in reference to (131)I and radiocesium concentrations detected in Fukushima prefecture, Japan, for March and April 2011. The results of the simulations suggested that a protocol that allocates sample size to milk and spinach based on the estimation of (131)I and radiocesium concentrations using the apparent decay rate constants sequentially calculated from past monitoring data can most effectively minimize the potential risks of internal radiation exposure. © 2014 Society for Risk Analysis.

Novel joint selection methods can reduce sample size for rheumatoid arthritis clinical trials with ultrasound endpoints.

PubMed

Allen, John C; Thumboo, Julian; Lye, Weng Kit; Conaghan, Philip G; Chew, Li-Ching; Tan, York Kiat

2018-03-01

To determine whether novel methods of selecting joints through (i) ultrasonography (individualized-ultrasound [IUS] method), or (ii) ultrasonography and clinical examination (individualized-composite-ultrasound [ICUS] method) translate into smaller rheumatoid arthritis (RA) clinical trial sample sizes when compared to existing methods utilizing predetermined joint sites for ultrasonography. Cohen's effect size (ES) was estimated (ES^) and a 95% CI (ES^L, ES^U) calculated on a mean change in 3-month total inflammatory score for each method. Corresponding 95% CIs [nL(ES^U), nU(ES^L)] were obtained on a post hoc sample size reflecting the uncertainty in ES^. Sample size calculations were based on a one-sample t-test as the patient numbers needed to provide 80% power at α = 0.05 to reject a null hypothesis H 0 : ES = 0 versus alternative hypotheses H 1 : ES = ES^, ES = ES^L and ES = ES^U. We aimed to provide point and interval estimates on projected sample sizes for future studies reflecting the uncertainty in our study ES^S. Twenty-four treated RA patients were followed up for 3 months. Utilizing the 12-joint approach and existing methods, the post hoc sample size (95% CI) was 22 (10-245). Corresponding sample sizes using ICUS and IUS were 11 (7-40) and 11 (6-38), respectively. Utilizing a seven-joint approach, the corresponding sample sizes using ICUS and IUS methods were nine (6-24) and 11 (6-35), respectively. Our pilot study suggests that sample size for RA clinical trials with ultrasound endpoints may be reduced using the novel methods, providing justification for larger studies to confirm these observations. © 2017 Asia Pacific League of Associations for Rheumatology and John Wiley & Sons Australia, Ltd.

On the validity of the Poisson assumption in sampling nanometer-sized aerosols

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 withmore » 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.« less

Sample Size in Clinical Cardioprotection Trials Using Myocardial Salvage Index, Infarct Size, or Biochemical Markers as Endpoint.

PubMed

Engblom, Henrik; Heiberg, Einar; Erlinge, David; Jensen, Svend Eggert; Nordrehaug, Jan Erik; Dubois-Randé, Jean-Luc; Halvorsen, Sigrun; Hoffmann, Pavel; Koul, Sasha; Carlsson, Marcus; Atar, Dan; Arheden, Håkan

2016-03-09

Cardiac magnetic resonance (CMR) can quantify myocardial infarct (MI) size and myocardium at risk (MaR), enabling assessment of myocardial salvage index (MSI). We assessed how MSI impacts the number of patients needed to reach statistical power in relation to MI size alone and levels of biochemical markers in clinical cardioprotection trials and how scan day affect sample size. Controls (n=90) from the recent CHILL-MI and MITOCARE trials were included. MI size, MaR, and MSI were assessed from CMR. High-sensitivity troponin T (hsTnT) and creatine kinase isoenzyme MB (CKMB) levels were assessed in CHILL-MI patients (n=50). Utilizing distribution of these variables, 100 000 clinical trials were simulated for calculation of sample size required to reach sufficient power. For a treatment effect of 25% decrease in outcome variables, 50 patients were required in each arm using MSI compared to 93, 98, 120, 141, and 143 for MI size alone, hsTnT (area under the curve [AUC] and peak), and CKMB (AUC and peak) in order to reach a power of 90%. If average CMR scan day between treatment and control arms differed by 1 day, sample size needs to be increased by 54% (77 vs 50) to avoid scan day bias masking a treatment effect of 25%. Sample size in cardioprotection trials can be reduced 46% to 65% without compromising statistical power when using MSI by CMR as an outcome variable instead of MI size alone or biochemical markers. It is essential to ensure lack of bias in scan day between treatment and control arms to avoid compromising statistical power. © 2016 The Authors. Published on behalf of the American Heart Association, Inc., by Wiley Blackwell.

Sample size adjustments for varying cluster sizes in cluster randomized trials with binary outcomes analyzed with second-order PQL mixed logistic regression.

PubMed

Candel, Math J J M; Van Breukelen, Gerard J P

2010-06-30

Adjustments of sample size formulas are given for varying cluster sizes in cluster randomized trials with a binary outcome when testing the treatment effect with mixed effects logistic regression using second-order penalized quasi-likelihood estimation (PQL). Starting from first-order marginal quasi-likelihood (MQL) estimation of the treatment effect, the asymptotic relative efficiency of unequal versus equal cluster sizes is derived. A Monte Carlo simulation study shows this asymptotic relative efficiency to be rather accurate for realistic sample sizes, when employing second-order PQL. An approximate, simpler formula is presented to estimate the efficiency loss due to varying cluster sizes when planning a trial. In many cases sampling 14 per cent more clusters is sufficient to repair the efficiency loss due to varying cluster sizes. Since current closed-form formulas for sample size calculation are based on first-order MQL, planning a trial also requires a conversion factor to obtain the variance of the second-order PQL estimator. In a second Monte Carlo study, this conversion factor turned out to be 1.25 at most. (c) 2010 John Wiley & Sons, Ltd.

Sample size for estimating mean and coefficient of variation in species of crotalarias.

PubMed

Toebe, Marcos; Machado, Letícia N; Tartaglia, Francieli L; Carvalho, Juliana O DE; Bandeira, Cirineu T; Cargnelutti Filho, Alberto

2018-04-16

The objective of this study was to determine the sample size necessary to estimate the mean and coefficient of variation in four species of crotalarias (C. juncea, C. spectabilis, C. breviflora and C. ochroleuca). An experiment was carried out for each species during the season 2014/15. At harvest, 1,000 pods of each species were randomly collected. In each pod were measured: mass of pod with and without seeds, length, width and height of pods, number and mass of seeds per pod, and mass of hundred seeds. Measures of central tendency, variability and distribution were calculated, and the normality was verified. The sample size necessary to estimate the mean and coefficient of variation with amplitudes of the confidence interval of 95% (ACI95%) of 2%, 4%, ..., 20% was determined by resampling with replacement. The sample size varies among species and characters, being necessary a larger sample size to estimate the mean in relation of the necessary for the coefficient of variation.

Development of a sampling strategy and sample size calculation to estimate the distribution of mammographic breast density in Korean women.

PubMed

Jun, Jae Kwan; Kim, Mi Jin; Choi, Kui Son; Suh, Mina; Jung, Kyu-Won

2012-01-01

Mammographic breast density is a known risk factor for breast cancer. To conduct a survey to estimate the distribution of mammographic breast density in Korean women, appropriate sampling strategies for representative and efficient sampling design were evaluated through simulation. Using the target population from the National Cancer Screening Programme (NCSP) for breast cancer in 2009, we verified the distribution estimate by repeating the simulation 1,000 times using stratified random sampling to investigate the distribution of breast density of 1,340,362 women. According to the simulation results, using a sampling design stratifying the nation into three groups (metropolitan, urban, and rural), with a total sample size of 4,000, we estimated the distribution of breast density in Korean women at a level of 0.01% tolerance. Based on the results of our study, a nationwide survey for estimating the distribution of mammographic breast density among Korean women can be conducted efficiently.

Sample size, confidence, and contingency judgement.

PubMed

Clément, Mélanie; Mercier, Pierre; Pastò, Luigi

2002-06-01

According to statistical models, the acquisition function of contingency judgement is due to confidence increasing with sample size. According to associative models, the function reflects the accumulation of associative strength on which the judgement is based. Which view is right? Thirty university students assessed the relation between a fictitious medication and a symptom of skin discoloration in conditions that varied sample size (4, 6, 8 or 40 trials) and contingency (delta P = .20, .40, .60 or .80). Confidence was also collected. Contingency judgement was lower for smaller samples, while confidence level correlated inversely with sample size. This dissociation between contingency judgement and confidence contradicts the statistical perspective.

The size of a pilot study for a clinical trial should be calculated in relation to considerations of precision and efficiency.

PubMed

Sim, Julius; Lewis, Martyn

2012-03-01

To investigate methods to determine the size of a pilot study to inform a power calculation for a randomized controlled trial (RCT) using an interval/ratio outcome measure. Calculations based on confidence intervals (CIs) for the sample standard deviation (SD). Based on CIs for the sample SD, methods are demonstrated whereby (1) the observed SD can be adjusted to secure the desired level of statistical power in the main study with a specified level of confidence; (2) the sample for the main study, if calculated using the observed SD, can be adjusted, again to obtain the desired level of statistical power in the main study; (3) the power of the main study can be calculated for the situation in which the SD in the pilot study proves to be an underestimate of the true SD; and (4) an "efficient" pilot size can be determined to minimize the combined size of the pilot and main RCT. Trialists should calculate the appropriate size of a pilot study, just as they should the size of the main RCT, taking into account the twin needs to demonstrate efficiency in terms of recruitment and to produce precise estimates of treatment effect. Copyright © 2012 Elsevier Inc. All rights reserved.

Assessing the precision of a time-sampling-based study among GPs: balancing sample size and measurement frequency.

PubMed

van Hassel, Daniël; van der Velden, Lud; de Bakker, Dinny; van der Hoek, Lucas; Batenburg, Ronald

2017-12-04

Our research is based on a technique for time sampling, an innovative method for measuring the working hours of Dutch general practitioners (GPs), which was deployed in an earlier study. In this study, 1051 GPs were questioned about their activities in real time by sending them one SMS text message every 3 h during 1 week. The required sample size for this study is important for health workforce planners to know if they want to apply this method to target groups who are hard to reach or if fewer resources are available. In this time-sampling method, however, standard power analyses is not sufficient for calculating the required sample size as this accounts only for sample fluctuation and not for the fluctuation of measurements taken from every participant. We investigated the impact of the number of participants and frequency of measurements per participant upon the confidence intervals (CIs) for the hours worked per week. Statistical analyses of the time-use data we obtained from GPs were performed. Ninety-five percent CIs were calculated, using equations and simulation techniques, for various different numbers of GPs included in the dataset and for various frequencies of measurements per participant. Our results showed that the one-tailed CI, including sample and measurement fluctuation, decreased from 21 until 3 h between one and 50 GPs. As a result of the formulas to calculate CIs, the increase of the precision continued and was lower with the same additional number of GPs. Likewise, the analyses showed how the number of participants required decreased if more measurements per participant were taken. For example, one measurement per 3-h time slot during the week requires 300 GPs to achieve a CI of 1 h, while one measurement per hour requires 100 GPs to obtain the same result. The sample size needed for time-use research based on a time-sampling technique depends on the design and aim of the study. In this paper, we showed how the precision of the

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…

What is the optimum sample size for the study of peatland testate amoeba assemblages?

PubMed

Mazei, Yuri A; Tsyganov, Andrey N; Esaulov, Anton S; Tychkov, Alexander Yu; Payne, Richard J

2017-10-01

Testate amoebae are widely used in ecological and palaeoecological studies of peatlands, particularly as indicators of surface wetness. To ensure data are robust and comparable it is important to consider methodological factors which may affect results. One significant question which has not been directly addressed in previous studies is how sample size (expressed here as number of Sphagnum stems) affects data quality. In three contrasting locations in a Russian peatland we extracted samples of differing size, analysed testate amoebae and calculated a number of widely-used indices: species richness, Simpson diversity, compositional dissimilarity from the largest sample and transfer function predictions of water table depth. We found that there was a trend for larger samples to contain more species across the range of commonly-used sample sizes in ecological studies. Smaller samples sometimes failed to produce counts of testate amoebae often considered minimally adequate. It seems likely that analyses based on samples of different sizes may not produce consistent data. Decisions about sample size need to reflect trade-offs between logistics, data quality, spatial resolution and the disturbance involved in sample extraction. For most common ecological applications we suggest that samples of more than eight Sphagnum stems are likely to be desirable. Copyright © 2017 Elsevier GmbH. All rights reserved.

On sample size of the kruskal-wallis test with application to a mouse peritoneal cavity study.

PubMed

Fan, Chunpeng; Zhang, Donghui; Zhang, Cun-Hui

2011-03-01

As the nonparametric generalization of the one-way analysis of variance model, the Kruskal-Wallis test applies when the goal is to test the difference between multiple samples and the underlying population distributions are nonnormal or unknown. Although the Kruskal-Wallis test has been widely used for data analysis, power and sample size methods for this test have been investigated to a much lesser extent. This article proposes new power and sample size calculation methods for the Kruskal-Wallis test based on the pilot study in either a completely nonparametric model or a semiparametric location model. No assumption is made on the shape of the underlying population distributions. Simulation results show that, in terms of sample size calculation for the Kruskal-Wallis test, the proposed methods are more reliable and preferable to some more traditional methods. A mouse peritoneal cavity study is used to demonstrate the application of the methods. © 2010, The International Biometric Society.

Confidence intervals and sample size calculations for the standardized mean difference effect size between two normal populations under heteroscedasticity.

PubMed

Shieh, G

2013-12-01

The use of effect sizes and associated confidence intervals in all empirical research has been strongly emphasized by journal publication guidelines. To help advance theory and practice in the social sciences, this article describes an improved procedure for constructing confidence intervals of the standardized mean difference effect size between two independent normal populations with unknown and possibly unequal variances. The presented approach has advantages over the existing formula in both theoretical justification and computational simplicity. In addition, simulation results show that the suggested one- and two-sided confidence intervals are more accurate in achieving the nominal coverage probability. The proposed estimation method provides a feasible alternative to the most commonly used measure of Cohen's d and the corresponding interval procedure when the assumption of homogeneous variances is not tenable. To further improve the potential applicability of the suggested methodology, the sample size procedures for precise interval estimation of the standardized mean difference are also delineated. The desired precision of a confidence interval is assessed with respect to the control of expected width and to the assurance probability of interval width within a designated value. Supplementary computer programs are developed to aid in the usefulness and implementation of the introduced techniques.

Optimal flexible sample size design with robust power.

PubMed

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. Copyright © 2016 John Wiley & Sons, Ltd.

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…

Detecting spatial structures in throughfall data: The effect of extent, sample size, sampling design, and variogram estimation method

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

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling.

PubMed

Luchko, Tyler; Blinov, Nikolay; Limon, Garrett C; Joyce, Kevin P; Kovalenko, Andriy

2016-11-01

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing ([Formula: see text] for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining [Formula: see text] compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to [Formula: see text]. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple [Formula: see text] correction improved agreement with experiment from [Formula: see text] to [Formula: see text], despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling

NASA Astrophysics Data System (ADS)

Luchko, Tyler; Blinov, Nikolay; Limon, Garrett C.; Joyce, Kevin P.; Kovalenko, Andriy

2016-11-01

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing (R=0.98 for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining R=0.73 compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to R=0.93. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple pK_{ {a}} correction improved agreement with experiment from R=0.54 to R=0.66, despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.

Treatment Trials for Neonatal Seizures: The Effect of Design on Sample Size

PubMed Central

Stevenson, Nathan J.; Boylan, Geraldine B.; Hellström-Westas, Lena; Vanhatalo, Sampsa

2016-01-01

Neonatal seizures are common in the neonatal intensive care unit. Clinicians treat these seizures with several anti-epileptic drugs (AEDs) to reduce seizures in a neonate. Current AEDs exhibit sub-optimal efficacy and several randomized control trials (RCT) of novel AEDs are planned. The aim of this study was to measure the influence of trial design on the required sample size of a RCT. We used seizure time courses from 41 term neonates with hypoxic ischaemic encephalopathy to build seizure treatment trial simulations. We used five outcome measures, three AED protocols, eight treatment delays from seizure onset (Td) and four levels of trial AED efficacy to simulate different RCTs. We performed power calculations for each RCT design and analysed the resultant sample size. We also assessed the rate of false positives, or placebo effect, in typical uncontrolled studies. We found that the false positive rate ranged from 5 to 85% of patients depending on RCT design. For controlled trials, the choice of outcome measure had the largest effect on sample size with median differences of 30.7 fold (IQR: 13.7–40.0) across a range of AED protocols, Td and trial AED efficacy (p<0.001). RCTs that compared the trial AED with positive controls required sample sizes with a median fold increase of 3.2 (IQR: 1.9–11.9; p<0.001). Delays in AED administration from seizure onset also increased the required sample size 2.1 fold (IQR: 1.7–2.9; p<0.001). Subgroup analysis showed that RCTs in neonates treated with hypothermia required a median fold increase in sample size of 2.6 (IQR: 2.4–3.0) compared to trials in normothermic neonates (p<0.001). These results show that RCT design has a profound influence on the required sample size. Trials that use a control group, appropriate outcome measure, and control for differences in Td between groups in analysis will be valid and minimise sample size. PMID:27824913

Simple, Defensible Sample Sizes Based on Cost Efficiency

PubMed Central

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

Blinded sample size re-estimation in three-arm trials with 'gold standard' design.

PubMed

Mütze, Tobias; Friede, Tim

2017-10-15

In this article, we study blinded sample size re-estimation in the 'gold standard' design with internal pilot study for normally distributed outcomes. The 'gold standard' design is a three-arm clinical trial design that includes an active and a placebo control in addition to an experimental treatment. We focus on the absolute margin approach to hypothesis testing in three-arm trials at which the non-inferiority of the experimental treatment and the assay sensitivity are assessed by pairwise comparisons. We compare several blinded sample size re-estimation procedures in a simulation study assessing operating characteristics including power and type I error. We find that sample size re-estimation based on the popular one-sample variance estimator results in overpowered trials. Moreover, sample size re-estimation based on unbiased variance estimators such as the Xing-Ganju variance estimator results in underpowered trials, as it is expected because an overestimation of the variance and thus the sample size is in general required for the re-estimation procedure to eventually meet the target power. To overcome this problem, we propose an inflation factor for the sample size re-estimation with the Xing-Ganju variance estimator and show that this approach results in adequately powered trials. Because of favorable features of the Xing-Ganju variance estimator such as unbiasedness and a distribution independent of the group means, the inflation factor does not depend on the nuisance parameter and, therefore, can be calculated prior to a trial. Moreover, we prove that the sample size re-estimation based on the Xing-Ganju variance estimator does not bias the effect estimate. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

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.

A modified approach to estimating sample size for simple logistic regression with one continuous covariate.

PubMed

Novikov, I; Fund, N; Freedman, L S

2010-01-15

Different methods for the calculation of sample size for simple logistic regression (LR) with one normally distributed continuous covariate give different results. Sometimes the difference can be large. Furthermore, some methods require the user to specify the prevalence of cases when the covariate equals its population mean, rather than the more natural population prevalence. We focus on two commonly used methods and show through simulations that the power for a given sample size may differ substantially from the nominal value for one method, especially when the covariate effect is large, while the other method performs poorly if the user provides the population prevalence instead of the required parameter. We propose a modification of the method of Hsieh et al. that requires specification of the population prevalence and that employs Schouten's sample size formula for a t-test with unequal variances and group sizes. This approach appears to increase the accuracy of the sample size estimates for LR with one continuous covariate.

Species richness in soil bacterial communities: a proposed approach to overcome sample size bias.

PubMed

Youssef, Noha H; Elshahed, Mostafa S

2008-09-01

Estimates of species richness based on 16S rRNA gene clone libraries are increasingly utilized to gauge the level of bacterial diversity within various ecosystems. However, previous studies have indicated that regardless of the utilized approach, species richness estimates obtained are dependent on the size of the analyzed clone libraries. We here propose an approach to overcome sample size bias in species richness estimates in complex microbial communities. Parametric (Maximum likelihood-based and rarefaction curve-based) and non-parametric approaches were used to estimate species richness in a library of 13,001 near full-length 16S rRNA clones derived from soil, as well as in multiple subsets of the original library. Species richness estimates obtained increased with the increase in library size. To obtain a sample size-unbiased estimate of species richness, we calculated the theoretical clone library sizes required to encounter the estimated species richness at various clone library sizes, used curve fitting to determine the theoretical clone library size required to encounter the "true" species richness, and subsequently determined the corresponding sample size-unbiased species richness value. Using this approach, sample size-unbiased estimates of 17,230, 15,571, and 33,912 were obtained for the ML-based, rarefaction curve-based, and ACE-1 estimators, respectively, compared to bias-uncorrected values of 15,009, 11,913, and 20,909.

Element enrichment factor calculation using grain-size distribution and functional data regression.

PubMed

Sierra, C; Ordóñez, C; Saavedra, A; Gallego, J R

2015-01-01

In environmental geochemistry studies it is common practice to normalize element concentrations in order to remove the effect of grain size. Linear regression with respect to a particular grain size or conservative element is a widely used method of normalization. In this paper, the utility of functional linear regression, in which the grain-size curve is the independent variable and the concentration of pollutant the dependent variable, is analyzed and applied to detrital sediment. After implementing functional linear regression and classical linear regression models to normalize and calculate enrichment factors, we concluded that the former regression technique has some advantages over the latter. First, functional linear regression directly considers the grain-size distribution of the samples as the explanatory variable. Second, as the regression coefficients are not constant values but functions depending on the grain size, it is easier to comprehend the relationship between grain size and pollutant concentration. Third, regularization can be introduced into the model in order to establish equilibrium between reliability of the data and smoothness of the solutions. Copyright © 2014 Elsevier Ltd. All rights reserved.

Threshold-dependent sample sizes for selenium assessment with stream fish tissue

USGS Publications Warehouse

Hitt, Nathaniel P.; Smith, David R.

2015-01-01

Natural resource managers are developing assessments of selenium (Se) contamination in freshwater ecosystems based on fish tissue concentrations. We evaluated the effects of sample size (i.e., number of fish per site) on the probability of correctly detecting mean whole-body Se values above a range of potential management thresholds. We modeled Se concentrations as gamma distributions with shape and scale parameters fitting an empirical mean-to-variance relationship in data from southwestern West Virginia, USA (63 collections, 382 individuals). We used parametric bootstrapping techniques to calculate statistical power as the probability of detecting true mean concentrations up to 3 mg Se/kg above management thresholds ranging from 4 to 8 mg Se/kg. Sample sizes required to achieve 80% power varied as a function of management thresholds and Type I error tolerance (α). Higher thresholds required more samples than lower thresholds because populations were more heterogeneous at higher mean Se levels. For instance, to assess a management threshold of 4 mg Se/kg, a sample of eight fish could detect an increase of approximately 1 mg Se/kg with 80% power (given α = 0.05), but this sample size would be unable to detect such an increase from a management threshold of 8 mg Se/kg with more than a coin-flip probability. Increasing α decreased sample size requirements to detect above-threshold mean Se concentrations with 80% power. For instance, at an α-level of 0.05, an 8-fish sample could detect an increase of approximately 2 units above a threshold of 8 mg Se/kg with 80% power, but when α was relaxed to 0.2, this sample size was more sensitive to increasing mean Se concentrations, allowing detection of an increase of approximately 1.2 units with equivalent power. Combining individuals into 2- and 4-fish composite samples for laboratory analysis did not decrease power because the reduced number of laboratory samples was compensated for by increased

Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications

PubMed Central

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

Detecting spatial structures in throughfall data: the effect of extent, sample size, sampling design, and variogram estimation method

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

Understanding the cluster randomised crossover design: a graphical illustraton of the components of variation and a sample size tutorial.

PubMed

Arnup, Sarah J; McKenzie, Joanne E; Hemming, Karla; Pilcher, David; Forbes, Andrew B

2017-08-15

In a cluster randomised crossover (CRXO) design, a sequence of interventions is assigned to a group, or 'cluster' of individuals. Each cluster receives each intervention in a separate period of time, forming 'cluster-periods'. Sample size calculations for CRXO trials need to account for both the cluster randomisation and crossover aspects of the design. Formulae are available for the two-period, two-intervention, cross-sectional CRXO design, however implementation of these formulae is known to be suboptimal. The aims of this tutorial are to illustrate the intuition behind the design; and provide guidance on performing sample size calculations. Graphical illustrations are used to describe the effect of the cluster randomisation and crossover aspects of the design on the correlation between individual responses in a CRXO trial. Sample size calculations for binary and continuous outcomes are illustrated using parameters estimated from the Australia and New Zealand Intensive Care Society - Adult Patient Database (ANZICS-APD) for patient mortality and length(s) of stay (LOS). The similarity between individual responses in a CRXO trial can be understood in terms of three components of variation: variation in cluster mean response; variation in the cluster-period mean response; and variation between individual responses within a cluster-period; or equivalently in terms of the correlation between individual responses in the same cluster-period (within-cluster within-period correlation, WPC), and between individual responses in the same cluster, but in different periods (within-cluster between-period correlation, BPC). The BPC lies between zero and the WPC. When the WPC and BPC are equal the precision gained by crossover aspect of the CRXO design equals the precision lost by cluster randomisation. When the BPC is zero there is no advantage in a CRXO over a parallel-group cluster randomised trial. Sample size calculations illustrate that small changes in the specification of

Enhanced Ligand Sampling for Relative Protein–Ligand Binding Free Energy Calculations

PubMed Central

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

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…

Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs

PubMed Central

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

Sample sizes to control error estimates in determining soil bulk density in California forest soils

Treesearch

Youzhi Han; Jianwei Zhang; Kim G. Mattson; Weidong Zhang; Thomas A. Weber

2016-01-01

Characterizing forest soil properties with high variability is challenging, sometimes requiring large numbers of soil samples. Soil bulk density is a standard variable needed along with element concentrations to calculate nutrient pools. This study aimed to determine the optimal sample size, the number of observation (n), for predicting the soil bulk density with a...

40 CFR 89.424 - Dilute emission sampling calculations.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 20 2010-07-01 2010-07-01 false Dilute emission sampling calculations... Emission Test Procedures § 89.424 Dilute emission sampling calculations. (a) The final reported emission... concentration. For cases where exhaust sampling of CO2 is not performed, the following approximation is...

40 CFR 89.424 - Dilute emission sampling calculations.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 20 2011-07-01 2011-07-01 false Dilute emission sampling calculations... Emission Test Procedures § 89.424 Dilute emission sampling calculations. (a) The final reported emission... concentration. For cases where exhaust sampling of CO2 is not performed, the following approximation is...

40 CFR 80.127 - Sample size guidelines.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 16 2010-07-01 2010-07-01 false Sample size guidelines. 80.127 Section 80.127 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) REGULATION OF FUELS AND FUEL ADDITIVES Attest Engagements § 80.127 Sample size guidelines. In performing the...

Power and sample size for multivariate logistic modeling of unmatched case-control studies.

PubMed

Gail, Mitchell H; Haneuse, Sebastien

2017-01-01

Sample size calculations are needed to design and assess the feasibility of case-control studies. Although such calculations are readily available for simple case-control designs and univariate analyses, there is limited theory and software for multivariate unconditional logistic analysis of case-control data. Here we outline the theory needed to detect scalar exposure effects or scalar interactions while controlling for other covariates in logistic regression. Both analytical and simulation methods are presented, together with links to the corresponding software.

mHealth Series: Factors influencing sample size calculations for mHealth–based studies – A mixed methods study in rural China

PubMed Central

van Velthoven, Michelle Helena; Li, Ye; Wang, Wei; Du, Xiaozhen; Chen, Li; Wu, Qiong; Majeed, Azeem; Zhang, Yanfeng; Car, Josip

2013-01-01

Background An important issue for mHealth evaluation is the lack of information for sample size calculations. Objective To explore factors that influence sample size calculations for mHealth–based studies and to suggest strategies for increasing the participation rate. Methods We explored factors influencing recruitment and follow–up of participants (caregivers of children) in an mHealth text messaging data collection cross–over study. With help of village doctors, we recruited 1026 (25%) caregivers of children under five out of the 4170 registered. To explore factors influencing recruitment and provide recommendations for improving recruitment, we conducted semi–structured interviews with village doctors. Of the 1014 included participants, 662 (65%) responded to the first question about willingness to participate, 538 (53%) responded to the first survey question and 356 (35%) completed the text message survey. To explore factors influencing follow–up and provide recommendations for improving follow–up, we conducted interviews with participants. We added views from the researchers who were involved in the study to contextualize the findings. Results We found several factors influencing recruitment related to the following themes: experiences with recruitment, village doctors’ work, village doctors’ motivations, caregivers’ characteristics, caregivers’ motivations. Village doctors gave several recommendations for ways to recruit more caregivers and we added our views to these. We found the following factors influencing follow–up: mobile phone usage, ability to use mobile phone, problems with mobile phone, checking mobile phone, available time, paying back text message costs, study incentives, subjective norm, culture, trust, perceived usefulness of process, perceived usefulness of outcome, perceived ease of use, attitude, behavioural intention to use, and actual use. From our perspective, factors influencing follow–up were: different

Determination of the optimal sample size for a clinical trial accounting for the population size.

PubMed

Stallard, Nigel; Miller, Frank; Day, Simon; Hee, Siew Wan; Madan, Jason; Zohar, Sarah; Posch, Martin

2017-07-01

The problem of choosing a sample size for a clinical trial is a very common one. In some settings, such as rare diseases or other small populations, the large sample sizes usually associated with the standard frequentist approach may be infeasible, suggesting that the sample size chosen should reflect the size of the population under consideration. Incorporation of the population size is possible in a decision-theoretic approach either explicitly by assuming that the population size is fixed and known, or implicitly through geometric discounting of the gain from future patients reflecting the expected population size. This paper develops such approaches. Building on previous work, an asymptotic expression is derived for the sample size for single and two-arm clinical trials in the general case of a clinical trial with a primary endpoint with a distribution of one parameter exponential family form that optimizes a utility function that quantifies the cost and gain per patient as a continuous function of this parameter. It is shown that as the size of the population, N, or expected size, N∗ in the case of geometric discounting, becomes large, the optimal trial size is O(N1/2) or O(N∗1/2). The sample size obtained from the asymptotic expression is also compared with the exact optimal sample size in examples with responses with Bernoulli and Poisson distributions, showing that the asymptotic approximations can also be reasonable in relatively small sample sizes. © 2016 The Author. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Computer program for the calculation of grain size statistics by the method of moments

USGS Publications Warehouse

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.

Evaluation of Sampling Recommendations From the Influenza Virologic Surveillance Right Size Roadmap for Idaho

PubMed Central

2017-01-01

Background The Right Size Roadmap was developed by the Association of Public Health Laboratories and the Centers for Disease Control and Prevention to improve influenza virologic surveillance efficiency. Guidelines were provided to state health departments regarding representativeness and statistical estimates of specimen numbers needed for seasonal influenza situational awareness, rare or novel influenza virus detection, and rare or novel influenza virus investigation. Objective The aim of this study was to compare Roadmap sampling recommendations with Idaho’s influenza virologic surveillance to determine implementation feasibility. Methods We calculated the proportion of medically attended influenza-like illness (MA-ILI) from Idaho’s influenza-like illness surveillance among outpatients during October 2008 to May 2014, applied data to Roadmap-provided sample size calculators, and compared calculations with actual numbers of specimens tested for influenza by the Idaho Bureau of Laboratories (IBL). We assessed representativeness among patients’ tested specimens to census estimates by age, sex, and health district residence. Results Among outpatients surveilled, Idaho’s mean annual proportion of MA-ILI was 2.30% (20,834/905,818) during a 5-year period. Thus, according to Roadmap recommendations, Idaho needs to collect 128 specimens from MA-ILI patients/week for situational awareness, 1496 influenza-positive specimens/week for detection of a rare or novel influenza virus at 0.2% prevalence, and after detection, 478 specimens/week to confirm true prevalence is ≤2% of influenza-positive samples. The mean number of respiratory specimens Idaho tested for influenza/week, excluding the 2009-2010 influenza season, ranged from 6 to 24. Various influenza virus types and subtypes were collected and specimen submission sources were representative in terms of geographic distribution, patient age range and sex, and disease severity. Conclusions Insufficient numbers of

Selection of the effect size for sample size determination for a continuous response in a superiority clinical trial using a hybrid classical and Bayesian procedure.

PubMed

Ciarleglio, Maria M; Arendt, Christopher D; Peduzzi, Peter N

2016-06-01

When designing studies that have a continuous outcome as the primary endpoint, the hypothesized effect size ([Formula: see text]), that is, the hypothesized difference in means ([Formula: see text]) relative to the assumed variability of the endpoint ([Formula: see text]), plays an important role in sample size and power calculations. Point estimates for [Formula: see text] and [Formula: see text] are often calculated using historical data. However, the uncertainty in these estimates is rarely addressed. This article presents a hybrid classical and Bayesian procedure that formally integrates prior information on the distributions of [Formula: see text] and [Formula: see text] into the study's power calculation. Conditional expected power, which averages the traditional power curve using the prior distributions of [Formula: see text] and [Formula: see text] as the averaging weight, is used, and the value of [Formula: see text] is found that equates the prespecified frequentist power ([Formula: see text]) and the conditional expected power of the trial. This hypothesized effect size is then used in traditional sample size calculations when determining sample size for the study. The value of [Formula: see text] found using this method may be expressed as a function of the prior means of [Formula: see text] and [Formula: see text], [Formula: see text], and their prior standard deviations, [Formula: see text]. We show that the "naïve" estimate of the effect size, that is, the ratio of prior means, should be down-weighted to account for the variability in the parameters. An example is presented for designing a placebo-controlled clinical trial testing the antidepressant effect of alprazolam as monotherapy for major depression. Through this method, we are able to formally integrate prior information on the uncertainty and variability of both the treatment effect and the common standard deviation into the design of the study while maintaining a frequentist framework for

[Practical aspects regarding sample size in clinical research].

PubMed

Vega Ramos, B; Peraza Yanes, O; Herrera Correa, G; Saldívar Toraya, S

1996-01-01

The knowledge of the right sample size let us to be sure if the published results in medical papers had a suitable design and a proper conclusion according to the statistics analysis. To estimate the sample size we must consider the type I error, type II error, variance, the size of the effect, significance and power of the test. To decide what kind of mathematics formula will be used, we must define what kind of study we have, it means if its a prevalence study, a means values one or a comparative one. In this paper we explain some basic topics of statistics and we describe four simple samples of estimation of sample size.

a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

NASA Astrophysics Data System (ADS)

Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

Estimating the size of hidden populations using respondent-driven sampling data: Case examples from Morocco

PubMed Central

Johnston, Lisa G; McLaughlin, Katherine R; Rhilani, Houssine El; Latifi, Amina; Toufik, Abdalla; Bennani, Aziza; Alami, Kamal; Elomari, Boutaina; Handcock, Mark S

2015-01-01

Background Respondent-driven sampling is used worldwide to estimate the population prevalence of characteristics such as HIV/AIDS and associated risk factors in hard-to-reach populations. Estimating the total size of these populations is of great interest to national and international organizations, however reliable measures of population size often do not exist. Methods Successive Sampling-Population Size Estimation (SS-PSE) along with network size imputation allows population size estimates to be made without relying on separate studies or additional data (as in network scale-up, multiplier and capture-recapture methods), which may be biased. Results Ten population size estimates were calculated for people who inject drugs, female sex workers, men who have sex with other men, and migrants from sub-Sahara Africa in six different cities in Morocco. SS-PSE estimates fell within or very close to the likely values provided by experts and the estimates from previous studies using other methods. Conclusions SS-PSE is an effective method for estimating the size of hard-to-reach populations that leverages important information within respondent-driven sampling studies. The addition of a network size imputation method helps to smooth network sizes allowing for more accurate results. However, caution should be used particularly when there is reason to believe that clustered subgroups may exist within the population of interest or when the sample size is small in relation to the population. PMID:26258908

Re-estimating sample size in cluster randomised trials with active recruitment within clusters.

PubMed

van Schie, S; Moerbeek, M

2014-08-30

Often only a limited number of clusters can be obtained in cluster randomised trials, although many potential participants can be recruited within each cluster. Thus, active recruitment is feasible within the clusters. To obtain an efficient sample size in a cluster randomised trial, the cluster level and individual level variance should be known before the study starts, but this is often not the case. We suggest using an internal pilot study design to address this problem of unknown variances. A pilot can be useful to re-estimate the variances and re-calculate the sample size during the trial. Using simulated data, it is shown that an initially low or high power can be adjusted using an internal pilot with the type I error rate remaining within an acceptable range. The intracluster correlation coefficient can be re-estimated with more precision, which has a positive effect on the sample size. We conclude that an internal pilot study design may be used if active recruitment is feasible within a limited number of clusters. Copyright © 2014 John Wiley & Sons, Ltd.

40 CFR 600.208-77 - Sample calculation.

Code of Federal Regulations, 2010 CFR

2010-07-01

... ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Fuel Economy Regulations for 1977 and Later Model Year Automobiles-Procedures for Calculating Fuel Economy Values § 600.208-77 Sample calculation...

Distribution of the two-sample t-test statistic following blinded sample size re-estimation.

PubMed

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. Copyright © 2016 John Wiley & Sons, Ltd.

Optimality, sample size, and power calculations for the sequential parallel comparison design.

PubMed

Ivanova, Anastasia; Qaqish, Bahjat; Schoenfeld, David A

2011-10-15

The sequential parallel comparison design (SPCD) has been proposed to increase the likelihood of success of clinical trials in therapeutic areas where high-placebo response is a concern. The trial is run in two stages, and subjects are randomized into three groups: (i) placebo in both stages; (ii) placebo in the first stage and drug in the second stage; and (iii) drug in both stages. We consider the case of binary response data (response/no response). In the SPCD, all first-stage and second-stage data from placebo subjects who failed to respond in the first stage of the trial are utilized in the efficacy analysis. We develop 1 and 2 degree of freedom score tests for treatment effect in the SPCD. We give formulae for asymptotic power and for sample size computations and evaluate their accuracy via simulation studies. We compute the optimal allocation ratio between drug and placebo in stage 1 for the SPCD to determine from a theoretical viewpoint whether a single-stage design, a two-stage design with placebo only in the first stage, or a two-stage design is the best design for a given set of response rates. As response rates are not known before the trial, a two-stage approach with allocation to active drug in both stages is a robust design choice. Copyright © 2011 John Wiley & Sons, Ltd.

40 CFR 89.418 - Raw emission sampling calculations.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 20 2011-07-01 2011-07-01 false Raw emission sampling calculations. 89... Test Procedures § 89.418 Raw emission sampling calculations. (a) The final test results shall be... measured on a wet basis. This section is applicable only for measurements made on raw exhaust gas...

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... measured on a wet basis. This section is applicable only for measurements made on raw exhaust gas...

Estimation of sample size and testing power (Part 4).

PubMed

Hu, Liang-ping; Bao, Xiao-lei; Guan, Xue; Zhou, Shi-guo

2012-01-01

Sample size estimation is necessary for any experimental or survey research. An appropriate estimation of sample size based on known information and statistical knowledge is of great significance. This article introduces methods of sample size estimation of difference test for data with the design of one factor with two levels, including sample size estimation formulas and realization based on the formulas and the POWER procedure of SAS software for quantitative data and qualitative data with the design of one factor with two levels. In addition, this article presents examples for analysis, which will play a leading role for researchers to implement the repetition principle during the research design phase.

Designing image segmentation studies: Statistical power, sample size and reference standard quality.

PubMed

Gibson, Eli; Hu, Yipeng; Huisman, Henkjan J; Barratt, Dean C

2017-12-01

Segmentation algorithms are typically evaluated by comparison to an accepted reference standard. The cost of generating accurate reference standards for medical image segmentation can be substantial. Since the study cost and the likelihood of detecting a clinically meaningful difference in accuracy both depend on the size and on the quality of the study reference standard, balancing these trade-offs supports the efficient use of research resources. In this work, we derive a statistical power calculation that enables researchers to estimate the appropriate sample size to detect clinically meaningful differences in segmentation accuracy (i.e. the proportion of voxels matching the reference standard) between two algorithms. Furthermore, we derive a formula to relate reference standard errors to their effect on the sample sizes of studies using lower-quality (but potentially more affordable and practically available) reference standards. The accuracy of the derived sample size formula was estimated through Monte Carlo simulation, demonstrating, with 95% confidence, a predicted statistical power within 4% of simulated values across a range of model parameters. This corresponds to sample size errors of less than 4 subjects and errors in the detectable accuracy difference less than 0.6%. The applicability of the formula to real-world data was assessed using bootstrap resampling simulations for pairs of algorithms from the PROMISE12 prostate MR segmentation challenge data set. The model predicted the simulated power for the majority of algorithm pairs within 4% for simulated experiments using a high-quality reference standard and within 6% for simulated experiments using a low-quality reference standard. A case study, also based on the PROMISE12 data, illustrates using the formulae to evaluate whether to use a lower-quality reference standard in a prostate segmentation study. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

Evaluation of Sampling Recommendations From the Influenza Virologic Surveillance Right Size Roadmap for Idaho.

PubMed

Rosenthal, Mariana; Anderson, Katey; Tengelsen, Leslie; Carter, Kris; Hahn, Christine; Ball, Christopher

2017-08-24

The Right Size Roadmap was developed by the Association of Public Health Laboratories and the Centers for Disease Control and Prevention to improve influenza virologic surveillance efficiency. Guidelines were provided to state health departments regarding representativeness and statistical estimates of specimen numbers needed for seasonal influenza situational awareness, rare or novel influenza virus detection, and rare or novel influenza virus investigation. The aim of this study was to compare Roadmap sampling recommendations with Idaho's influenza virologic surveillance to determine implementation feasibility. We calculated the proportion of medically attended influenza-like illness (MA-ILI) from Idaho's influenza-like illness surveillance among outpatients during October 2008 to May 2014, applied data to Roadmap-provided sample size calculators, and compared calculations with actual numbers of specimens tested for influenza by the Idaho Bureau of Laboratories (IBL). We assessed representativeness among patients' tested specimens to census estimates by age, sex, and health district residence. Among outpatients surveilled, Idaho's mean annual proportion of MA-ILI was 2.30% (20,834/905,818) during a 5-year period. Thus, according to Roadmap recommendations, Idaho needs to collect 128 specimens from MA-ILI patients/week for situational awareness, 1496 influenza-positive specimens/week for detection of a rare or novel influenza virus at 0.2% prevalence, and after detection, 478 specimens/week to confirm true prevalence is ≤2% of influenza-positive samples. The mean number of respiratory specimens Idaho tested for influenza/week, excluding the 2009-2010 influenza season, ranged from 6 to 24. Various influenza virus types and subtypes were collected and specimen submission sources were representative in terms of geographic distribution, patient age range and sex, and disease severity. Insufficient numbers of respiratory specimens are submitted to IBL for influenza

Rock sampling. [apparatus for controlling particle size

NASA Technical Reports Server (NTRS)

Blum, P. (Inventor)

1971-01-01

An apparatus for sampling rock and other brittle materials and for controlling resultant particle sizes is described. The device includes grinding means for cutting grooves in the rock surface and to provide a grouping of thin, shallow, parallel ridges and cutter means to reduce these ridges to a powder specimen. Collection means is provided for the powder. The invention relates to rock grinding and particularly to the sampling of rock specimens with good size control.

Ranked set sampling: cost and optimal set size.

PubMed

Nahhas, Ramzi W; Wolfe, Douglas A; Chen, Haiying

2002-12-01

McIntyre (1952, Australian Journal of Agricultural Research 3, 385-390) introduced ranked set sampling (RSS) as a method for improving estimation of a population mean in settings where sampling and ranking of units from the population are inexpensive when compared with actual measurement of the units. Two of the major factors in the usefulness of RSS are the set size and the relative costs of the various operations of sampling, ranking, and measurement. In this article, we consider ranking error models and cost models that enable us to assess the effect of different cost structures on the optimal set size for RSS. For reasonable cost structures, we find that the optimal RSS set sizes are generally larger than had been anticipated previously. These results will provide a useful tool for determining whether RSS is likely to lead to an improvement over simple random sampling in a given setting and, if so, what RSS set size is best to use in this case.

Generalized SAMPLE SIZE Determination Formulas for Investigating Contextual Effects by a Three-Level Random Intercept Model.

PubMed

Usami, Satoshi

2017-03-01

Behavioral and psychological researchers have shown strong interests in investigating contextual effects (i.e., the influences of combinations of individual- and group-level predictors on individual-level outcomes). The present research provides generalized formulas for determining the sample size needed in investigating contextual effects according to the desired level of statistical power as well as width of confidence interval. These formulas are derived within a three-level random intercept model that includes one predictor/contextual variable at each level to simultaneously cover various kinds of contextual effects that researchers can show interest. The relative influences of indices included in the formulas on the standard errors of contextual effects estimates are investigated with the aim of further simplifying sample size determination procedures. In addition, simulation studies are performed to investigate finite sample behavior of calculated statistical power, showing that estimated sample sizes based on derived formulas can be both positively and negatively biased due to complex effects of unreliability of contextual variables, multicollinearity, and violation of assumption regarding the known variances. Thus, it is advisable to compare estimated sample sizes under various specifications of indices and to evaluate its potential bias, as illustrated in the example.

Sample size determination for equivalence assessment with multiple endpoints.

PubMed

Sun, Anna; Dong, Xiaoyu; Tsong, Yi

2014-01-01

Equivalence assessment between a reference and test treatment is often conducted by two one-sided tests (TOST). The corresponding power function and sample size determination can be derived from a joint distribution of the sample mean and sample variance. When an equivalence trial is designed with multiple endpoints, it often involves several sets of two one-sided tests. A naive approach for sample size determination in this case would select the largest sample size required for each endpoint. However, such a method ignores the correlation among endpoints. With the objective to reject all endpoints and when the endpoints are uncorrelated, the power function is the production of all power functions for individual endpoints. With correlated endpoints, the sample size and power should be adjusted for such a correlation. In this article, we propose the exact power function for the equivalence test with multiple endpoints adjusted for correlation under both crossover and parallel designs. We further discuss the differences in sample size for the naive method without and with correlation adjusted methods and illustrate with an in vivo bioequivalence crossover study with area under the curve (AUC) and maximum concentration (Cmax) as the two endpoints.

Optimum sample size allocation to minimize cost or maximize power for the two-sample trimmed mean test.

PubMed

Guo, Jiin-Huarng; Luh, Wei-Ming

2009-05-01

When planning a study, sample size determination is one of the most important tasks facing the researcher. The size will depend on the purpose of the study, the cost limitations, and the nature of the data. By specifying the standard deviation ratio and/or the sample size ratio, the present study considers the problem of heterogeneous variances and non-normality for Yuen's two-group test and develops sample size formulas to minimize the total cost or maximize the power of the test. For a given power, the sample size allocation ratio can be manipulated so that the proposed formulas can minimize the total cost, the total sample size, or the sum of total sample size and total cost. On the other hand, for a given total cost, the optimum sample size allocation ratio can maximize the statistical power of the test. After the sample size is determined, the present simulation applies Yuen's test to the sample generated, and then the procedure is validated in terms of Type I errors and power. Simulation results show that the proposed formulas can control Type I errors and achieve the desired power under the various conditions specified. Finally, the implications for determining sample sizes in experimental studies and future research are discussed.

Size Matters: FTIR Spectral Analysis of Apollo Regolith Samples Exhibits Grain Size Dependence.

NASA Astrophysics Data System (ADS)

Martin, Dayl; Joy, Katherine; Pernet-Fisher, John; Wogelius, Roy; Morlok, Andreas; Hiesinger, Harald

2017-04-01

The Mercury Thermal Infrared Spectrometer (MERTIS) on the upcoming BepiColombo mission is designed to analyse the surface of Mercury in thermal infrared wavelengths (7-14 μm) to investigate the physical properties of the surface materials [1]. Laboratory analyses of analogue materials are useful for investigating how various sample properties alter the resulting infrared spectrum. Laboratory FTIR analysis of Apollo fine (<1mm) soil samples 14259,672, 15401,147, and 67481,96 have provided an insight into how grain size, composition, maturity (i.e., exposure to space weathering processes), and proportion of glassy material affect their average infrared spectra. Each of these samples was analysed as a bulk sample and five size fractions: <25, 25-63, 63-125, 125-250, and <250 μm. Sample 14259,672 is a highly mature highlands regolith with a large proportion of agglutinates [2]. The high agglutinate content (>60%) causes a 'flattening' of the spectrum, with reduced reflectance in the Reststrahlen Band region (RB) as much as 30% in comparison to samples that are dominated by a high proportion of crystalline material. Apollo 15401,147 is an immature regolith with a high proportion of volcanic glass pyroclastic beads [2]. The high mafic mineral content results in a systematic shift in the Christiansen Feature (CF - the point of lowest reflectance) to longer wavelength: 8.6 μm. The glass beads dominate the spectrum, displaying a broad peak around the main Si-O stretch band (at 10.8 μm). As such, individual mineral components of this sample cannot be resolved from the average spectrum alone. Apollo 67481,96 is a sub-mature regolith composed dominantly of anorthite plagioclase [2]. The CF position of the average spectrum is shifted to shorter wavelengths (8.2 μm) due to the higher proportion of felsic minerals. Its average spectrum is dominated by anorthite reflectance bands at 8.7, 9.1, 9.8, and 10.8 μm. The average reflectance is greater than the other samples due to

Effects of sample size and sampling frequency on studies of brown bear home ranges and habitat use

USGS Publications Warehouse

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

Sample size determination for a three-arm equivalence trial of Poisson and negative binomial responses.

PubMed

Chang, Yu-Wei; Tsong, Yi; Zhao, Zhigen

2017-01-01

Assessing equivalence or similarity has drawn much attention recently as many drug products have lost or will lose their patents in the next few years, especially certain best-selling biologics. To claim equivalence between the test treatment and the reference treatment when assay sensitivity is well established from historical data, one has to demonstrate both superiority of the test treatment over placebo and equivalence between the test treatment and the reference treatment. Thus, there is urgency for practitioners to derive a practical way to calculate sample size for a three-arm equivalence trial. The primary endpoints of a clinical trial may not always be continuous, but may be discrete. In this paper, the authors derive power function and discuss sample size requirement for a three-arm equivalence trial with Poisson and negative binomial clinical endpoints. In addition, the authors examine the effect of the dispersion parameter on the power and the sample size by varying its coefficient from small to large. In extensive numerical studies, the authors demonstrate that required sample size heavily depends on the dispersion parameter. Therefore, misusing a Poisson model for negative binomial data may easily lose power up to 20%, depending on the value of the dispersion parameter.

Maximum type 1 error rate inflation in multiarmed clinical trials with adaptive interim sample size modifications.

PubMed

Graf, Alexandra C; Bauer, Peter; Glimm, Ekkehard; Koenig, Franz

2014-07-01

Sample size modifications in the interim analyses of an adaptive design can inflate the type 1 error rate, if test statistics and critical boundaries are used in the final analysis as if no modification had been made. While this is already true for designs with an overall change of the sample size in a balanced treatment-control comparison, the inflation can be much larger if in addition a modification of allocation ratios is allowed as well. In this paper, we investigate adaptive designs with several treatment arms compared to a single common control group. Regarding modifications, we consider treatment arm selection as well as modifications of overall sample size and allocation ratios. The inflation is quantified for two approaches: a naive procedure that ignores not only all modifications, but also the multiplicity issue arising from the many-to-one comparison, and a Dunnett procedure that ignores modifications, but adjusts for the initially started multiple treatments. The maximum inflation of the type 1 error rate for such types of design can be calculated by searching for the "worst case" scenarios, that are sample size adaptation rules in the interim analysis that lead to the largest conditional type 1 error rate in any point of the sample space. To show the most extreme inflation, we initially assume unconstrained second stage sample size modifications leading to a large inflation of the type 1 error rate. Furthermore, we investigate the inflation when putting constraints on the second stage sample sizes. It turns out that, for example fixing the sample size of the control group, leads to designs controlling the type 1 error rate. © 2014 The Author. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Automated sampling assessment for molecular simulations using the effective sample size

PubMed Central

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

Robustness of methods for blinded sample size re-estimation with overdispersed count data.

PubMed

Schneider, Simon; Schmidli, Heinz; Friede, Tim

2013-09-20

Counts of events are increasingly common as primary endpoints in randomized clinical trials. With between-patient heterogeneity leading to variances in excess of the mean (referred to as overdispersion), statistical models reflecting this heterogeneity by mixtures of Poisson distributions are frequently employed. Sample size calculation in the planning of such trials requires knowledge on the nuisance parameters, that is, the control (or overall) event rate and the overdispersion parameter. Usually, there is only little prior knowledge regarding these parameters in the design phase resulting in considerable uncertainty regarding the sample size. In this situation internal pilot studies have been found very useful and very recently several blinded procedures for sample size re-estimation have been proposed for overdispersed count data, one of which is based on an EM-algorithm. In this paper we investigate the EM-algorithm based procedure with respect to aspects of their implementation by studying the algorithm's dependence on the choice of convergence criterion and find that the procedure is sensitive to the choice of the stopping criterion in scenarios relevant to clinical practice. We also compare the EM-based procedure to other competing procedures regarding their operating characteristics such as sample size distribution and power. Furthermore, the robustness of these procedures to deviations from the model assumptions is explored. We find that some of the procedures are robust to at least moderate deviations. The results are illustrated using data from the US National Heart, Lung and Blood Institute sponsored Asymptomatic Cardiac Ischemia Pilot study. Copyright © 2013 John Wiley & Sons, Ltd.

Revisiting sample size: are big trials the answer?

PubMed

Lurati Buse, Giovanna A L; Botto, Fernando; Devereaux, P J

2012-07-18

The superiority of the evidence generated in randomized controlled trials over observational data is not only conditional to randomization. Randomized controlled trials require proper design and implementation to provide a reliable effect estimate. Adequate random sequence generation, allocation implementation, analyses based on the intention-to-treat principle, and sufficient power are crucial to the quality of a randomized controlled trial. Power, or the probability of the trial to detect a difference when a real difference between treatments exists, strongly depends on sample size. The quality of orthopaedic randomized controlled trials is frequently threatened by a limited sample size. This paper reviews basic concepts and pitfalls in sample-size estimation and focuses on the importance of large trials in the generation of valid evidence.

SNS Sample Activation Calculator Flux Recommendations and Validation

DOE Office of Scientific and Technical Information (OSTI.GOV)

McClanahan, Tucker C.; Gallmeier, Franz X.; Iverson, Erik B.

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.more » 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.« less

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. The...

Maximum inflation of the type 1 error rate when sample size and allocation rate are adapted in a pre-planned interim look.

PubMed

Graf, Alexandra C; Bauer, Peter

2011-06-30

We calculate the maximum type 1 error rate of the pre-planned conventional fixed sample size test for comparing the means of independent normal distributions (with common known variance) which can be yielded when sample size and allocation rate to the treatment arms can be modified in an interim analysis. Thereby it is assumed that the experimenter fully exploits knowledge of the unblinded interim estimates of the treatment effects in order to maximize the conditional type 1 error rate. The 'worst-case' strategies require knowledge of the unknown common treatment effect under the null hypothesis. Although this is a rather hypothetical scenario it may be approached in practice when using a standard control treatment for which precise estimates are available from historical data. The maximum inflation of the type 1 error rate is substantially larger than derived by Proschan and Hunsberger (Biometrics 1995; 51:1315-1324) for design modifications applying balanced samples before and after the interim analysis. Corresponding upper limits for the maximum type 1 error rate are calculated for a number of situations arising from practical considerations (e.g. restricting the maximum sample size, not allowing sample size to decrease, allowing only increase in the sample size in the experimental treatment). The application is discussed for a motivating example. Copyright © 2011 John Wiley & Sons, Ltd.

The special case of the 2 × 2 table: asymptotic unconditional McNemar test can be used to estimate sample size even for analysis based on GEE.

PubMed

Borkhoff, Cornelia M; Johnston, Patrick R; Stephens, Derek; Atenafu, Eshetu

2015-07-01

Aligning the method used to estimate sample size with the planned analytic method ensures the sample size needed to achieve the planned power. When using generalized estimating equations (GEE) to analyze a paired binary primary outcome with no covariates, many use an exact McNemar test to calculate sample size. We reviewed the approaches to sample size estimation for paired binary data and compared the sample size estimates on the same numerical examples. We used the hypothesized sample proportions for the 2 × 2 table to calculate the correlation between the marginal proportions to estimate sample size based on GEE. We solved the inside proportions based on the correlation and the marginal proportions to estimate sample size based on exact McNemar, asymptotic unconditional McNemar, and asymptotic conditional McNemar. The asymptotic unconditional McNemar test is a good approximation of GEE method by Pan. The exact McNemar is too conservative and yields unnecessarily large sample size estimates than all other methods. In the special case of a 2 × 2 table, even when a GEE approach to binary logistic regression is the planned analytic method, the asymptotic unconditional McNemar test can be used to estimate sample size. We do not recommend using an exact McNemar test. Copyright © 2015 Elsevier Inc. All rights reserved.

Estimation of sample size and testing power (part 5).

PubMed

Hu, Liang-ping; Bao, Xiao-lei; Guan, Xue; Zhou, Shi-guo

2012-02-01

Estimation of sample size and testing power is an important component of research design. This article introduced methods for sample size and testing power estimation of difference test for quantitative and qualitative data with the single-group design, the paired design or the crossover design. To be specific, this article introduced formulas for sample size and testing power estimation of difference test for quantitative and qualitative data with the above three designs, the realization based on the formulas and the POWER procedure of SAS software and elaborated it with examples, which will benefit researchers for implementing the repetition principle.

Sample size determination for GEE analyses of stepped wedge cluster randomized trials.

PubMed

Li, Fan; Turner, Elizabeth L; Preisser, John S

2018-06-19

In stepped wedge cluster randomized trials, intact clusters of individuals switch from control to intervention from a randomly assigned period onwards. Such trials are becoming increasingly popular in health services research. When a closed cohort is recruited from each cluster for longitudinal follow-up, proper sample size calculation should account for three distinct types of intraclass correlations: the within-period, the inter-period, and the within-individual correlations. Setting the latter two correlation parameters to be equal accommodates cross-sectional designs. We propose sample size procedures for continuous and binary responses within the framework of generalized estimating equations that employ a block exchangeable within-cluster correlation structure defined from the distinct correlation types. For continuous responses, we show that the intraclass correlations affect power only through two eigenvalues of the correlation matrix. We demonstrate that analytical power agrees well with simulated power for as few as eight clusters, when data are analyzed using bias-corrected estimating equations for the correlation parameters concurrently with a bias-corrected sandwich variance estimator. © 2018, The International Biometric Society.

Communication: Finite size correction in periodic coupled cluster theory calculations of solids.

PubMed

Liao, Ke; Grüneis, Andreas

2016-10-14

We present a method to correct for finite size errors in coupled cluster theory calculations of solids. The outlined technique shares similarities with electronic structure factor interpolation methods used in quantum Monte Carlo calculations. However, our approach does not require the calculation of density matrices. Furthermore we show that the proposed finite size corrections achieve chemical accuracy in the convergence of second-order Møller-Plesset perturbation and coupled cluster singles and doubles correlation energies per atom for insulating solids with two atomic unit cells using 2 × 2 × 2 and 3 × 3 × 3 k-point meshes only.

Frictional behaviour of sandstone: A sample-size dependent triaxial investigation

NASA Astrophysics Data System (ADS)

Roshan, Hamid; Masoumi, Hossein; Regenauer-Lieb, Klaus

2017-01-01

Frictional behaviour of rocks from the initial stage of loading to final shear displacement along the formed shear plane has been widely investigated in the past. However the effect of sample size on such frictional behaviour has not attracted much attention. This is mainly related to the limitations in rock testing facilities as well as the complex mechanisms involved in sample-size dependent frictional behaviour of rocks. In this study, a suite of advanced triaxial experiments was performed on Gosford sandstone samples at different sizes and confining pressures. The post-peak response of the rock along the formed shear plane has been captured for the analysis with particular interest in sample-size dependency. Several important phenomena have been observed from the results of this study: a) the rate of transition from brittleness to ductility in rock is sample-size dependent where the relatively smaller samples showed faster transition toward ductility at any confining pressure; b) the sample size influences the angle of formed shear band and c) the friction coefficient of the formed shear plane is sample-size dependent where the relatively smaller sample exhibits lower friction coefficient compared to larger samples. We interpret our results in terms of a thermodynamics approach in which the frictional properties for finite deformation are viewed as encompassing a multitude of ephemeral slipping surfaces prior to the formation of the through going fracture. The final fracture itself is seen as a result of the self-organisation of a sufficiently large ensemble of micro-slip surfaces and therefore consistent in terms of the theory of thermodynamics. This assumption vindicates the use of classical rock mechanics experiments to constrain failure of pressure sensitive rocks and the future imaging of these micro-slips opens an exciting path for research in rock failure mechanisms.

Calculation for tensile strength and fracture toughness of granite with three kinds of grain sizes using three-point-bending test.

PubMed

Yu, Miao; Wei, Chenhui; Niu, Leilei; Li, Shaohua; Yu, Yongjun

2018-01-01

Tensile strength and fracture toughness, important parameters of the rock for engineering applications are difficult to measure. Thus this paper selected three kinds of granite samples (grain sizes = 1.01mm, 2.12mm and 3mm), used the combined experiments of physical and numerical simulation (RFPA-DIP version) to conduct three-point-bending (3-p-b) tests with different notches and introduced the acoustic emission monitor system to analyze the fracture mechanism around the notch tips. To study the effects of grain size on the tensile strength and toughness of rock samples, a modified fracture model was established linking fictitious crack to the grain size so that the microstructure of the specimens and fictitious crack growth can be considered together. The fractal method was introduced to represent microstructure of three kinds of granites and used to determine the length of fictitious crack. It is a simple and novel method to calculate the tensile strength and fracture toughness directly. Finally, the theoretical model was verified by the comparison to the numerical experiments by calculating the nominal strength σn and maximum loads Pmax.

Effects of Calibration Sample Size and Item Bank Size on Ability Estimation in Computerized Adaptive Testing

ERIC Educational Resources Information Center

Sahin, Alper; Weiss, David J.

2015-01-01

This study aimed to investigate the effects of calibration sample size and item bank size on examinee ability estimation in computerized adaptive testing (CAT). For this purpose, a 500-item bank pre-calibrated using the three-parameter logistic model with 10,000 examinees was simulated. Calibration samples of varying sizes (150, 250, 350, 500,…

Variability of carotid artery measurements on 3-Tesla MRI and its impact on sample size calculation for clinical research.

PubMed

Syed, Mushabbar A; Oshinski, John N; Kitchen, Charles; Ali, Arshad; Charnigo, Richard J; Quyyumi, Arshed A

2009-08-01

Carotid MRI measurements are increasingly being employed in research studies for atherosclerosis imaging. The majority of carotid imaging studies use 1.5 T MRI. Our objective was to investigate intra-observer and inter-observer variability in carotid measurements using high resolution 3 T MRI. We performed 3 T carotid MRI on 10 patients (age 56 +/- 8 years, 7 male) with atherosclerosis risk factors and ultrasound intima-media thickness > or =0.6 mm. A total of 20 transverse images of both right and left carotid arteries were acquired using T2 weighted black-blood sequence. The lumen and outer wall of the common carotid and internal carotid arteries were manually traced; vessel wall area, vessel wall volume, and average wall thickness measurements were then assessed for intra-observer and inter-observer variability. Pearson and intraclass correlations were used in these assessments, along with Bland-Altman plots. For inter-observer variability, Pearson correlations ranged from 0.936 to 0.996 and intraclass correlations from 0.927 to 0.991. For intra-observer variability, Pearson correlations ranged from 0.934 to 0.954 and intraclass correlations from 0.831 to 0.948. Calculations showed that inter-observer variability and other sources of error would inflate sample size requirements for a clinical trial by no more than 7.9%, indicating that 3 T MRI is nearly optimal in this respect. In patients with subclinical atherosclerosis, 3 T carotid MRI measurements are highly reproducible and have important implications for clinical trial design.

A comparison study of size-specific dose estimate calculation methods.

PubMed

Parikh, Roshni A; Wien, Michael A; Novak, Ronald D; Jordan, David W; Klahr, Paul; Soriano, Stephanie; Ciancibello, Leslie; Berlin, Sheila C

2018-01-01

The size-specific dose estimate (SSDE) has emerged as an improved metric for use by medical physicists and radiologists for estimating individual patient dose. Several methods of calculating SSDE have been described, ranging from patient thickness or attenuation-based (automated and manual) measurements to weight-based techniques. To compare the accuracy of thickness vs. weight measurement of body size to allow for the calculation of the size-specific dose estimate (SSDE) in pediatric body CT. We retrospectively identified 109 pediatric body CT examinations for SSDE calculation. We examined two automated methods measuring a series of level-specific diameters of the patient's body: method A used the effective diameter and method B used the water-equivalent diameter. Two manual methods measured patient diameter at two predetermined levels: the superior endplate of L2, where body width is typically most thin, and the superior femoral head or iliac crest (for scans that did not include the pelvis), where body width is typically most thick; method C averaged lateral measurements at these two levels from the CT projection scan, and method D averaged lateral and anteroposterior measurements at the same two levels from the axial CT images. Finally, we used body weight to characterize patient size, method E, and compared this with the various other measurement methods. Methods were compared across the entire population as well as by subgroup based on body width. Concordance correlation (ρ c ) between each of the SSDE calculation methods (methods A-E) was greater than 0.92 across the entire population, although the range was wider when analyzed by subgroup (0.42-0.99). When we compared each SSDE measurement method with CTDI vol, there was poor correlation, ρ c <0.77, with percentage differences between 20.8% and 51.0%. Automated computer algorithms are accurate and efficient in the calculation of SSDE. Manual methods based on patient thickness provide acceptable dose

Estimating population size with correlated sampling unit estimates

Treesearch

David C. Bowden; Gary C. White; Alan B. Franklin; Joseph L. Ganey

2003-01-01

Finite population sampling theory is useful in estimating total population size (abundance) from abundance estimates of each sampled unit (quadrat). We develop estimators that allow correlated quadrat abundance estimates, even for quadrats in different sampling strata. Correlated quadrat abundance estimates based on mark–recapture or distance sampling methods occur...

Approximate sample sizes required to estimate length distributions

USGS Publications Warehouse

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.

Sample Size in Qualitative Interview Studies: Guided by Information Power.

PubMed

Malterud, Kirsti; Siersma, Volkert Dirk; Guassora, Ann Dorrit

2015-11-27

Sample sizes must be ascertained in qualitative studies like in quantitative studies but not by the same means. The prevailing concept for sample size in qualitative studies is "saturation." Saturation is closely tied to a specific methodology, and the term is inconsistently applied. We propose the concept "information power" to guide adequate sample size for qualitative studies. Information power indicates that the more information the sample holds, relevant for the actual study, the lower amount of participants is needed. We suggest that the size of a sample with sufficient information power depends on (a) the aim of the study, (b) sample specificity, (c) use of established theory, (d) quality of dialogue, and (e) analysis strategy. We present a model where these elements of information and their relevant dimensions are related to information power. Application of this model in the planning and during data collection of a qualitative study is discussed. © The Author(s) 2015.

Rasch fit statistics and sample size considerations for polytomous data.

PubMed

Smith, Adam B; Rush, Robert; Fallowfield, Lesley J; Velikova, Galina; Sharpe, Michael

2008-05-29

Previous research on educational data has demonstrated that Rasch fit statistics (mean squares and t-statistics) are highly susceptible to sample size variation for dichotomously scored rating data, although little is known about this relationship for polytomous data. These statistics help inform researchers about how well items fit to a unidimensional latent trait, and are an important adjunct to modern psychometrics. Given the increasing use of Rasch models in health research the purpose of this study was therefore to explore the relationship between fit statistics and sample size for polytomous data. Data were collated from a heterogeneous sample of cancer patients (n = 4072) who had completed both the Patient Health Questionnaire - 9 and the Hospital Anxiety and Depression Scale. Ten samples were drawn with replacement for each of eight sample sizes (n = 25 to n = 3200). The Rating and Partial Credit Models were applied and the mean square and t-fit statistics (infit/outfit) derived for each model. The results demonstrated that t-statistics were highly sensitive to sample size, whereas mean square statistics remained relatively stable for polytomous data. It was concluded that mean square statistics were relatively independent of sample size for polytomous data and that misfit to the model could be identified using published recommended ranges.

Air and smear sample calculational tool for Fluor Hanford Radiological control

DOE Office of Scientific and Technical Information (OSTI.GOV)

BAUMANN, B.L.

2003-07-11

A spreadsheet calculation tool was developed to automate the calculations performed for determining the concentration of airborne radioactivity and smear counting as outlined in HNF-13536, Section 5.2.7, ''Analyzing Air and Smear Samples''. This document reports on the design and testing of the calculation tool. Radiological Control Technicians (RCTs) will save time and reduce hand written and calculation errors by using an electronic form for documenting and calculating work place air samples. Current expectations are RCTs will perform an air sample and collect the filter or perform a smear for surface contamination. RCTs will then survey the filter for gross alphamore » and beta/gamma radioactivity and with the gross counts utilize either hand calculation method or a calculator to determine activity on the filter. The electronic form will allow the RCT with a few key strokes to document the individual's name, payroll, gross counts, instrument identifiers; produce an error free record. This productivity gain is realized by the enhanced ability to perform mathematical calculations electronically (reducing errors) and at the same time, documenting the air sample.« less

A computer program for sample size computations for banding studies

USGS Publications Warehouse

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.

On sample size and different interpretations of snow stability datasets

NASA Astrophysics Data System (ADS)

Schirmer, M.; Mitterer, C.; Schweizer, J.

2009-04-01

Interpretations of snow stability variations need an assessment of the stability itself, independent of the scale investigated in the study. Studies on stability variations at a regional scale have often chosen stability tests such as the Rutschblock test or combinations of various tests in order to detect differences in aspect and elevation. The question arose: ‘how capable are such stability interpretations in drawing conclusions'. There are at least three possible errors sources: (i) the variance of the stability test itself; (ii) the stability variance at an underlying slope scale, and (iii) that the stability interpretation might not be directly related to the probability of skier triggering. Various stability interpretations have been proposed in the past that provide partly different results. We compared a subjective one based on expert knowledge with a more objective one based on a measure derived from comparing skier-triggered slopes vs. slopes that have been skied but not triggered. In this study, the uncertainties are discussed and their effects on regional scale stability variations will be quantified in a pragmatic way. An existing dataset with very large sample sizes was revisited. This dataset contained the variance of stability at a regional scale for several situations. The stability in this dataset was determined using the subjective interpretation scheme based on expert knowledge. The question to be answered was how many measurements were needed to obtain similar results (mainly stability differences in aspect or elevation) as with the complete dataset. The optimal sample size was obtained in several ways: (i) assuming a nominal data scale the sample size was determined with a given test, significance level and power, and by calculating the mean and standard deviation of the complete dataset. With this method it can also be determined if the complete dataset consists of an appropriate sample size. (ii) Smaller subsets were created with similar

The choice of sample size: a mixed Bayesian / frequentist approach.

PubMed

Pezeshk, Hamid; Nematollahi, Nader; Maroufy, Vahed; Gittins, John

2009-04-01

Sample size computations are largely based on frequentist or classical methods. In the Bayesian approach the prior information on the unknown parameters is taken into account. In this work we consider a fully Bayesian approach to the sample size determination problem which was introduced by Grundy et al. and developed by Lindley. This approach treats the problem as a decision problem and employs a utility function to find the optimal sample size of a trial. Furthermore, we assume that a regulatory authority, which is deciding on whether or not to grant a licence to a new treatment, uses a frequentist approach. We then find the optimal sample size for the trial by maximising the expected net benefit, which is the expected benefit of subsequent use of the new treatment minus the cost of the trial.

Rasch fit statistics and sample size considerations for polytomous data

PubMed Central

Smith, Adam B; Rush, Robert; Fallowfield, Lesley J; Velikova, Galina; Sharpe, Michael

2008-01-01

Background Previous research on educational data has demonstrated that Rasch fit statistics (mean squares and t-statistics) are highly susceptible to sample size variation for dichotomously scored rating data, although little is known about this relationship for polytomous data. These statistics help inform researchers about how well items fit to a unidimensional latent trait, and are an important adjunct to modern psychometrics. Given the increasing use of Rasch models in health research the purpose of this study was therefore to explore the relationship between fit statistics and sample size for polytomous data. Methods Data were collated from a heterogeneous sample of cancer patients (n = 4072) who had completed both the Patient Health Questionnaire – 9 and the Hospital Anxiety and Depression Scale. Ten samples were drawn with replacement for each of eight sample sizes (n = 25 to n = 3200). The Rating and Partial Credit Models were applied and the mean square and t-fit statistics (infit/outfit) derived for each model. Results The results demonstrated that t-statistics were highly sensitive to sample size, whereas mean square statistics remained relatively stable for polytomous data. Conclusion It was concluded that mean square statistics were relatively independent of sample size for polytomous data and that misfit to the model could be identified using published recommended ranges. PMID:18510722

Calculation for tensile strength and fracture toughness of granite with three kinds of grain sizes using three-point-bending test

PubMed Central

Yu, Miao; Wei, Chenhui; Niu, Leilei; Li, Shaohua; Yu, Yongjun

2018-01-01

Tensile strength and fracture toughness, important parameters of the rock for engineering applications are difficult to measure. Thus this paper selected three kinds of granite samples (grain sizes = 1.01mm, 2.12mm and 3mm), used the combined experiments of physical and numerical simulation (RFPA-DIP version) to conduct three-point-bending (3-p-b) tests with different notches and introduced the acoustic emission monitor system to analyze the fracture mechanism around the notch tips. To study the effects of grain size on the tensile strength and toughness of rock samples, a modified fracture model was established linking fictitious crack to the grain size so that the microstructure of the specimens and fictitious crack growth can be considered together. The fractal method was introduced to represent microstructure of three kinds of granites and used to determine the length of fictitious crack. It is a simple and novel method to calculate the tensile strength and fracture toughness directly. Finally, the theoretical model was verified by the comparison to the numerical experiments by calculating the nominal strength σn and maximum loads Pmax. PMID:29596422

Rule-of-thumb adjustment of sample sizes to accommodate dropouts in a two-stage analysis of repeated measurements.

PubMed

Overall, John E; Tonidandel, Scott; Starbuck, Robert R

2006-01-01

Recent contributions to the statistical literature have provided elegant model-based solutions to the problem of estimating sample sizes for testing the significance of differences in mean rates of change across repeated measures in controlled longitudinal studies with differentially correlated error and missing data due to dropouts. However, the mathematical complexity and model specificity of these solutions make them generally inaccessible to most applied researchers who actually design and undertake treatment evaluation research in psychiatry. In contrast, this article relies on a simple two-stage analysis in which dropout-weighted slope coefficients fitted to the available repeated measurements for each subject separately serve as the dependent variable for a familiar ANCOVA test of significance for differences in mean rates of change. This article is about how a sample of size that is estimated or calculated to provide desired power for testing that hypothesis without considering dropouts can be adjusted appropriately to take dropouts into account. Empirical results support the conclusion that, whatever reasonable level of power would be provided by a given sample size in the absence of dropouts, essentially the same power can be realized in the presence of dropouts simply by adding to the original dropout-free sample size the number of subjects who would be expected to drop from a sample of that original size under conditions of the proposed study.

Sample Size and Allocation of Effort in Point Count Sampling of Birds in Bottomland Hardwood Forests

Treesearch

Winston P. Smith; Daniel J. Twedt; Robert J. Cooper; David A. Wiedenfeld; Paul B. Hamel; Robert P. Ford

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...

Sampling of Stochastic Input Parameters for Rockfall Calculations and for Structural Response Calculations Under Vibratory Ground Motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 inmore » 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

Simple and multiple linear regression: sample size considerations.

PubMed

Hanley, James A

2016-11-01

The suggested "two subjects per variable" (2SPV) rule of thumb in the Austin and Steyerberg article is a chance to bring out some long-established and quite intuitive sample size considerations for both simple and multiple linear regression. This article distinguishes two of the major uses of regression models that imply very different sample size considerations, neither served well by the 2SPV rule. The first is etiological research, which contrasts mean Y levels at differing "exposure" (X) values and thus tends to focus on a single regression coefficient, possibly adjusted for confounders. The second research genre guides clinical practice. It addresses Y levels for individuals with different covariate patterns or "profiles." It focuses on the profile-specific (mean) Y levels themselves, estimating them via linear compounds of regression coefficients and covariates. By drawing on long-established closed-form variance formulae that lie beneath the standard errors in multiple regression, and by rearranging them for heuristic purposes, one arrives at quite intuitive sample size considerations for both research genres. Copyright © 2016 Elsevier Inc. All rights reserved.

The Statistics and Mathematics of High Dimension Low Sample Size Asymptotics.

PubMed

Shen, Dan; Shen, Haipeng; Zhu, Hongtu; Marron, J S

2016-10-01

The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal an asymptotic conical structure in critical sample eigendirections under the spike models with distinguishable (or indistinguishable) eigenvalues, when the sample size and/or the number of variables (or dimension) tend to infinity. The consistency of the sample eigenvectors relative to their population counterparts is determined by the ratio between the dimension and the product of the sample size with the spike size. When this ratio converges to a nonzero constant, the sample eigenvector converges to a cone, with a certain angle to its corresponding population eigenvector. In the High Dimension, Low Sample Size case, the angle between the sample eigenvector and its population counterpart converges to a limiting distribution. Several generalizations of the multi-spike covariance models are also explored, and additional theoretical results are presented.

Breaking Free of Sample Size Dogma to Perform Innovative Translational Research

PubMed Central

Bacchetti, Peter; Deeks, Steven G.; McCune, Joseph M.

2011-01-01

Innovative clinical and translational research is often delayed or prevented by reviewers’ expectations that any study performed in humans must be shown in advance to have high statistical power. This supposed requirement is not justifiable and is contradicted by the reality that increasing sample size produces diminishing marginal returns. Studies of new ideas often must start small (sometimes even with an N of 1) because of cost and feasibility concerns, and recent statistical work shows that small sample sizes for such research can produce more projected scientific value per dollar spent than larger sample sizes. Renouncing false dogma about sample size would remove a serious barrier to innovation and translation. PMID:21677197

Sample size re-assessment leading to a raised sample size does not inflate type I error rate under mild conditions.

PubMed

Broberg, Per

2013-07-19

One major concern with adaptive designs, such as the sample size adjustable designs, has been the fear of inflating the type I error rate. In (Stat Med 23:1023-1038, 2004) it is however proven that when observations follow a normal distribution and the interim result show promise, meaning that the conditional power exceeds 50%, type I error rate is protected. This bound and the distributional assumptions may seem to impose undesirable restrictions on the use of these designs. In (Stat Med 30:3267-3284, 2011) the possibility of going below 50% is explored and a region that permits an increased sample size without inflation is defined in terms of the conditional power at the interim. A criterion which is implicit in (Stat Med 30:3267-3284, 2011) is derived by elementary methods and expressed in terms of the test statistic at the interim to simplify practical use. Mathematical and computational details concerning this criterion are exhibited. Under very general conditions the type I error rate is preserved under sample size adjustable schemes that permit a raise. The main result states that for normally distributed observations raising the sample size when the result looks promising, where the definition of promising depends on the amount of knowledge gathered so far, guarantees the protection of the type I error rate. Also, in the many situations where the test statistic approximately follows a normal law, the deviation from the main result remains negligible. This article provides details regarding the Weibull and binomial distributions and indicates how one may approach these distributions within the current setting. There is thus reason to consider such designs more often, since they offer a means of adjusting an important design feature at little or no cost in terms of error rate.

Estimating the Size of the Methamphetamine-Using Population in New York City Using Network Sampling Techniques.

PubMed

Dombrowski, Kirk; Khan, Bilal; Wendel, Travis; McLean, Katherine; Misshula, Evan; Curtis, Ric

2012-12-01

As part of a recent study of the dynamics of the retail market for methamphetamine use in New York City, we used network sampling methods to estimate the size of the total networked population. This process involved sampling from respondents' list of co-use contacts, which in turn became the basis for capture-recapture estimation. Recapture sampling was based on links to other respondents derived from demographic and "telefunken" matching procedures-the latter being an anonymized version of telephone number matching. This paper describes the matching process used to discover the links between the solicited contacts and project respondents, the capture-recapture calculation, the estimation of "false matches", and the development of confidence intervals for the final population estimates. A final population of 12,229 was estimated, with a range of 8235 - 23,750. The techniques described here have the special virtue of deriving an estimate for a hidden population while retaining respondent anonymity and the anonymity of network alters, but likely require larger sample size than the 132 persons interviewed to attain acceptable confidence levels for the estimate.

Sensitivity and specificity of normality tests and consequences on reference interval accuracy at small sample size: a computer-simulation study.

PubMed

Le Boedec, Kevin

2016-12-01

According to international guidelines, parametric methods must be chosen for RI construction when the sample size is small and the distribution is Gaussian. However, normality tests may not be accurate at small sample size. The purpose of the study was to evaluate normality test performance to properly identify samples extracted from a Gaussian population at small sample sizes, and assess the consequences on RI accuracy of applying parametric methods to samples that falsely identified the parent population as Gaussian. Samples of n = 60 and n = 30 values were randomly selected 100 times from simulated Gaussian, lognormal, and asymmetric populations of 10,000 values. The sensitivity and specificity of 4 normality tests were compared. Reference intervals were calculated using 6 different statistical methods from samples that falsely identified the parent population as Gaussian, and their accuracy was compared. Shapiro-Wilk and D'Agostino-Pearson tests were the best performing normality tests. However, their specificity was poor at sample size n = 30 (specificity for P < .05: .51 and .50, respectively). The best significance levels identified when n = 30 were 0.19 for Shapiro-Wilk test and 0.18 for D'Agostino-Pearson test. Using parametric methods on samples extracted from a lognormal population but falsely identified as Gaussian led to clinically relevant inaccuracies. At small sample size, normality tests may lead to erroneous use of parametric methods to build RI. Using nonparametric methods (or alternatively Box-Cox transformation) on all samples regardless of their distribution or adjusting, the significance level of normality tests depending on sample size would limit the risk of constructing inaccurate RI. © 2016 American Society for Veterinary Clinical Pathology.

Development of size reduction equations for calculating power input for grinding pine wood chips using hammer mill

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naimi, Ladan J.; Collard, Flavien; Bi, Xiaotao

Size reduction is an unavoidable operation for preparing biomass for biofuels and bioproduct conversion. Yet, there is considerable uncertainty in power input requirement and the uniformity of ground biomass. Considerable gains are possible if the required power input for a size reduction ratio is estimated accurately. In this research three well-known mechanistic equations attributed to Rittinger, Kick, and Bond available for predicting energy input for grinding pine wood chips were tested against experimental grinding data. Prior to testing, samples of pine wood chips were conditioned to 11.7% wb, moisture content. The wood chips were successively ground in a hammer millmore » using screen sizes of 25.4 mm, 10 mm, 6.4 mm, and 3.2 mm. The input power and the flow of material into the grinder were recorded continuously. The recorded power input vs. mean particle size showed that the Rittinger equation had the best fit to the experimental data. The ground particle sizes were 4 to 7 times smaller than the size of installed screen. Geometric mean size of particles were calculated using two methods (1) Tyler sieves and using particle size analysis and (2) Sauter mean diameter calculated from the ratio of volume to surface that were estimated from measured length and width. The two mean diameters agreed well, pointing to the fact that either mechanical sieving or particle imaging can be used to characterize particle size. In conclusion, specific energy input to the hammer mill increased from 1.4 kWh t –1 (5.2 J g –1) for large 25.1-mm screen to 25 kWh t –1 (90.4 J g –1) for small 3.2-mm screen.« less

Development of size reduction equations for calculating power input for grinding pine wood chips using hammer mill

DOE PAGES

Naimi, Ladan J.; Collard, Flavien; Bi, Xiaotao; ...

2016-01-05

Size reduction is an unavoidable operation for preparing biomass for biofuels and bioproduct conversion. Yet, there is considerable uncertainty in power input requirement and the uniformity of ground biomass. Considerable gains are possible if the required power input for a size reduction ratio is estimated accurately. In this research three well-known mechanistic equations attributed to Rittinger, Kick, and Bond available for predicting energy input for grinding pine wood chips were tested against experimental grinding data. Prior to testing, samples of pine wood chips were conditioned to 11.7% wb, moisture content. The wood chips were successively ground in a hammer millmore » using screen sizes of 25.4 mm, 10 mm, 6.4 mm, and 3.2 mm. The input power and the flow of material into the grinder were recorded continuously. The recorded power input vs. mean particle size showed that the Rittinger equation had the best fit to the experimental data. The ground particle sizes were 4 to 7 times smaller than the size of installed screen. Geometric mean size of particles were calculated using two methods (1) Tyler sieves and using particle size analysis and (2) Sauter mean diameter calculated from the ratio of volume to surface that were estimated from measured length and width. The two mean diameters agreed well, pointing to the fact that either mechanical sieving or particle imaging can be used to characterize particle size. In conclusion, specific energy input to the hammer mill increased from 1.4 kWh t –1 (5.2 J g –1) for large 25.1-mm screen to 25 kWh t –1 (90.4 J g –1) for small 3.2-mm screen.« less

Effects of growth rate, size, and light availability on tree survival across life stages: a demographic analysis accounting for missing values and small sample sizes.

PubMed

Moustakas, Aristides; Evans, Matthew R

2015-02-28

Plant survival is a key factor in forest dynamics and survival probabilities often vary across life stages. Studies specifically aimed at assessing tree survival are unusual and so data initially designed for other purposes often need to be used; such data are more likely to contain errors than data collected for this specific purpose. We investigate the survival rates of ten tree species in a dataset designed to monitor growth rates. As some individuals were not included in the census at some time points we use capture-mark-recapture methods both to allow us to account for missing individuals, and to estimate relocation probabilities. Growth rates, size, and light availability were included as covariates in the model predicting survival rates. The study demonstrates that tree mortality is best described as constant between years and size-dependent at early life stages and size independent at later life stages for most species of UK hardwood. We have demonstrated that even with a twenty-year dataset it is possible to discern variability both between individuals and between species. Our work illustrates the potential utility of the method applied here for calculating plant population dynamics parameters in time replicated datasets with small sample sizes and missing individuals without any loss of sample size, and including explanatory covariates.

Small sample sizes in the study of ontogenetic allometry; implications for palaeobiology

PubMed Central

Vavrek, Matthew J.

2015-01-01

Quantitative morphometric analyses, particularly ontogenetic allometry, are common methods used in quantifying shape, and changes therein, in both extinct and extant organisms. Due to incompleteness and the potential for restricted sample sizes in the fossil record, palaeobiological analyses of allometry may encounter higher rates of error. Differences in sample size between fossil and extant studies and any resulting effects on allometric analyses have not been thoroughly investigated, and a logical lower threshold to sample size is not clear. Here we show that studies based on fossil datasets have smaller sample sizes than those based on extant taxa. A similar pattern between vertebrates and invertebrates indicates this is not a problem unique to either group, but common to both. We investigate the relationship between sample size, ontogenetic allometric relationship and statistical power using an empirical dataset of skull measurements of modern Alligator mississippiensis. Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the null hypothesis). This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms. These limitations are not restricted to fossil data and are equally applicable to allometric analyses of rare extant taxa. No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes. PMID:25780770

Geometrical characteristics of sandstone with different sample sizes

NASA Astrophysics Data System (ADS)

Cheon, D. S.; Takahashi, M., , Dr

2017-12-01

In many rock engineering projects such as CO2 underground storage, engineering geothermal system, it is important things to understand the fluid flow behavior in the deep geological conditions. This fluid flow is generally affected by the geometrical characteristics of rock, especially porous media. Furthermore, physical properties in rock may depend on the existence of voids space in rock. Total porosity and pore size distribution can be measured by Mercury Intrusion Porosimetry and the other geometrical and spatial information of pores can be obtained through micro-focus X-ray CT. Using the micro-focus X-ray CT, we obtained the extracted void space and transparent image from the original CT voxel images of with different sample sizes like 1 mm, 2 mm, 3 mm cubes. The test samples are Berea sandstone and Otway sandstone. The former is well-known sandstone and it is used for the standard sample to compared to the result from the Otway sandstone. Otway sandstone was obtained from the CO2CRC Otway pilot site for the CO2 geosequestraion project. From the X-ray scan and ExFACT software, we get the informations including effective pore radii, coordination number, tortuosity and effective throat/pore radius ratio etc. The geometrical information analysis showed that for Berea sandstone and Otway sandstone, there is rarely differences with different sample sizes and total value of coordination number show high porosity, the tortuosity of Berea sandstone is higher than the Otway sandstone. In the future, these information will be used for the permeability of the samples.

Sample Size Requirements and Study Duration for Testing Main Effects and Interactions in Completely Randomized Factorial Designs When Time to Event is the Outcome

PubMed Central

Moser, Barry Kurt; Halabi, Susan

2013-01-01

In this paper we develop the methodology for designing clinical trials with any factorial arrangement when the primary outcome is time to event. We provide a matrix formulation for calculating the sample size and study duration necessary to test any effect with a pre-specified type I error rate and power. Assuming that a time to event follows an exponential distribution, we describe the relationships between the effect size, the power, and the sample size. We present examples for illustration purposes. We provide a simulation study to verify the numerical calculations of the expected number of events and the duration of the trial. The change in the power produced by a reduced number of observations or by accruing no patients to certain factorial combinations is also described. PMID:25530661

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…

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 is...

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 is...

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 is...

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 is...

Chi-Squared Test of Fit and Sample Size-A Comparison between a Random Sample Approach and a Chi-Square Value Adjustment Method.

PubMed

Bergh, Daniel

2015-01-01

Chi-square statistics are commonly used for tests of fit of measurement models. Chi-square is also sensitive to sample size, which is why several approaches to handle large samples in test of fit analysis have been developed. One strategy to handle the sample size problem may be to adjust the sample size in the analysis of fit. An alternative is to adopt a random sample approach. The purpose of this study was to analyze and to compare these two strategies using simulated data. Given an original sample size of 21,000, for reductions of sample sizes down to the order of 5,000 the adjusted sample size function works as good as the random sample approach. In contrast, when applying adjustments to sample sizes of lower order the adjustment function is less effective at approximating the chi-square value for an actual random sample of the relevant size. Hence, the fit is exaggerated and misfit under-estimated using the adjusted sample size function. Although there are big differences in chi-square values between the two approaches at lower sample sizes, the inferences based on the p-values may be the same.

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.

Confidence intervals for the population mean tailored to small sample sizes, with applications to survey sampling.

PubMed

Rosenblum, Michael A; Laan, Mark J van der

2009-01-07

The validity of standard confidence intervals constructed in survey sampling is based on the central limit theorem. For small sample sizes, the central limit theorem may give a poor approximation, resulting in confidence intervals that are misleading. We discuss this issue and propose methods for constructing confidence intervals for the population mean tailored to small sample sizes. We present a simple approach for constructing confidence intervals for the population mean based on tail bounds for the sample mean that are correct for all sample sizes. Bernstein's inequality provides one such tail bound. The resulting confidence intervals have guaranteed coverage probability under much weaker assumptions than are required for standard methods. A drawback of this approach, as we show, is that these confidence intervals are often quite wide. In response to this, we present a method for constructing much narrower confidence intervals, which are better suited for practical applications, and that are still more robust than confidence intervals based on standard methods, when dealing with small sample sizes. We show how to extend our approaches to much more general estimation problems than estimating the sample mean. We describe how these methods can be used to obtain more reliable confidence intervals in survey sampling. As a concrete example, we construct confidence intervals using our methods for the number of violent deaths between March 2003 and July 2006 in Iraq, based on data from the study "Mortality after the 2003 invasion of Iraq: A cross sectional cluster sample survey," by Burnham et al. (2006).

Sample size and power considerations in network meta-analysis

PubMed Central

2012-01-01

Background Network meta-analysis is becoming increasingly popular for establishing comparative effectiveness among multiple interventions for the same disease. Network meta-analysis inherits all methodological challenges of standard pairwise meta-analysis, but with increased complexity due to the multitude of intervention comparisons. One issue that is now widely recognized in pairwise meta-analysis is the issue of sample size and statistical power. This issue, however, has so far only received little attention in network meta-analysis. To date, no approaches have been proposed for evaluating the adequacy of the sample size, and thus power, in a treatment network. Findings In this article, we develop easy-to-use flexible methods for estimating the ‘effective sample size’ in indirect comparison meta-analysis and network meta-analysis. The effective sample size for a particular treatment comparison can be interpreted as the number of patients in a pairwise meta-analysis that would provide the same degree and strength of evidence as that which is provided in the indirect comparison or network meta-analysis. We further develop methods for retrospectively estimating the statistical power for each comparison in a network meta-analysis. We illustrate the performance of the proposed methods for estimating effective sample size and statistical power using data from a network meta-analysis on interventions for smoking cessation including over 100 trials. Conclusion The proposed methods are easy to use and will be of high value to regulatory agencies and decision makers who must assess the strength of the evidence supporting comparative effectiveness estimates. PMID:22992327

Statistical grand rounds: a review of analysis and sample size calculation considerations for Wilcoxon tests.

PubMed

Divine, George; Norton, H James; Hunt, Ronald; Dienemann, Jacqueline

2013-09-01

When a study uses an ordinal outcome measure with unknown differences in the anchors and a small range such as 4 or 7, use of the Wilcoxon rank sum test or the Wilcoxon signed rank test may be most appropriate. However, because nonparametric methods are at best indirect functions of standard measures of location such as means or medians, the choice of the most appropriate summary measure can be difficult. The issues underlying use of these tests are discussed. The Wilcoxon-Mann-Whitney odds directly reflects the quantity that the rank sum procedure actually tests, and thus it can be a superior summary measure. Unlike the means and medians, its value will have a one-to-one correspondence with the Wilcoxon rank sum test result. The companion article appearing in this issue of Anesthesia & Analgesia ("Aromatherapy as Treatment for Postoperative Nausea: A Randomized Trial") illustrates these issues and provides an example of a situation for which the medians imply no difference between 2 groups, even though the groups are, in fact, quite different. The trial cited also provides an example of a single sample that has a median of zero, yet there is a substantial shift for much of the nonzero data, and the Wilcoxon signed rank test is quite significant. These examples highlight the potential discordance between medians and Wilcoxon test results. Along with the issues surrounding the choice of a summary measure, there are considerations for the computation of sample size and power, confidence intervals, and multiple comparison adjustment. In addition, despite the increased robustness of the Wilcoxon procedures relative to parametric tests, some circumstances in which the Wilcoxon tests may perform poorly are noted, along with alternative versions of the procedures that correct for such limitations. 

Stocking, Forest Type, and Stand Size Class - The Southern Forest Inventory and Analysis Unit's Calculation of Three Important Stand Descriptors

Treesearch

Dennis M. May

1990-01-01

The procedures by which the Southern Forest Inventory and Analysis unit calculates stocking from tree data collected on inventory sample plots are described in this report. Stocking is then used to ascertain two other important stand descriptors: forest type and stand size class. Inventory data for three plots from the recently completed 1989 Tennessee survey are used...

Sample size allocation in multiregional equivalence studies.

PubMed

Liao, Jason J Z; Yu, Ziji; Li, Yulan

2018-06-17

With the increasing globalization of drug development, the multiregional clinical trial (MRCT) has gained extensive use. The data from MRCTs could be accepted by regulatory authorities across regions and countries as the primary sources of evidence to support global marketing drug approval simultaneously. The MRCT can speed up patient enrollment and drug approval, and it makes the effective therapies available to patients all over the world simultaneously. However, there are many challenges both operationally and scientifically in conducting a drug development globally. One of many important questions to answer for the design of a multiregional study is how to partition sample size into each individual region. In this paper, two systematic approaches are proposed for the sample size allocation in a multiregional equivalence trial. A numerical evaluation and a biosimilar trial are used to illustrate the characteristics of the proposed approaches. Copyright © 2018 John Wiley & Sons, Ltd.

Sampling strategies for estimating brook trout effective population size

Treesearch

Andrew R. Whiteley; Jason A. Coombs; Mark Hudy; Zachary Robinson; Keith H. Nislow; Benjamin H. Letcher

2012-01-01

The influence of sampling strategy on estimates of effective population size (Ne) from single-sample genetic methods has not been rigorously examined, though these methods are increasingly used. For headwater salmonids, spatially close kin association among age-0 individuals suggests that sampling strategy (number of individuals and location from...

Influences of sampling size and pattern on the uncertainty of correlation estimation between soil water content and its influencing factors

NASA Astrophysics Data System (ADS)

Lai, Xiaoming; Zhu, Qing; Zhou, Zhiwen; Liao, Kaihua

2017-12-01

In this study, seven random combination sampling strategies were applied to investigate the uncertainties in estimating the hillslope mean soil water content (SWC) and correlation coefficients between the SWC and soil/terrain properties on a tea + bamboo hillslope. One of the sampling strategies is the global random sampling and the other six are the stratified random sampling on the top, middle, toe, top + mid, top + toe and mid + toe slope positions. When each sampling strategy was applied, sample sizes were gradually reduced and each sampling size contained 3000 replicates. Under each sampling size of each sampling strategy, the relative errors (REs) and coefficients of variation (CVs) of the estimated hillslope mean SWC and correlation coefficients between the SWC and soil/terrain properties were calculated to quantify the accuracy and uncertainty. The results showed that the uncertainty of the estimations decreased as the sampling size increasing. However, larger sample sizes were required to reduce the uncertainty in correlation coefficient estimation than in hillslope mean SWC estimation. Under global random sampling, 12 randomly sampled sites on this hillslope were adequate to estimate the hillslope mean SWC with RE and CV ≤10%. However, at least 72 randomly sampled sites were needed to ensure the estimated correlation coefficients with REs and CVs ≤10%. Comparing with all sampling strategies, reducing sampling sites on the middle slope had the least influence on the estimation of hillslope mean SWC and correlation coefficients. Under this strategy, 60 sites (10 on the middle slope and 50 on the top and toe slopes) were enough to ensure the estimated correlation coefficients with REs and CVs ≤10%. This suggested that when designing the SWC sampling, the proportion of sites on the middle slope can be reduced to 16.7% of the total number of sites. Findings of this study will be useful for the optimal SWC sampling design.

Standard Deviation for Small Samples

ERIC Educational Resources Information Center

Joarder, Anwar H.; Latif, Raja M.

2006-01-01

Neater representations for variance are given for small sample sizes, especially for 3 and 4. With these representations, variance can be calculated without a calculator if sample sizes are small and observations are integers, and an upper bound for the standard deviation is immediate. Accessible proofs of lower and upper bounds are presented for…

Small Sample Sizes Yield Biased Allometric Equations in Temperate Forests

PubMed Central

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

40 CFR 90.419 - Raw emission sampling calculations-gasoline fueled engines.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 20 2011-07-01 2011-07-01 false Raw emission sampling calculations... KILOWATTS Gaseous Exhaust Test Procedures § 90.419 Raw emission sampling calculations—gasoline fueled... selected as the basis for mass emission calculations using the raw gas method. ER03JY95.022 Where: WHC...

40 CFR 90.419 - Raw emission sampling calculations-gasoline fueled engines.

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... KILOWATTS Gaseous Exhaust Test Procedures § 90.419 Raw emission sampling calculations—gasoline fueled... selected as the basis for mass emission calculations using the raw gas method. ER03JY95.022 Where: WHC...

Methods for flexible sample-size design in clinical trials: Likelihood, weighted, dual test, and promising zone approaches.

PubMed

Shih, Weichung Joe; Li, Gang; Wang, Yining

2016-03-01

Sample size plays a crucial role in clinical trials. Flexible sample-size designs, as part of the more general category of adaptive designs that utilize interim data, have been a popular topic in recent years. In this paper, we give a comparative review of four related methods for such a design. The likelihood method uses the likelihood ratio test with an adjusted critical value. The weighted method adjusts the test statistic with given weights rather than the critical value. The dual test method requires both the likelihood ratio statistic and the weighted statistic to be greater than the unadjusted critical value. The promising zone approach uses the likelihood ratio statistic with the unadjusted value and other constraints. All four methods preserve the type-I error rate. In this paper we explore their properties and compare their relationships and merits. We show that the sample size rules for the dual test are in conflict with the rules of the promising zone approach. We delineate what is necessary to specify in the study protocol to ensure the validity of the statistical procedure and what can be kept implicit in the protocol so that more flexibility can be attained for confirmatory phase III trials in meeting regulatory requirements. We also prove that under mild conditions, the likelihood ratio test still preserves the type-I error rate when the actual sample size is larger than the re-calculated one. Copyright © 2015 Elsevier Inc. All rights reserved.

40 CFR 90.706 - Engine sample selection.

Code of Federal Regulations, 2010 CFR

2010-07-01

... = emission test result for an individual engine. x = mean of emission test results of the actual sample. FEL... test with the last test result from the previous model year and then calculate the required sample size.... Test results used to calculate the variables in the following Sample Size Equation must be final...

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 Appendix II to Part 600 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App. II Appendix II to Part 600—Sample Fuel Economy Calculations (...

7 CFR 51.308 - Methods of sampling and calculation of percentages.

Code of Federal Regulations, 2013 CFR

2013-01-01

... Grades of Apples Methods of Sampling and Calculation of Percentages § 51.308 Methods of sampling and... weigh ten pounds or less, or in any container where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be calculated...

7 CFR 51.308 - Methods of sampling and calculation of percentages.

Code of Federal Regulations, 2014 CFR

2014-01-01

... Grades of Apples Methods of Sampling and Calculation of Percentages § 51.308 Methods of sampling and... weigh ten pounds or less, or in any container where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be calculated...

Analysis of Sample Size, Counting Time, and Plot Size from an Avian Point Count Survey on Hoosier National Forest, Indiana

Treesearch

Frank R. Thompson; Monica J. Schwalbach

1995-01-01

We report results of a point count survey of breeding birds on Hoosier National Forest in Indiana. We determined sample size requirements to detect differences in means and the effects of count duration and plot size on individual detection rates. Sample size requirements ranged from 100 to >1000 points with Type I and II error rates of <0.1 and 0.2. Sample...

Sample size determination in group-sequential clinical trials with two co-primary endpoints

PubMed Central

Asakura, Koko; Hamasaki, Toshimitsu; Sugimoto, Tomoyuki; Hayashi, Kenichi; Evans, Scott R; Sozu, Takashi

2014-01-01

We discuss sample size determination in group-sequential designs with two endpoints as co-primary. We derive the power and sample size within two decision-making frameworks. One is to claim the test intervention’s benefit relative to control when superiority is achieved for the two endpoints at the same interim timepoint of the trial. The other is when the superiority is achieved for the two endpoints at any interim timepoint, not necessarily simultaneously. We evaluate the behaviors of sample size and power with varying design elements and provide a real example to illustrate the proposed sample size methods. In addition, we discuss sample size recalculation based on observed data and evaluate the impact on the power and Type I error rate. PMID:24676799

Got power? A systematic review of sample size adequacy in health professions education research.

PubMed

Cook, David A; Hatala, Rose

2015-03-01

Many education research studies employ small samples, which in turn lowers statistical power. We re-analyzed the results of a meta-analysis of simulation-based education to determine study power across a range of effect sizes, and the smallest effect that could be plausibly excluded. We systematically searched multiple databases through May 2011, and included all studies evaluating simulation-based education for health professionals in comparison with no intervention or another simulation intervention. Reviewers working in duplicate abstracted information to calculate standardized mean differences (SMD's). We included 897 original research studies. Among the 627 no-intervention-comparison studies the median sample size was 25. Only two studies (0.3%) had ≥80% power to detect a small difference (SMD > 0.2 standard deviations) and 136 (22%) had power to detect a large difference (SMD > 0.8). 110 no-intervention-comparison studies failed to find a statistically significant difference, but none excluded a small difference and only 47 (43%) excluded a large difference. Among 297 studies comparing alternate simulation approaches the median sample size was 30. Only one study (0.3%) had ≥80% power to detect a small difference and 79 (27%) had power to detect a large difference. Of the 128 studies that did not detect a statistically significant effect, 4 (3%) excluded a small difference and 91 (71%) excluded a large difference. In conclusion, most education research studies are powered only to detect effects of large magnitude. For most studies that do not reach statistical significance, the possibility of large and important differences still exists.

Accelerating potential of mean force calculations for lipid membrane permeation: System size, reaction coordinate, solute-solute distance, and cutoffs

NASA Astrophysics Data System (ADS)

Nitschke, Naomi; Atkovska, Kalina; Hub, Jochen S.

2016-09-01

Molecular dynamics simulations are capable of predicting the permeability of lipid membranes for drug-like solutes, but the calculations have remained prohibitively expensive for high-throughput studies. Here, we analyze simple measures for accelerating potential of mean force (PMF) calculations of membrane permeation, namely, (i) using smaller simulation systems, (ii) simulating multiple solutes per system, and (iii) using shorter cutoffs for the Lennard-Jones interactions. We find that PMFs for membrane permeation are remarkably robust against alterations of such parameters, suggesting that accurate PMF calculations are possible at strongly reduced computational cost. In addition, we evaluated the influence of the definition of the membrane center of mass (COM), used to define the transmembrane reaction coordinate. Membrane-COM definitions based on all lipid atoms lead to artifacts due to undulations and, consequently, to PMFs dependent on membrane size. In contrast, COM definitions based on a cylinder around the solute lead to size-independent PMFs, down to systems of only 16 lipids per monolayer. In summary, compared to popular setups that simulate a single solute in a membrane of 128 lipids with a Lennard-Jones cutoff of 1.2 nm, the measures applied here yield a speedup in sampling by factor of ˜40, without reducing the accuracy of the calculated PMF.

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…

A computer module used to calculate the horizontal control surface size of a conceptual aircraft design

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.

Sample-size needs for forestry herbicide trials

Treesearch

S.M. Zedaker; T.G. Gregoire; James H. Miller

1994-01-01

Forest herbicide experiments are increasingly being designed to evaluate smaller treatment differences when comparing existing effective treatments, tank mix ratios, surfactants, and new low-rate products. The ability to detect small differences in efficacy is dependent upon the relationship among sample size. type I and II error probabilities, and the coefficients of...

Estimating the Effective Sample Size of Tree Topologies from Bayesian Phylogenetic Analyses

PubMed Central

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

Drying step optimization to obtain large-size transparent magnesium-aluminate spinel samples

NASA Astrophysics Data System (ADS)

Petit, Johan; Lallemant, Lucile

2017-05-01

In the transparent ceramics processing, the green body elaboration step is probably the most critical one. Among the known techniques, wet shaping processes are particularly interesting because they enable the particles to find an optimum position on their own. Nevertheless, the presence of water molecules leads to drying issues. During the water removal, its concentration gradient induces cracks limiting the sample size: laboratory samples are generally less damaged because of their small size but upscaling the samples for industrial applications lead to an increasing cracking probability. Thanks to the drying step optimization, large size spinel samples were obtained.

Sample size for post-marketing safety studies based on historical controls.

PubMed

Wu, Yu-te; Makuch, Robert W

2010-08-01

As part of a drug's entire life cycle, post-marketing studies are an important part in the identification of rare, serious adverse events. Recently, the US Food and Drug Administration (FDA) has begun to implement new post-marketing safety mandates as a consequence of increased emphasis on safety. The purpose of this research is to provide exact sample size formula for the proposed hybrid design, based on a two-group cohort study with incorporation of historical external data. Exact sample size formula based on the Poisson distribution is developed, because the detection of rare events is our outcome of interest. Performance of exact method is compared to its approximate large-sample theory counterpart. The proposed hybrid design requires a smaller sample size compared to the standard, two-group prospective study design. In addition, the exact method reduces the number of subjects required in the treatment group by up to 30% compared to the approximate method for the study scenarios examined. The proposed hybrid design satisfies the advantages and rationale of the two-group design with smaller sample sizes generally required. 2010 John Wiley & Sons, Ltd.

Determining Sample Size for Accurate Estimation of the Squared Multiple Correlation Coefficient.

ERIC Educational Resources Information Center

Algina, James; Olejnik, Stephen

2000-01-01

Discusses determining sample size for estimation of the squared multiple correlation coefficient and presents regression equations that permit determination of the sample size for estimating this parameter for up to 20 predictor variables. (SLD)

Post-stratified estimation: with-in strata and total sample size recommendations

Treesearch

James A. Westfall; Paul L. Patterson; John W. Coulston

2011-01-01

Post-stratification is used to reduce the variance of estimates of the mean. Because the stratification is not fixed in advance, within-strata sample sizes can be quite small. The survey statistics literature provides some guidance on minimum within-strata sample sizes; however, the recommendations and justifications are inconsistent and apply broadly for many...

Sample size in psychological research over the past 30 years.

PubMed

Marszalek, Jacob M; Barber, Carolyn; Kohlhart, Julie; Holmes, Cooper B

2011-04-01

The American Psychological Association (APA) Task Force on Statistical Inference was formed in 1996 in response to a growing body of research demonstrating methodological issues that threatened the credibility of psychological research, and made recommendations to address them. One issue was the small, even dramatically inadequate, size of samples used in studies published by leading journals. The present study assessed the progress made since the Task Force's final report in 1999. Sample sizes reported in four leading APA journals in 1955, 1977, 1995, and 2006 were compared using nonparametric statistics, while data from the last two waves were fit to a hierarchical generalized linear growth model for more in-depth analysis. Overall, results indicate that the recommendations for increasing sample sizes have not been integrated in core psychological research, although results slightly vary by field. This and other implications are discussed in the context of current methodological critique and practice.

Framework for cascade size calculations on random networks

NASA Astrophysics Data System (ADS)

Burkholz, Rebekka; Schweitzer, Frank

2018-04-01

We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary degree distribution, degree-degree correlations, and, in case of threshold models, for arbitrary threshold distribution. With our approach, we shift the perspective from the known branching process approximations to the iterative update of suitable probability distributions. Such distributions are key to capture cascade dynamics that involve possibly continuous quantities and that depend on the cascade history, e.g., if load is accumulated over time. As a proof of concept, we provide two examples: (a) Constant load models that cover many of the analytically tractable casacade models, and, as a highlight, (b) a fiber bundle model that was not tractable by branching process approximations before. Our derivations cover the whole cascade dynamics, not only their steady state. This allows us to include interventions in time or further model complexity in the analysis.

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…

Determining sample size for tree utilization surveys

Treesearch

Stanley J. Zarnoch; James W. Bentley; Tony G. Johnson

2004-01-01

The U.S. Department of Agriculture Forest Service has conducted many studies to determine what proportion of the timber harvested in the South is actually utilized. This paper describes the statistical methods used to determine required sample sizes for estimating utilization ratios for a required level of precision. The data used are those for 515 hardwood and 1,557...

Unequal cluster sizes in stepped-wedge cluster randomised trials: a systematic review.

PubMed

Kristunas, Caroline; Morris, Tom; Gray, Laura

2017-11-15

To investigate the extent to which cluster sizes vary in stepped-wedge cluster randomised trials (SW-CRT) and whether any variability is accounted for during the sample size calculation and analysis of these trials. Any, not limited to healthcare settings. Any taking part in an SW-CRT published up to March 2016. The primary outcome is the variability in cluster sizes, measured by the coefficient of variation (CV) in cluster size. Secondary outcomes include the difference between the cluster sizes assumed during the sample size calculation and those observed during the trial, any reported variability in cluster sizes and whether the methods of sample size calculation and methods of analysis accounted for any variability in cluster sizes. Of the 101 included SW-CRTs, 48% mentioned that the included clusters were known to vary in size, yet only 13% of these accounted for this during the calculation of the sample size. However, 69% of the trials did use a method of analysis appropriate for when clusters vary in size. Full trial reports were available for 53 trials. The CV was calculated for 23 of these: the median CV was 0.41 (IQR: 0.22-0.52). Actual cluster sizes could be compared with those assumed during the sample size calculation for 14 (26%) of the trial reports; the cluster sizes were between 29% and 480% of that which had been assumed. Cluster sizes often vary in SW-CRTs. Reporting of SW-CRTs also remains suboptimal. The effect of unequal cluster sizes on the statistical power of SW-CRTs needs further exploration and methods appropriate to studies with unequal cluster sizes need to be employed. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

Unequal cluster sizes in stepped-wedge cluster randomised trials: a systematic review

PubMed Central

Morris, Tom; Gray, Laura

2017-01-01

Objectives To investigate the extent to which cluster sizes vary in stepped-wedge cluster randomised trials (SW-CRT) and whether any variability is accounted for during the sample size calculation and analysis of these trials. Setting Any, not limited to healthcare settings. Participants Any taking part in an SW-CRT published up to March 2016. Primary and secondary outcome measures The primary outcome is the variability in cluster sizes, measured by the coefficient of variation (CV) in cluster size. Secondary outcomes include the difference between the cluster sizes assumed during the sample size calculation and those observed during the trial, any reported variability in cluster sizes and whether the methods of sample size calculation and methods of analysis accounted for any variability in cluster sizes. Results Of the 101 included SW-CRTs, 48% mentioned that the included clusters were known to vary in size, yet only 13% of these accounted for this during the calculation of the sample size. However, 69% of the trials did use a method of analysis appropriate for when clusters vary in size. Full trial reports were available for 53 trials. The CV was calculated for 23 of these: the median CV was 0.41 (IQR: 0.22–0.52). Actual cluster sizes could be compared with those assumed during the sample size calculation for 14 (26%) of the trial reports; the cluster sizes were between 29% and 480% of that which had been assumed. Conclusions Cluster sizes often vary in SW-CRTs. Reporting of SW-CRTs also remains suboptimal. The effect of unequal cluster sizes on the statistical power of SW-CRTs needs further exploration and methods appropriate to studies with unequal cluster sizes need to be employed. PMID:29146637

Sample size requirements for the design of reliability studies: precision consideration.

PubMed

Shieh, Gwowen

2014-09-01

In multilevel modeling, the intraclass correlation coefficient based on the one-way random-effects model is routinely employed to measure the reliability or degree of resemblance among group members. To facilitate the advocated practice of reporting confidence intervals in future reliability studies, this article presents exact sample size procedures for precise interval estimation of the intraclass correlation coefficient under various allocation and cost structures. Although the suggested approaches do not admit explicit sample size formulas and require special algorithms for carrying out iterative computations, they are more accurate than the closed-form formulas constructed from large-sample approximations with respect to the expected width and assurance probability criteria. This investigation notes the deficiency of existing methods and expands the sample size methodology for the design of reliability studies that have not previously been discussed in the literature.

Influence of sampling window size and orientation on parafoveal cone packing density

PubMed Central

Lombardo, Marco; Serrao, Sebastiano; Ducoli, Pietro; Lombardo, Giuseppe

2013-01-01

We assessed the agreement between sampling windows of different size and orientation on packing density estimates in images of the parafoveal cone mosaic acquired using a flood-illumination adaptive optics retinal camera. Horizontal and vertical oriented sampling windows of different size (320x160 µm, 160x80 µm and 80x40 µm) were selected in two retinal locations along the horizontal meridian in one eye of ten subjects. At each location, cone density tended to decline with decreasing sampling area. Although the differences in cone density estimates were not statistically significant, Bland-Altman plots showed that the agreement between cone density estimated within the different sampling window conditions was moderate. The percentage of the preferred packing arrangements of cones by Voronoi tiles was slightly affected by window size and orientation. The results illustrated the high importance of specifying the size and orientation of the sampling window used to derive cone metric estimates to facilitate comparison of different studies. PMID:24009995

Simulation analyses of space use: Home range estimates, variability, and sample size

USGS Publications Warehouse

Bekoff, Marc; Mech, L. David

1984-01-01

Simulations of space use by animals were run to determine the relationship among home range area estimates, variability, and sample size (number of locations). As sample size increased, home range size increased asymptotically, whereas variability decreased among mean home range area estimates generated by multiple simulations for the same sample size. Our results suggest that field workers should ascertain between 100 and 200 locations in order to estimate reliably home range area. In some cases, this suggested guideline is higher than values found in the few published studies in which the relationship between home range area and number of locations is addressed. Sampling differences for small species occupying relatively small home ranges indicate that fewer locations may be sufficient to allow for a reliable estimate of home range. Intraspecific variability in social status (group member, loner, resident, transient), age, sex, reproductive condition, and food resources also have to be considered, as do season, habitat, and differences in sampling and analytical methods. Comparative data still are needed.

A normative inference approach for optimal sample sizes in decisions from experience

PubMed Central

Ostwald, Dirk; Starke, Ludger; Hertwig, Ralph

2015-01-01

“Decisions from experience” (DFE) refers to a body of work that emerged in research on behavioral decision making over the last decade. One of the major experimental paradigms employed to study experience-based choice is the “sampling paradigm,” which serves as a model of decision making under limited knowledge about the statistical structure of the world. In this paradigm respondents are presented with two payoff distributions, which, in contrast to standard approaches in behavioral economics, are specified not in terms of explicit outcome-probability information, but by the opportunity to sample outcomes from each distribution without economic consequences. Participants are encouraged to explore the distributions until they feel confident enough to decide from which they would prefer to draw from in a final trial involving real monetary payoffs. One commonly employed measure to characterize the behavior of participants in the sampling paradigm is the sample size, that is, the number of outcome draws which participants choose to obtain from each distribution prior to terminating sampling. A natural question that arises in this context concerns the “optimal” sample size, which could be used as a normative benchmark to evaluate human sampling behavior in DFE. In this theoretical study, we relate the DFE sampling paradigm to the classical statistical decision theoretic literature and, under a probabilistic inference assumption, evaluate optimal sample sizes for DFE. In our treatment we go beyond analytically established results by showing how the classical statistical decision theoretic framework can be used to derive optimal sample sizes under arbitrary, but numerically evaluable, constraints. Finally, we critically evaluate the value of deriving optimal sample sizes under this framework as testable predictions for the experimental study of sampling behavior in DFE. PMID:26441720

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.

10 CFR Appendix to Part 474 - Sample Petroleum-Equivalent Fuel Economy Calculations

Code of Federal Regulations, 2010 CFR

2010-01-01

... 10 Energy 3 2010-01-01 2010-01-01 false Sample Petroleum-Equivalent Fuel Economy Calculations Appendix to Part 474 Energy DEPARTMENT OF ENERGY ENERGY CONSERVATION ELECTRIC AND HYBRID VEHICLE RESEARCH, DEVELOPMENT, AND DEMONSTRATION PROGRAM; PETROLEUM-EQUIVALENT FUEL ECONOMY CALCULATION Pt. 474, App. Appendix to Part 474—Sample...

Sample size and number of outcome measures of veterinary randomised controlled trials of pharmaceutical interventions funded by different sources, a cross-sectional study.

PubMed

Wareham, K J; Hyde, R M; Grindlay, D; Brennan, M L; Dean, R S

2017-10-04

Randomised controlled trials (RCTs) are a key component of the veterinary evidence base. Sample sizes and defined outcome measures are crucial components of RCTs. To describe the sample size and number of outcome measures of veterinary RCTs either funded by the pharmaceutical industry or not, published in 2011. A structured search of PubMed identified RCTs examining the efficacy of pharmaceutical interventions. Number of outcome measures, number of animals enrolled per trial, whether a primary outcome was identified, and the presence of a sample size calculation were extracted from the RCTs. The source of funding was identified for each trial and groups compared on the above parameters. Literature searches returned 972 papers; 86 papers comprising 126 individual trials were analysed. The median number of outcomes per trial was 5.0; there were no significant differences across funding groups (p = 0.133). The median number of animals enrolled per trial was 30.0; this was similar across funding groups (p = 0.302). A primary outcome was identified in 40.5% of trials and was significantly more likely to be stated in trials funded by a pharmaceutical company. A very low percentage of trials reported a sample size calculation (14.3%). Failure to report primary outcomes, justify sample sizes and the reporting of multiple outcome measures was a common feature in all of the clinical trials examined in this study. It is possible some of these factors may be affected by the source of funding of the studies, but the influence of funding needs to be explored with a larger number of trials. Some veterinary RCTs provide a weak evidence base and targeted strategies are required to improve the quality of veterinary RCTs to ensure there is reliable evidence on which to base clinical decisions.

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…

XAFSmass: a program for calculating the optimal mass of XAFS samples

NASA Astrophysics Data System (ADS)

Klementiev, K.; Chernikov, R.

2016-05-01

We present a new implementation of the XAFSmass program that calculates the optimal mass of XAFS samples. It has several improvements as compared to the old Windows based program XAFSmass: 1) it is truly platform independent, as provided by Python language, 2) it has an improved parser of chemical formulas that enables parentheses and nested inclusion-to-matrix weight percentages. The program calculates the absorption edge height given the total optical thickness, operates with differently determined sample amounts (mass, pressure, density or sample area) depending on the aggregate state of the sample and solves the inverse problem of finding the elemental composition given the experimental absorption edge jump and the chemical formula.

Sample size considerations for paired experimental design with incomplete observations of continuous outcomes.

PubMed

Zhu, Hong; Xu, Xiaohan; Ahn, Chul

2017-01-01

Paired experimental design is widely used in clinical and health behavioral studies, where each study unit contributes a pair of observations. Investigators often encounter incomplete observations of paired outcomes in the data collected. Some study units contribute complete pairs of observations, while the others contribute either pre- or post-intervention observations. Statistical inference for paired experimental design with incomplete observations of continuous outcomes has been extensively studied in literature. However, sample size method for such study design is sparsely available. We derive a closed-form sample size formula based on the generalized estimating equation approach by treating the incomplete observations as missing data in a linear model. The proposed method properly accounts for the impact of mixed structure of observed data: a combination of paired and unpaired outcomes. The sample size formula is flexible to accommodate different missing patterns, magnitude of missingness, and correlation parameter values. We demonstrate that under complete observations, the proposed generalized estimating equation sample size estimate is the same as that based on the paired t-test. In the presence of missing data, the proposed method would lead to a more accurate sample size estimate comparing with the crude adjustment. Simulation studies are conducted to evaluate the finite-sample performance of the generalized estimating equation sample size formula. A real application example is presented for illustration.

Improved patient size estimates for accurate dose calculations in abdomen computed tomography

NASA Astrophysics Data System (ADS)

Lee, Chang-Lae

2017-07-01

The radiation dose of CT (computed tomography) is generally represented by the CTDI (CT dose index). CTDI, however, does not accurately predict the actual patient doses for different human body sizes because it relies on a cylinder-shaped head (diameter : 16 cm) and body (diameter : 32 cm) phantom. The purpose of this study was to eliminate the drawbacks of the conventional CTDI and to provide more accurate radiation dose information. Projection radiographs were obtained from water cylinder phantoms of various sizes, and the sizes of the water cylinder phantoms were calculated and verified using attenuation profiles. The effective diameter was also calculated using the attenuation of the abdominal projection radiographs of 10 patients. When the results of the attenuation-based method and the geometry-based method shown were compared with the results of the reconstructed-axial-CT-image-based method, the effective diameter of the attenuation-based method was found to be similar to the effective diameter of the reconstructed-axial-CT-image-based method, with a difference of less than 3.8%, but the geometry-based method showed a difference of less than 11.4%. This paper proposes a new method of accurately computing the radiation dose of CT based on the patient sizes. This method computes and provides the exact patient dose before the CT scan, and can therefore be effectively used for imaging and dose control.

Effects of sample size on KERNEL home range estimates

USGS Publications Warehouse

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.

Efficiency of whole-body counter for various body size calculated by MCNP5 software.

PubMed

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.

A U-statistics based approach to sample size planning of two-arm trials with discrete outcome criterion aiming to establish either superiority or noninferiority.

PubMed

Wellek, Stefan

2017-02-28

In current practice, the most frequently applied approach to the handling of ties in the Mann-Whitney-Wilcoxon (MWW) test is based on the conditional distribution of the sum of mid-ranks, given the observed pattern of ties. Starting from this conditional version of the testing procedure, a sample size formula was derived and investigated by Zhao et al. (Stat Med 2008). In contrast, the approach we pursue here is a nonconditional one exploiting explicit representations for the variances of and the covariance between the two U-statistics estimators involved in the Mann-Whitney form of the test statistic. The accuracy of both ways of approximating the sample sizes required for attaining a prespecified level of power in the MWW test for superiority with arbitrarily tied data is comparatively evaluated by means of simulation. The key qualitative conclusions to be drawn from these numerical comparisons are as follows: With the sample sizes calculated by means of the respective formula, both versions of the test maintain the level and the prespecified power with about the same degree of accuracy. Despite the equivalence in terms of accuracy, the sample size estimates obtained by means of the new formula are in many cases markedly lower than that calculated for the conditional test. Perhaps, a still more important advantage of the nonconditional approach based on U-statistics is that it can be also adopted for noninferiority trials. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

An analysis of Apollo lunar soil samples 12070,889, 12030,187, and 12070,891: Basaltic diversity at the Apollo 12 landing site and implications for classification of small-sized lunar samples

NASA Astrophysics Data System (ADS)

Alexander, Louise; Snape, Joshua F.; Joy, Katherine H.; Downes, Hilary; Crawford, Ian A.

2016-09-01

Lunar mare basalts provide insights into the compositional diversity of the Moon's interior. Basalt fragments from the lunar regolith can potentially sample lava flows from regions of the Moon not previously visited, thus, increasing our understanding of lunar geological evolution. As part of a study of basaltic diversity at the Apollo 12 landing site, detailed petrological and geochemical data are provided here for 13 basaltic chips. In addition to bulk chemistry, we have analyzed the major, minor, and trace element chemistry of mineral phases which highlight differences between basalt groups. Where samples contain olivine, the equilibrium parent melt magnesium number (Mg#; atomic Mg/[Mg + Fe]) can be calculated to estimate parent melt composition. Ilmenite and plagioclase chemistry can also determine differences between basalt groups. We conclude that samples of approximately 1-2 mm in size can be categorized provided that appropriate mineral phases (olivine, plagioclase, and ilmenite) are present. Where samples are fine-grained (grain size <0.3 mm), a "paired samples t-test" can provide a statistical comparison between a particular sample and known lunar basalts. Of the fragments analyzed here, three are found to belong to each of the previously identified olivine and ilmenite basalt suites, four to the pigeonite basalt suite, one is an olivine cumulate, and two could not be categorized because of their coarse grain sizes and lack of appropriate mineral phases. Our approach introduces methods that can be used to investigate small sample sizes (i.e., fines) from future sample return missions to investigate lava flow diversity and petrological significance.

Sample sizes and model comparison metrics for species distribution models

Treesearch

B.B. Hanberry; H.S. He; D.C. Dey

2012-01-01

Species distribution models use small samples to produce continuous distribution maps. The question of how small a sample can be to produce an accurate model generally has been answered based on comparisons to maximum sample sizes of 200 observations or fewer. In addition, model comparisons often are made with the kappa statistic, which has become controversial....

Forward flux sampling calculation of homogeneous nucleation rates from aqueous NaCl solutions.

PubMed

Jiang, Hao; Haji-Akbari, Amir; Debenedetti, Pablo G; Panagiotopoulos, Athanassios Z

2018-01-28

We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the Extended Simple Point Charge (SPC/E) water model. The calculated nucleation rates are significantly lower than the available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwald's step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.

Forward flux sampling calculation of homogeneous nucleation rates from aqueous NaCl solutions

NASA Astrophysics Data System (ADS)

Jiang, Hao; Haji-Akbari, Amir; Debenedetti, Pablo G.; Panagiotopoulos, Athanassios Z.

2018-01-01

We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the Extended Simple Point Charge (SPC/E) water model. The calculated nucleation rates are significantly lower than the available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwald's step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.

Calculating Confidence, Uncertainty, and Numbers of Samples When Using Statistical Sampling Approaches to Characterize and Clear Contaminated Areas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piepel, Gregory F.; Matzke, Brett D.; Sego, Landon H.

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 amore » 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

Sample size determination for disease prevalence studies with partially validated data.

PubMed

Qiu, Shi-Fang; Poon, Wai-Yin; Tang, Man-Lai

2016-02-01

Disease prevalence is an important topic in medical research, and its study is based on data that are obtained by classifying subjects according to whether a disease has been contracted. Classification can be conducted with high-cost gold standard tests or low-cost screening tests, but the latter are subject to the misclassification of subjects. As a compromise between the two, many research studies use partially validated datasets in which all data points are classified by fallible tests, and some of the data points are validated in the sense that they are also classified by the completely accurate gold-standard test. In this article, we investigate the determination of sample sizes for disease prevalence studies with partially validated data. We use two approaches. The first is to find sample sizes that can achieve a pre-specified power of a statistical test at a chosen significance level, and the second is to find sample sizes that can control the width of a confidence interval with a pre-specified confidence level. Empirical studies have been conducted to demonstrate the performance of various testing procedures with the proposed sample sizes. The applicability of the proposed methods are illustrated by a real-data example. © The Author(s) 2012.

On Using a Pilot Sample Variance for Sample Size Determination in the Detection of Differences between Two Means: Power Consideration

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…

A Note on Sample Size and Solution Propriety for Confirmatory Factor Analytic Models

ERIC Educational Resources Information Center

Jackson, Dennis L.; Voth, Jennifer; Frey, Marc P.

2013-01-01

Determining an appropriate sample size for use in latent variable modeling techniques has presented ongoing challenges to researchers. In particular, small sample sizes are known to present concerns over sampling error for the variances and covariances on which model estimation is based, as well as for fit indexes and convergence failures. The…

Sample Size Requirements for Studies of Treatment Effects on Beta-Cell Function in Newly Diagnosed Type 1 Diabetes

PubMed Central

Lachin, John M.; McGee, Paula L.; Greenbaum, Carla J.; Palmer, Jerry; Gottlieb, Peter; Skyler, Jay

2011-01-01

Preservation of -cell function as measured by stimulated C-peptide has recently been accepted as a therapeutic target for subjects with newly diagnosed type 1 diabetes. In recently completed studies conducted by the Type 1 Diabetes Trial Network (TrialNet), repeated 2-hour Mixed Meal Tolerance Tests (MMTT) were obtained for up to 24 months from 156 subjects with up to 3 months duration of type 1 diabetes at the time of study enrollment. These data provide the information needed to more accurately determine the sample size needed for future studies of the effects of new agents on the 2-hour area under the curve (AUC) of the C-peptide values. The natural log(), log(+1) and square-root transformations of the AUC were assessed. In general, a transformation of the data is needed to better satisfy the normality assumptions for commonly used statistical tests. Statistical analysis of the raw and transformed data are provided to estimate the mean levels over time and the residual variation in untreated subjects that allow sample size calculations for future studies at either 12 or 24 months of follow-up and among children 8–12 years of age, adolescents (13–17 years) and adults (18+ years). The sample size needed to detect a given relative (percentage) difference with treatment versus control is greater at 24 months than at 12 months of follow-up, and differs among age categories. Owing to greater residual variation among those 13–17 years of age, a larger sample size is required for this age group. Methods are also described for assessment of sample size for mixtures of subjects among the age categories. Statistical expressions are presented for the presentation of analyses of log(+1) and transformed values in terms of the original units of measurement (pmol/ml). Analyses using different transformations are described for the TrialNet study of masked anti-CD20 (rituximab) versus masked placebo. These results provide the information needed to accurately evaluate the

Sample size requirements for studies of treatment effects on beta-cell function in newly diagnosed type 1 diabetes.

PubMed

Lachin, John M; McGee, Paula L; Greenbaum, Carla J; Palmer, Jerry; Pescovitz, Mark D; Gottlieb, Peter; Skyler, Jay

2011-01-01

Preservation of β-cell function as measured by stimulated C-peptide has recently been accepted as a therapeutic target for subjects with newly diagnosed type 1 diabetes. In recently completed studies conducted by the Type 1 Diabetes Trial Network (TrialNet), repeated 2-hour Mixed Meal Tolerance Tests (MMTT) were obtained for up to 24 months from 156 subjects with up to 3 months duration of type 1 diabetes at the time of study enrollment. These data provide the information needed to more accurately determine the sample size needed for future studies of the effects of new agents on the 2-hour area under the curve (AUC) of the C-peptide values. The natural log(x), log(x+1) and square-root (√x) transformations of the AUC were assessed. In general, a transformation of the data is needed to better satisfy the normality assumptions for commonly used statistical tests. Statistical analysis of the raw and transformed data are provided to estimate the mean levels over time and the residual variation in untreated subjects that allow sample size calculations for future studies at either 12 or 24 months of follow-up and among children 8-12 years of age, adolescents (13-17 years) and adults (18+ years). The sample size needed to detect a given relative (percentage) difference with treatment versus control is greater at 24 months than at 12 months of follow-up, and differs among age categories. Owing to greater residual variation among those 13-17 years of age, a larger sample size is required for this age group. Methods are also described for assessment of sample size for mixtures of subjects among the age categories. Statistical expressions are presented for the presentation of analyses of log(x+1) and √x transformed values in terms of the original units of measurement (pmol/ml). Analyses using different transformations are described for the TrialNet study of masked anti-CD20 (rituximab) versus masked placebo. These results provide the information needed to accurately

Using the Student's "t"-Test with Extremely Small Sample Sizes

ERIC Educational Resources Information Center

de Winter, J. C .F.

2013-01-01

Researchers occasionally have to work with an extremely small sample size, defined herein as "N" less than or equal to 5. Some methodologists have cautioned against using the "t"-test when the sample size is extremely small, whereas others have suggested that using the "t"-test is feasible in such a case. The present…

Size and modal analyses of fines and ultrafines from some Apollo 17 samples

NASA Technical Reports Server (NTRS)

Greene, G. M.; King, D. T., Jr.; Banholzer, G. S., Jr.; King, E. A.

1975-01-01

Scanning electron and optical microscopy techniques have been used to determine the grain-size frequency distributions and morphology-based modal analyses of fine and ultrafine fractions of some Apollo 17 regolith samples. There are significant and large differences between the grain-size frequency distributions of the less than 10-micron size fraction of Apollo 17 samples, but there are no clear relations to the local geologic setting from which individual samples have been collected. This may be due to effective lateral mixing of regolith particles in this size range by micrometeoroid impacts. None of the properties of the frequency distributions support the idea of selective transport of any fine grain-size fraction, as has been proposed by other workers. All of the particle types found in the coarser size fractions also occur in the less than 10-micron particles. In the size range from 105 to 10 microns there is a strong tendency for the percentage of regularly shaped glass to increase as the graphic mean grain size of the less than 1-mm size fraction decreases, both probably being controlled by exposure age.

Scalable free energy calculation of proteins via multiscale essential sampling

NASA Astrophysics Data System (ADS)

Moritsugu, Kei; Terada, Tohru; Kidera, Akinori

2010-12-01

A multiscale simulation method, "multiscale essential sampling (MSES)," is proposed for calculating free energy surface of proteins in a sizable dimensional space with good scalability. In MSES, the configurational sampling of a full-dimensional model is enhanced by coupling with the accelerated dynamics of the essential degrees of freedom. Applying the Hamiltonian exchange method to MSES can remove the biasing potential from the coupling term, deriving the free energy surface of the essential degrees of freedom. The form of the coupling term ensures good scalability in the Hamiltonian exchange. As a test application, the free energy surface of the folding process of a miniprotein, chignolin, was calculated in the continuum solvent model. Results agreed with the free energy surface derived from the multicanonical simulation. Significantly improved scalability with the MSES method was clearly shown in the free energy calculation of chignolin in explicit solvent, which was achieved without increasing the number of replicas in the Hamiltonian exchange.

Optimal sample sizes for the design of reliability studies: power consideration.

PubMed

Shieh, Gwowen

2014-09-01

Intraclass correlation coefficients are used extensively to measure the reliability or degree of resemblance among group members in multilevel research. This study concerns the problem of the necessary sample size to ensure adequate statistical power for hypothesis tests concerning the intraclass correlation coefficient in the one-way random-effects model. In view of the incomplete and problematic numerical results in the literature, the approximate sample size formula constructed from Fisher's transformation is reevaluated and compared with an exact approach across a wide range of model configurations. These comprehensive examinations showed that the Fisher transformation method is appropriate only under limited circumstances, and therefore it is not recommended as a general method in practice. For advance design planning of reliability studies, the exact sample size procedures are fully described and illustrated for various allocation and cost schemes. Corresponding computer programs are also developed to implement the suggested algorithms.

SU-E-T-374: Evaluation and Verification of Dose Calculation Accuracy with Different Dose Grid Sizes for Intracranial Stereotactic Radiosurgery

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, C; Schultheiss, T

Purpose: In this study, we aim to evaluate the effect of dose grid size on the accuracy of calculated dose for small lesions in intracranial stereotactic radiosurgery (SRS), and to verify dose calculation accuracy with radiochromic film dosimetry. Methods: 15 intracranial lesions from previous SRS patients were retrospectively selected for this study. The planning target volume (PTV) ranged from 0.17 to 2.3 cm{sup 3}. A commercial treatment planning system was used to generate SRS plans using the volumetric modulated arc therapy (VMAT) technique using two arc fields. Two convolution-superposition-based dose calculation algorithms (Anisotropic Analytical Algorithm and Acuros XB algorithm) weremore » used to calculate volume dose distribution with dose grid size ranging from 1 mm to 3 mm with 0.5 mm step size. First, while the plan monitor units (MU) were kept constant, PTV dose variations were analyzed. Second, with 95% of the PTV covered by the prescription dose, variations of the plan MUs as a function of dose grid size were analyzed. Radiochomic films were used to compare the delivered dose and profile with the calculated dose distribution with different dose grid sizes. Results: The dose to the PTV, in terms of the mean dose, maximum, and minimum dose, showed steady decrease with increasing dose grid size using both algorithms. With 95% of the PTV covered by the prescription dose, the total MU increased with increasing dose grid size in most of the plans. Radiochromic film measurements showed better agreement with dose distributions calculated with 1-mm dose grid size. Conclusion: Dose grid size has significant impact on calculated dose distribution in intracranial SRS treatment planning with small target volumes. Using the default dose grid size could lead to under-estimation of delivered dose. A small dose grid size should be used to ensure calculation accuracy and agreement with QA measurements.« less

GPU-based ultra-fast dose calculation using a finite size pencil beam model.

PubMed

Gu, Xuejun; Choi, Dongju; Men, Chunhua; Pan, Hubert; Majumdar, Amitava; Jiang, Steve B

2009-10-21

Online adaptive radiation therapy (ART) is an attractive concept that promises the ability to deliver an optimal treatment in response to the inter-fraction variability in patient anatomy. However, it has yet to be realized due to technical limitations. Fast dose deposit coefficient calculation is a critical component of the online planning process that is required for plan optimization of intensity-modulated radiation therapy (IMRT). Computer graphics processing units (GPUs) are well suited to provide the requisite fast performance for the data-parallel nature of dose calculation. In this work, we develop a dose calculation engine based on a finite-size pencil beam (FSPB) algorithm and a GPU parallel computing framework. The developed framework can accommodate any FSPB model. We test our implementation in the case of a water phantom and the case of a prostate cancer patient with varying beamlet and voxel sizes. All testing scenarios achieved speedup ranging from 200 to 400 times when using a NVIDIA Tesla C1060 card in comparison with a 2.27 GHz Intel Xeon CPU. The computational time for calculating dose deposition coefficients for a nine-field prostate IMRT plan with this new framework is less than 1 s. This indicates that the GPU-based FSPB algorithm is well suited for online re-planning for adaptive radiotherapy.

The impact of sample size on the reproducibility of voxel-based lesion-deficit mappings.

PubMed

Lorca-Puls, Diego L; Gajardo-Vidal, Andrea; White, Jitrachote; Seghier, Mohamed L; Leff, Alexander P; Green, David W; Crinion, Jenny T; Ludersdorfer, Philipp; Hope, Thomas M H; Bowman, Howard; Price, Cathy J

2018-07-01

This study investigated how sample size affects the reproducibility of findings from univariate voxel-based lesion-deficit analyses (e.g., voxel-based lesion-symptom mapping and voxel-based morphometry). Our effect of interest was the strength of the mapping between brain damage and speech articulation difficulties, as measured in terms of the proportion of variance explained. First, we identified a region of interest by searching on a voxel-by-voxel basis for brain areas where greater lesion load was associated with poorer speech articulation using a large sample of 360 right-handed English-speaking stroke survivors. We then randomly drew thousands of bootstrap samples from this data set that included either 30, 60, 90, 120, 180, or 360 patients. For each resample, we recorded effect size estimates and p values after conducting exactly the same lesion-deficit analysis within the previously identified region of interest and holding all procedures constant. The results show (1) how often small effect sizes in a heterogeneous population fail to be detected; (2) how effect size and its statistical significance varies with sample size; (3) how low-powered studies (due to small sample sizes) can greatly over-estimate as well as under-estimate effect sizes; and (4) how large sample sizes (N ≥ 90) can yield highly significant p values even when effect sizes are so small that they become trivial in practical terms. The implications of these findings for interpreting the results from univariate voxel-based lesion-deficit analyses are discussed. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Elemental analysis of size-fractionated particulate matter sampled in Göteborg, Sweden

NASA Astrophysics Data System (ADS)

Wagner, Annemarie; Boman, Johan; Gatari, Michael J.

2008-12-01

The aim of the study was to investigate the mass distribution of trace elements in aerosol samples collected in the urban area of Göteborg, Sweden, with special focus on the impact of different air masses and anthropogenic activities. Three measurement campaigns were conducted during December 2006 and January 2007. A PIXE cascade impactor was used to collect particulate matter in 9 size fractions ranging from 16 to 0.06 µm aerodynamic diameter. Polished quartz carriers were chosen as collection substrates for the subsequent direct analysis by TXRF. To investigate the sources of the analyzed air masses, backward trajectories were calculated. Our results showed that diurnal sampling was sufficient to investigate the mass distribution for Br, Ca, Cl, Cu, Fe, K, Sr and Zn, whereas a 5-day sampling period resulted in additional information on mass distribution for Cr and S. Unimodal mass distributions were found in the study area for the elements Ca, Cl, Fe and Zn, whereas the distributions for Br, Cu, Cr, K, Ni and S were bimodal, indicating high temperature processes as source of the submicron particle components. The measurement period including the New Year firework activities showed both an extensive increase in concentrations as well as a shift to the submicron range for K and Sr, elements that are typically found in fireworks. Further research is required to validate the quantification of trace elements directly collected on sample carriers.

Does increasing the size of bi-weekly samples of records influence results when using the Global Trigger Tool? An observational study of retrospective record reviews of two different sample sizes.

PubMed

Mevik, Kjersti; Griffin, Frances A; Hansen, Tonje E; Deilkås, Ellen T; Vonen, Barthold

2016-04-25

To investigate the impact of increasing sample of records reviewed bi-weekly with the Global Trigger Tool method to identify adverse events in hospitalised patients. Retrospective observational study. A Norwegian 524-bed general hospital trust. 1920 medical records selected from 1 January to 31 December 2010. Rate, type and severity of adverse events identified in two different samples sizes of records selected as 10 and 70 records, bi-weekly. In the large sample, 1.45 (95% CI 1.07 to 1.97) times more adverse events per 1000 patient days (39.3 adverse events/1000 patient days) were identified than in the small sample (27.2 adverse events/1000 patient days). Hospital-acquired infections were the most common category of adverse events in both the samples, and the distributions of the other categories of adverse events did not differ significantly between the samples. The distribution of severity level of adverse events did not differ between the samples. The findings suggest that while the distribution of categories and severity are not dependent on the sample size, the rate of adverse events is. Further studies are needed to conclude if the optimal sample size may need to be adjusted based on the hospital size in order to detect a more accurate rate of adverse events. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Effect size calculation in meta-analyses of psychotherapy outcome research.

PubMed

Hoyt, William T; Del Re, A C

2018-05-01

Meta-analysis of psychotherapy intervention research normally examines differences between treatment groups and some form of comparison group (e.g., wait list control; alternative treatment group). The effect of treatment is normally quantified as a standardized mean difference (SMD). We describe procedures for computing unbiased estimates of the population SMD from sample data (e.g., group Ms and SDs), and provide guidance about a number of complications that may arise related to effect size computation. These complications include (a) incomplete data in research reports; (b) use of baseline data in computing SMDs and estimating the population standard deviation (σ); (c) combining effect size data from studies using different research designs; and (d) appropriate techniques for analysis of data from studies providing multiple estimates of the effect of interest (i.e., dependent effect sizes). Clinical or Methodological Significance of this article: Meta-analysis is a set of techniques for producing valid summaries of existing research. The initial computational step for meta-analyses of research on intervention outcomes involves computing an effect size quantifying the change attributable to the intervention. We discuss common issues in the computation of effect sizes and provide recommended procedures to address them.

Repopulation of calibrations with samples from the target site: effect of the size of the calibration.

NASA Astrophysics Data System (ADS)

Guerrero, C.; Zornoza, R.; Gómez, I.; Mataix-Solera, J.; Navarro-Pedreño, J.; Mataix-Beneyto, J.; García-Orenes, F.

2009-04-01

squares regression, and leave-one-out cross validation as methods of calibration. Two methods were used to select the different quantities (size of models) of samples: (1) Based on Characteristics of Spectra (BCS), and (2) Based on NKj Values of Samples (BVS). Both methods tried to select representative samples. Each of the calibrations (containing the 5, 10, 25, 50, 75 or 100% of the total samples of the library) was repopulated with samples from the target site and then recalibrated (by leave-one-out cross validation). This procedure was sequential. In each step, 2 samples from the target site were added to the models, and then recalibrated. This process was repeated successively 10 times, being 20 the total number of samples added. A local model was also created with the 20 samples used for repopulation. The repopulated, non-repopulated and local calibrations were used to predict the NKj content in those samples from the target site not included in repopulations. For the measurement of the accuracy of the predictions, the r2, RMSEP and slopes were calculated comparing predicted with analysed NKj values. This scheme was repeated for each of the four target sites studied. In general, scarce differences can be found between results obtained with BCS and BVS models. We observed that the repopulation of models increased the r2 of the predictions in sites 1 and 3. The repopulation caused scarce changes of the r2 of the predictions in sites 2 and 4, maybe due to the high initial values (using non-repopulated models r2 >0.90). As consequence of repopulation, the RMSEP decreased in all the sites except in site 2, where a very low RMESP was obtained before the repopulation (0.4 g×kg-1). The slopes trended to approximate to 1, but this value was reached only in site 4 and after the repopulation with 20 samples. In sites 3 and 4, accurate predictions were obtained using the local models. Predictions obtained with models using similar size of samples (similar %) were averaged with

Sample size considerations for studies of intervention efficacy in the occupational setting.

PubMed

Lazovich, Deann; Murray, David M; Brosseau, Lisa M; Parker, David L; Milton, F Thomas; Dugan, Siobhan K

2002-03-01

Due to a shared environment and similarities among workers within a worksite, the strongest analytical design to evaluate the efficacy of an intervention to reduce occupational health or safety hazards is to randomly assign worksites, not workers, to the intervention and comparison conditions. Statistical methods are well described for estimating the sample size when the unit of assignment is a group but these methods have not been applied in the evaluation of occupational health and safety interventions. We review and apply the statistical methods for group-randomized trials in planning a study to evaluate the effectiveness of technical/behavioral interventions to reduce wood dust levels among small woodworking businesses. We conducted a pilot study in five small woodworking businesses to estimate variance components between and within worksites and between and within workers. In each worksite, 8 h time-weighted dust concentrations were obtained for each production employee on between two and five occasions. With these data, we estimated the parameters necessary to calculate the percent change in dust concentrations that we could detect (alpha = 0.05, power = 80%) for a range of worksites per condition, workers per worksite and repeat measurements per worker. The mean wood dust concentration across woodworking businesses was 4.53 mg/m3. The measure of similarity among workers within a woodworking business was large (intraclass correlation = 0.5086). Repeated measurements within a worker were weakly correlated (r = 0.1927) while repeated measurements within a worksite were strongly correlated (r = 0.8925). The dominant factor in the sample size calculation was the number of worksites per condition, with the number of workers per worksite playing a lesser role. We also observed that increasing the number of repeat measurements per person had little benefit given the low within-worker correlation in our data. We found that 30 worksites per condition and 10 workers

Size selective isocyanate aerosols personal air sampling using porous plastic foams

NASA Astrophysics Data System (ADS)

Khanh Huynh, Cong; Duc, Trinh Vu

2009-02-01

As part of a European project (SMT4-CT96-2137), various European institutions specialized in occupational hygiene (BGIA, HSL, IOM, INRS, IST, Ambiente e Lavoro) have established a program of scientific collaboration to develop one or more prototypes of European personal samplers for the collection of simultaneous three dust fractions: inhalable, thoracic and respirable. These samplers based on existing sampling heads (IOM, GSP and cassettes) use Polyurethane Plastic Foam (PUF) according to their porosity to support sampling and separator size of the particles. In this study, the authors present an original application of size selective personal air sampling using chemical impregnated PUF to perform isocyanate aerosols capturing and derivatizing in industrial spray-painting shops.

Calculating the dim light melatonin onset: the impact of threshold and sampling rate.

PubMed

Molina, Thomas A; Burgess, Helen J

2011-10-01

The dim light melatonin onset (DLMO) is the most reliable circadian phase marker in humans, but the cost of assaying samples is relatively high. Therefore, the authors examined differences between DLMOs calculated from hourly versus half-hourly sampling and differences between DLMOs calculated with two recommended thresholds (a fixed threshold of 3 pg/mL and a variable "3k" threshold equal to the mean plus two standard deviations of the first three low daytime points). The authors calculated these DLMOs from salivary dim light melatonin profiles collected from 122 individuals (64 women) at baseline. DLMOs derived from hourly sampling occurred on average only 6-8 min earlier than the DLMOs derived from half-hourly saliva sampling, and they were highly correlated with each other (r ≥ 0.89, p < .001). However, in up to 19% of cases the DLMO derived from hourly sampling was >30 min from the DLMO derived from half-hourly sampling. The 3 pg/mL threshold produced significantly less variable DLMOs than the 3k threshold. However, the 3k threshold was significantly lower than the 3 pg/mL threshold (p < .001). The DLMOs calculated with the 3k method were significantly earlier (by 22-24 min) than the DLMOs calculated with the 3 pg/mL threshold, regardless of sampling rate. These results suggest that in large research studies and clinical settings, the more affordable and practical option of hourly sampling is adequate for a reasonable estimate of circadian phase. Although the 3 pg/mL fixed threshold is less variable than the 3k threshold, it produces estimates of the DLMO that are further from the initial rise of melatonin.

7 CFR 51.308 - Methods of sampling and calculation of percentages.

Code of Federal Regulations, 2012 CFR

2012-01-01

..., CERTIFICATION, AND STANDARDS) United States Standards for Grades of Apples Methods of Sampling and Calculation... where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be calculated on the basis of count. (b) In all other...

7 CFR 51.308 - Methods of sampling and calculation of percentages.

Code of Federal Regulations, 2011 CFR

2011-01-01

..., CERTIFICATION, AND STANDARDS) United States Standards for Grades of Apples Methods of Sampling and Calculation... where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be calculated on the basis of count. (b) In all other...

7 CFR 51.308 - Methods of sampling and calculation of percentages.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., CERTIFICATION, AND STANDARDS) United States Standards for Grades of Apples Methods of Sampling and Calculation... where the minimum diameter of the smallest apple does not vary more than 1/2 inch from the minimum diameter of the largest apple, percentages shall be calculated on the basis of count. (b) In all other...

Additive scales in degenerative disease--calculation of effect sizes and clinical judgment.

PubMed

Riepe, Matthias W; Wilkinson, David; Förstl, Hans; Brieden, Andreas

2011-12-16

The therapeutic efficacy of an intervention is often assessed in clinical trials by scales measuring multiple diverse activities that are added to produce a cumulative global score. Medical communities and health care systems subsequently use these data to calculate pooled effect sizes to compare treatments. This is done because major doubt has been cast over the clinical relevance of statistically significant findings relying on p values with the potential to report chance findings. Hence in an aim to overcome this pooling the results of clinical studies into a meta-analyses with a statistical calculus has been assumed to be a more definitive way of deciding of efficacy. We simulate the therapeutic effects as measured with additive scales in patient cohorts with different disease severity and assess the limitations of an effect size calculation of additive scales which are proven mathematically. We demonstrate that the major problem, which cannot be overcome by current numerical methods, is the complex nature and neurobiological foundation of clinical psychiatric endpoints in particular and additive scales in general. This is particularly relevant for endpoints used in dementia research. 'Cognition' is composed of functions such as memory, attention, orientation and many more. These individual functions decline in varied and non-linear ways. Here we demonstrate that with progressive diseases cumulative values from multidimensional scales are subject to distortion by the limitations of the additive scale. The non-linearity of the decline of function impedes the calculation of effect sizes based on cumulative values from these multidimensional scales. Statistical analysis needs to be guided by boundaries of the biological condition. Alternatively, we suggest a different approach avoiding the error imposed by over-analysis of cumulative global scores from additive scales.

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,…

Estimation of sample size and testing power (Part 3).

PubMed

Hu, Liang-ping; Bao, Xiao-lei; Guan, Xue; Zhou, Shi-guo

2011-12-01

This article introduces the definition and sample size estimation of three special tests (namely, non-inferiority test, equivalence test and superiority test) for qualitative data with the design of one factor with two levels having a binary response variable. Non-inferiority test refers to the research design of which the objective is to verify that the efficacy of the experimental drug is not clinically inferior to that of the positive control drug. Equivalence test refers to the research design of which the objective is to verify that the experimental drug and the control drug have clinically equivalent efficacy. Superiority test refers to the research design of which the objective is to verify that the efficacy of the experimental drug is clinically superior to that of the control drug. By specific examples, this article introduces formulas of sample size estimation for the three special tests, and their SAS realization in detail.

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review

PubMed Central

Miao, Yinglong; McCammon, J. Andrew

2016-01-01

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations. PMID:27453631

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review.

PubMed

Miao, Yinglong; McCammon, J Andrew

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.

A Model Based Approach to Sample Size Estimation in Recent Onset Type 1 Diabetes

PubMed Central

Bundy, Brian; Krischer, Jeffrey P.

2016-01-01

The area under the curve C-peptide following a 2-hour mixed meal tolerance test from 481 individuals enrolled on 5 prior TrialNet studies of recent onset type 1 diabetes from baseline to 12 months after enrollment were modelled to produce estimates of its rate of loss and variance. Age at diagnosis and baseline C-peptide were found to be significant predictors and adjusting for these in an ANCOVA resulted in estimates with lower variance. Using these results as planning parameters for new studies results in a nearly 50% reduction in the target sample size. The modelling also produces an expected C-peptide that can be used in Observed vs. Expected calculations to estimate the presumption of benefit in ongoing trials. PMID:26991448

Critical analysis of consecutive unilateral cleft lip repairs: determining ideal sample size.

PubMed

Power, Stephanie M; Matic, Damir B

2013-03-01

Objective : Cleft surgeons often show 10 consecutive lip repairs to reduce presentation bias, however the validity remains unknown. The purpose of this study is to determine the number of consecutive cases that represent average outcomes. Secondary objectives are to determine if outcomes correlate with cleft severity and to calculate interrater reliability. Design : Consecutive preoperative and 2-year postoperative photographs of the unilateral cleft lip-nose complex were randomized and evaluated by cleft surgeons. Parametric analysis was performed according to chronologic, consecutive order. The mean standard deviation over all raters enabled calculation of expected 95% confidence intervals around a mean tested for various sample sizes. Setting : Meeting of the American Cleft Palate-Craniofacial Association in 2009. Patients, Participants : Ten senior cleft surgeons evaluated 39 consecutive lip repairs. Main Outcome Measures : Preoperative severity and postoperative outcomes were evaluated using descriptive and quantitative scales. Results : Intraclass correlation coefficients for cleft severity and postoperative evaluations were 0.65 and 0.21, respectively. Outcomes did not correlate with cleft severity (P  =  .28). Calculations for 10 consecutive cases demonstrated wide 95% confidence intervals, spanning two points on both postoperative grading scales. Ninety-five percent confidence intervals narrowed within one qualitative grade (±0.30) and one point (±0.50) on the 10-point scale for 27 consecutive cases. Conclusions : Larger numbers of consecutive cases (n > 27) are increasingly representative of average results, but less practical in presentation format. Ten consecutive cases lack statistical support. Cleft surgeons showed low interrater reliability for postoperative assessments, which may reflect personal bias when evaluating another surgeon's results.

Generating Random Samples of a Given Size Using Social Security Numbers.

ERIC Educational Resources Information Center

Erickson, Richard C.; Brauchle, Paul E.

1984-01-01

The purposes of this article are (1) to present a method by which social security numbers may be used to draw cluster samples of a predetermined size and (2) to describe procedures used to validate this method of drawing random samples. (JOW)

Global Sensitivity Analysis with Small Sample Sizes: Ordinary Least Squares Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davis, Michael J.; Liu, Wei; Sivaramakrishnan, Raghu

2016-12-21

A new version of global sensitivity analysis is developed in this paper. This new version coupled with tools from statistics, machine learning, and optimization can devise small sample sizes that allow for the accurate ordering of sensitivity coefficients for the first 10-30 most sensitive chemical reactions in complex chemical-kinetic mechanisms, and is particularly useful for studying the chemistry in realistic devices. A key part of the paper is calibration of these small samples. Because these small sample sizes are developed for use in realistic combustion devices, the calibration is done over the ranges of conditions in such devices, with amore » test case being the operating conditions of a compression ignition engine studied earlier. Compression ignition engines operate under low-temperature combustion conditions with quite complicated chemistry making this calibration difficult, leading to the possibility of false positives and false negatives in the ordering of the reactions. So an important aspect of the paper is showing how to handle the trade-off between false positives and false negatives using ideas from the multiobjective optimization literature. The combination of the new global sensitivity method and the calibration are sample sizes a factor of approximately 10 times smaller than were available with our previous algorithm.« less

Microdosimetry calculations for monoenergetic electrons using Geant4-DNA combined with a weighted track sampling algorithm.

PubMed

Famulari, Gabriel; Pater, Piotr; Enger, Shirin A

2017-07-07

The aim of this study was to calculate microdosimetric distributions for low energy electrons simulated using the Monte Carlo track structure code Geant4-DNA. Tracks for monoenergetic electrons with kinetic energies ranging from 100 eV to 1 MeV were simulated in an infinite spherical water phantom using the Geant4-DNA extension included in Geant4 toolkit version 10.2 (patch 02). The microdosimetric distributions were obtained through random sampling of transfer points and overlaying scoring volumes within the associated volume of the tracks. Relative frequency distributions of energy deposition f(>E)/f(>0) and dose mean lineal energy ([Formula: see text]) values were calculated in nanometer-sized spherical and cylindrical targets. The effects of scoring volume and scoring techniques were examined. The results were compared with published data generated using MOCA8B and KURBUC. Geant4-DNA produces a lower frequency of higher energy deposits than MOCA8B. The [Formula: see text] values calculated with Geant4-DNA are smaller than those calculated using MOCA8B and KURBUC. The differences are mainly due to the lower ionization and excitation cross sections of Geant4-DNA for low energy electrons. To a lesser extent, discrepancies can also be attributed to the implementation in this study of a new and fast scoring technique that differs from that used in previous studies. For the same mean chord length ([Formula: see text]), the [Formula: see text] calculated in cylindrical volumes are larger than those calculated in spherical volumes. The discrepancies due to cross sections and scoring geometries increase with decreasing scoring site dimensions. A new set of [Formula: see text] values has been presented for monoenergetic electrons using a fast track sampling algorithm and the most recent physics models implemented in Geant4-DNA. This dataset can be combined with primary electron spectra to predict the radiation quality of photon and electron beams.

Finite-size correction scheme for supercell calculations in Dirac-point two-dimensional materials.

PubMed

Rocha, C G; Rocha, A R; Venezuela, P; Garcia, J H; Ferreira, M S

2018-06-19

Modern electronic structure calculations are predominantly implemented within the super cell representation in which unit cells are periodically arranged in space. Even in the case of non-crystalline materials, defect-embedded unit cells are commonly used to describe doped structures. However, this type of computation becomes prohibitively demanding when convergence rates are sufficiently slow and may require calculations with very large unit cells. Here we show that a hitherto unexplored feature displayed by several 2D materials may be used to achieve convergence in formation- and adsorption-energy calculations with relatively small unit-cell sizes. The generality of our method is illustrated with Density Functional Theory calculations for different 2D hosts doped with different impurities, all of which providing accuracy levels that would otherwise require enormously large unit cells. This approach provides an efficient route to calculating the physical properties of 2D systems in general but is particularly suitable for Dirac-point materials doped with impurities that break their sublattice symmetry.

Support vector regression to predict porosity and permeability: Effect of sample size

NASA Astrophysics Data System (ADS)

Al-Anazi, A. F.; Gates, I. D.

2012-02-01

Porosity and permeability are key petrophysical parameters obtained from laboratory core analysis. Cores, obtained from drilled wells, are often few in number for most oil and gas fields. Porosity and permeability correlations based on conventional techniques such as linear regression or neural networks trained with core and geophysical logs suffer poor generalization to wells with only geophysical logs. The generalization problem of correlation models often becomes pronounced when the training sample size is small. This is attributed to the underlying assumption that conventional techniques employing the empirical risk minimization (ERM) inductive principle converge asymptotically to the true risk values as the number of samples increases. In small sample size estimation problems, the available training samples must span the complexity of the parameter space so that the model is able both to match the available training samples reasonably well and to generalize to new data. This is achieved using the structural risk minimization (SRM) inductive principle by matching the capability of the model to the available training data. One method that uses SRM is support vector regression (SVR) network. In this research, the capability of SVR to predict porosity and permeability in a heterogeneous sandstone reservoir under the effect of small sample size is evaluated. Particularly, the impact of Vapnik's ɛ-insensitivity loss function and least-modulus loss function on generalization performance was empirically investigated. The results are compared to the multilayer perception (MLP) neural network, a widely used regression method, which operates under the ERM principle. The mean square error and correlation coefficients were used to measure the quality of predictions. The results demonstrate that SVR yields consistently better predictions of the porosity and permeability with small sample size than the MLP method. Also, the performance of SVR depends on both kernel function

Pairing mechanism in Bi-O superconductors: A finite-size chain calculation

NASA Astrophysics Data System (ADS)

Aligia, A. A.; Nuez Regueiro, M. D.; Gagliano, E. R.

1989-09-01

We have studied the pairing mechanism in BiO3 systems by calculating the binding energy of a pair of holes in finite Bi-O chains, for parameters that simulate three-dimensional behavior. In agreement with previous results using perturbation theory in the hopping t, for covalent Bi-O binding and parameters for which the parent compound has a disproportionate ground state, pairing induced by the presence of biexcitons is obtained for sufficiently large interatomic Coulomb repulsion. The analysis of appropriate correlation functions shows a rapid metallization of the system as t and the number of holes increase. This fact shrinks the region of parameters for which the finite-size calculations can be trusted without further study. The same model for other parameters yields pairing in two other regimes: bipolaronic and magnetic excitonic.

Demonstration of Multi- and Single-Reader Sample Size Program for Diagnostic Studies software.

PubMed

Hillis, Stephen L; Schartz, Kevin M

2015-02-01

The recently released software Multi- and Single-Reader Sample Size Sample Size Program for Diagnostic Studies , written by Kevin Schartz and Stephen Hillis, performs sample size computations for diagnostic reader-performance studies. The program computes the sample size needed to detect a specified difference in a reader performance measure between two modalities, when using the analysis methods initially proposed by Dorfman, Berbaum, and Metz (DBM) and Obuchowski and Rockette (OR), and later unified and improved by Hillis and colleagues. A commonly used reader performance measure is the area under the receiver-operating-characteristic curve. The program can be used with typical common reader-performance measures which can be estimated parametrically or nonparametrically. The program has an easy-to-use step-by-step intuitive interface that walks the user through the entry of the needed information. Features of the software include the following: (1) choice of several study designs; (2) choice of inputs obtained from either OR or DBM analyses; (3) choice of three different inference situations: both readers and cases random, readers fixed and cases random, and readers random and cases fixed; (4) choice of two types of hypotheses: equivalence or noninferiority; (6) choice of two output formats: power for specified case and reader sample sizes, or a listing of case-reader combinations that provide a specified power; (7) choice of single or multi-reader analyses; and (8) functionality in Windows, Mac OS, and Linux.

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

Calculating an optimal box size for ligand docking and virtual screening against experimental and predicted binding pockets.

PubMed

Feinstein, Wei P; Brylinski, Michal

2015-01-01

Computational approaches have emerged as an instrumental methodology in modern research. For example, virtual screening by molecular docking is routinely used in computer-aided drug discovery. One of the critical parameters for ligand docking is the size of a search space used to identify low-energy binding poses of drug candidates. Currently available docking packages often come with a default protocol for calculating the box size, however, many of these procedures have not been systematically evaluated. In this study, we investigate how the docking accuracy of AutoDock Vina is affected by the selection of a search space. We propose a new procedure for calculating the optimal docking box size that maximizes the accuracy of binding pose prediction against a non-redundant and representative dataset of 3,659 protein-ligand complexes selected from the Protein Data Bank. Subsequently, we use the Directory of Useful Decoys, Enhanced to demonstrate that the optimized docking box size also yields an improved ranking in virtual screening. Binding pockets in both datasets are derived from the experimental complex structures and, additionally, predicted by eFindSite. A systematic analysis of ligand binding poses generated by AutoDock Vina shows that the highest accuracy is achieved when the dimensions of the search space are 2.9 times larger than the radius of gyration of a docking compound. Subsequent virtual screening benchmarks demonstrate that this optimized docking box size also improves compound ranking. For instance, using predicted ligand binding sites, the average enrichment factor calculated for the top 1 % (10 %) of the screening library is 8.20 (3.28) for the optimized protocol, compared to 7.67 (3.19) for the default procedure. Depending on the evaluation metric, the optimal docking box size gives better ranking in virtual screening for about two-thirds of target proteins. This fully automated procedure can be used to optimize docking protocols in order to

Are power calculations useful? A multicentre neuroimaging study

PubMed Central

Suckling, John; Henty, Julian; Ecker, Christine; Deoni, Sean C; Lombardo, Michael V; Baron-Cohen, Simon; Jezzard, Peter; Barnes, Anna; Chakrabarti, Bhismadev; Ooi, Cinly; Lai, Meng-Chuan; Williams, Steven C; Murphy, Declan GM; Bullmore, Edward

2014-01-01

There are now many reports of imaging experiments with small cohorts of typical participants that precede large-scale, often multicentre studies of psychiatric and neurological disorders. Data from these calibration experiments are sufficient to make estimates of statistical power and predictions of sample size and minimum observable effect sizes. In this technical note, we suggest how previously reported voxel-based power calculations can support decision making in the design, execution and analysis of cross-sectional multicentre imaging studies. The choice of MRI acquisition sequence, distribution of recruitment across acquisition centres, and changes to the registration method applied during data analysis are considered as examples. The consequences of modification are explored in quantitative terms by assessing the impact on sample size for a fixed effect size and detectable effect size for a fixed sample size. The calibration experiment dataset used for illustration was a precursor to the now complete Medical Research Council Autism Imaging Multicentre Study (MRC-AIMS). Validation of the voxel-based power calculations is made by comparing the predicted values from the calibration experiment with those observed in MRC-AIMS. The effect of non-linear mappings during image registration to a standard stereotactic space on the prediction is explored with reference to the amount of local deformation. In summary, power calculations offer a validated, quantitative means of making informed choices on important factors that influence the outcome of studies that consume significant resources. PMID:24644267

Sample size and allocation of effort in point count sampling of birds in bottomland hardwood forests

USGS Publications Warehouse

Smith, W.P.; Twedt, D.J.; Cooper, R.J.; Wiedenfeld, D.A.; Hamel, P.B.; Ford, R.P.; Ralph, C. John; Sauer, John R.; Droege, Sam

1995-01-01

To examine sample size requirements and optimum allocation of effort in point count sampling of bottomland hardwood forests, we computed minimum sample sizes from variation recorded during 82 point counts (May 7-May 16, 1992) from three localities containing three habitat types across three regions of the Mississippi Alluvial Valley (MAV). Also, we estimated the effect of increasing the number of points or visits by comparing results of 150 four-minute point counts obtained from each of four stands on Delta Experimental Forest (DEF) during May 8-May 21, 1991 and May 30-June 12, 1992. For each stand, we obtained bootstrap estimates of mean cumulative number of species each year from all possible combinations of six points and six visits. ANOVA was used to model cumulative species as a function of number of points visited, number of visits to each point, and interaction of points and visits. There was significant variation in numbers of birds and species between regions and localities (nested within region); neither habitat, nor the interaction between region and habitat, was significant. For a = 0.05 and a = 0.10, minimum sample size estimates (per factor level) varied by orders of magnitude depending upon the observed or specified range of desired detectable difference. For observed regional variation, 20 and 40 point counts were required to accommodate variability in total individuals (MSE = 9.28) and species (MSE = 3.79), respectively, whereas ? 25 percent of the mean could be achieved with five counts per factor level. Sample size sufficient to detect actual differences of Wood Thrush (Hylocichla mustelina) was >200, whereas the Prothonotary Warbler (Protonotaria citrea) required <10 counts. Differences in mean cumulative species were detected among number of points visited and among number of visits to a point. In the lower MAV, mean cumulative species increased with each added point through five points and with each additional visit through four visits

45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations

Code of Federal Regulations, 2010 CFR

2010-10-01

... OF HUMAN DEVELOPMENT SERVICES, DEPARTMENT OF HEALTH AND HUMAN SERVICES THE ADMINISTRATION ON CHILDREN, YOUTH AND FAMILIES, FOSTER CARE MAINTENANCE PAYMENTS, ADOPTION ASSISTANCE, AND CHILD AND FAMILY SERVICES... applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more than...

[A Review on the Use of Effect Size in Nursing Research].

PubMed

Kang, Hyuncheol; Yeon, Kyupil; Han, Sang Tae

2015-10-01

The purpose of this study was to introduce the main concepts of statistical testing and effect size and to provide researchers in nursing science with guidance on how to calculate the effect size for the statistical analysis methods mainly used in nursing. For t-test, analysis of variance, correlation analysis, regression analysis which are used frequently in nursing research, the generally accepted definitions of the effect size were explained. Some formulae for calculating the effect size are described with several examples in nursing research. Furthermore, the authors present the required minimum sample size for each example utilizing G*Power 3 software that is the most widely used program for calculating sample size. It is noted that statistical significance testing and effect size measurement serve different purposes, and the reliance on only one side may be misleading. Some practical guidelines are recommended for combining statistical significance testing and effect size measure in order to make more balanced decisions in quantitative analyses.

Implications of sampling design and sample size for national carbon accounting systems.

PubMed

Köhl, Michael; Lister, Andrew; Scott, Charles T; Baldauf, Thomas; Plugge, Daniel

2011-11-08

Countries willing to adopt a REDD regime need to establish a national Measurement, Reporting and Verification (MRV) system that provides information on forest carbon stocks and carbon stock changes. Due to the extensive areas covered by forests the information is generally obtained by sample based surveys. Most operational sampling approaches utilize a combination of earth-observation data and in-situ field assessments as data sources. We compared the cost-efficiency of four different sampling design alternatives (simple random sampling, regression estimators, stratified sampling, 2-phase sampling with regression estimators) that have been proposed in the scope of REDD. Three of the design alternatives provide for a combination of in-situ and earth-observation data. Under different settings of remote sensing coverage, cost per field plot, cost of remote sensing imagery, correlation between attributes quantified in remote sensing and field data, as well as population variability and the percent standard error over total survey cost was calculated. The cost-efficiency of forest carbon stock assessments is driven by the sampling design chosen. Our results indicate that the cost of remote sensing imagery is decisive for the cost-efficiency of a sampling design. The variability of the sample population impairs cost-efficiency, but does not reverse the pattern of cost-efficiency of the individual design alternatives. Our results clearly indicate that it is important to consider cost-efficiency in the development of forest carbon stock assessments and the selection of remote sensing techniques. The development of MRV-systems for REDD need to be based on a sound optimization process that compares different data sources and sampling designs with respect to their cost-efficiency. This helps to reduce the uncertainties related with the quantification of carbon stocks and to increase the financial benefits from adopting a REDD regime.

Differentiating gold nanorod samples using particle size and shape distributions from transmission electron microscope images

NASA Astrophysics Data System (ADS)

Grulke, Eric A.; Wu, Xiaochun; Ji, Yinglu; Buhr, Egbert; Yamamoto, Kazuhiro; Song, Nam Woong; Stefaniak, Aleksandr B.; Schwegler-Berry, Diane; Burchett, Woodrow W.; Lambert, Joshua; Stromberg, Arnold J.

2018-04-01

Size and shape distributions of gold nanorod samples are critical to their physico-chemical properties, especially their longitudinal surface plasmon resonance. This interlaboratory comparison study developed methods for measuring and evaluating size and shape distributions for gold nanorod samples using transmission electron microscopy (TEM) images. The objective was to determine whether two different samples, which had different performance attributes in their application, were different with respect to their size and/or shape descriptor distributions. Touching particles in the captured images were identified using a ruggedness shape descriptor. Nanorods could be distinguished from nanocubes using an elongational shape descriptor. A non-parametric statistical test showed that cumulative distributions of an elongational shape descriptor, that is, the aspect ratio, were statistically different between the two samples for all laboratories. While the scale parameters of size and shape distributions were similar for both samples, the width parameters of size and shape distributions were statistically different. This protocol fulfills an important need for a standardized approach to measure gold nanorod size and shape distributions for applications in which quantitative measurements and comparisons are important. Furthermore, the validated protocol workflow can be automated, thus providing consistent and rapid measurements of nanorod size and shape distributions for researchers, regulatory agencies, and industry.

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 than...

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 than...

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 than...

Nano-sized graphene flakes: insights from experimental synthesis and first principles calculations.

PubMed

Lin, Pin-Chun; Chen, Yi-Rui; Hsu, Kuei-Ting; Lin, Tzu-Neng; Tung, Kuo-Lun; Shen, Ji-Lin; Liu, Wei-Ren

2017-03-01

In this study, we proposed a cost-effective method for preparing graphene nano-flakes (GNFs) derived from carbon nanotubes (CNTs) via three steps (pressing, homogenization and sonication exfoliation processes). Scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), laser scattering, as well as ultraviolet-visible and photoluminescence (PL) measurements were carried out. The results indicated that the size of as-synthesized GNFs was approximately 40-50 nm. Furthermore, we also used first principles calculations to understand the transformation from CNTs to GNFs from the viewpoints of the edge formation energies of GNFs in different shapes and sizes. The corresponding photoluminescence measurements of GNFs were carried out in this work.

Sample Size Estimation for Alzheimer's Disease Trials from Japanese ADNI Serial Magnetic Resonance Imaging.

PubMed

Fujishima, Motonobu; Kawaguchi, Atsushi; Maikusa, Norihide; Kuwano, Ryozo; Iwatsubo, Takeshi; Matsuda, Hiroshi

2017-01-01

Little is known about the sample sizes required for clinical trials of Alzheimer's disease (AD)-modifying treatments using atrophy measures from serial brain magnetic resonance imaging (MRI) in the Japanese population. The primary objective of the present study was to estimate how large a sample size would be needed for future clinical trials for AD-modifying treatments in Japan using atrophy measures of the brain as a surrogate biomarker. Sample sizes were estimated from the rates of change of the whole brain and hippocampus by the k-means normalized boundary shift integral (KN-BSI) and cognitive measures using the data of 537 Japanese Alzheimer's Neuroimaging Initiative (J-ADNI) participants with a linear mixed-effects model. We also examined the potential use of ApoE status as a trial enrichment strategy. The hippocampal atrophy rate required smaller sample sizes than cognitive measures of AD and mild cognitive impairment (MCI). Inclusion of ApoE status reduced sample sizes for AD and MCI patients in the atrophy measures. These results show the potential use of longitudinal hippocampal atrophy measurement using automated image analysis as a progression biomarker and ApoE status as a trial enrichment strategy in a clinical trial of AD-modifying treatment in Japanese people.

Sampling strategies for radio-tracking coyotes

USGS Publications Warehouse

Smith, G.J.; Cary, J.R.; Rongstad, O.J.

1981-01-01

Ten coyotes radio-tracked for 24 h periods were most active at night and moved little during daylight hours. Home-range size determined from radio-locations of 3 adult coyotes increased with the number of locations until an asymptote was reached at about 35-40 independent day locations or 3 6 nights of hourly radio-locations. Activity of the coyote did not affect the asymptotic nature of the home-range calculations, but home-range sizes determined from more than 3 nights of hourly locations were considerably larger than home-range sizes determined from daylight locations. Coyote home-range sizes were calculated from daylight locations, full-night tracking periods, and half-night tracking periods. Full- and half-lnight sampling strategies involved obtaining hourly radio-locations during 12 and 6 h periods, respectively. The half-night sampling strategy was the best compromise for our needs, as it adequately indexed the home-range size, reduced time and energy spent, and standardized the area calculation without requiring the researcher to become completely nocturnal. Sight tracking also provided information about coyote activity and sociability.

Effect of Reiki therapy on pain and anxiety in adults: an in-depth literature review of randomized trials with effect size calculations.

PubMed

Thrane, Susan; Cohen, Susan M

2014-12-01

The objective of this study was to calculate the effect of Reiki therapy for pain and anxiety in randomized clinical trials. A systematic search of PubMed, ProQuest, Cochrane, PsychInfo, CINAHL, Web of Science, Global Health, and Medline databases was conducted using the search terms pain, anxiety, and Reiki. The Center for Reiki Research also was examined for articles. Studies that used randomization and a control or usual care group, used Reiki therapy in one arm of the study, were published in 2000 or later in peer-reviewed journals in English, and measured pain or anxiety were included. After removing duplicates, 49 articles were examined and 12 articles received full review. Seven studies met the inclusion criteria: four articles studied cancer patients, one examined post-surgical patients, and two analyzed community dwelling older adults. Effect sizes were calculated for all studies using Cohen's d statistic. Effect sizes for within group differences ranged from d = 0.24 for decrease in anxiety in women undergoing breast biopsy to d = 2.08 for decreased pain in community dwelling adults. The between group differences ranged from d = 0.32 for decrease of pain in a Reiki versus rest intervention for cancer patients to d = 4.5 for decrease in pain in community dwelling adults. Although the number of studies is limited, based on the size Cohen's d statistics calculated in this review, there is evidence to suggest that Reiki therapy may be effective for pain and anxiety. Continued research using Reiki therapy with larger sample sizes, consistently randomized groups, and standardized treatment protocols is recommended. Copyright © 2014 American Society for Pain Management Nursing. Published by Elsevier Inc. All rights reserved.

Effect of Reiki Therapy on Pain and Anxiety in Adults: An In-Depth Literature Review of Randomized Trials with Effect Size Calculations

PubMed Central

Thrane, Susan; Cohen, Susan M.

2013-01-01

Objective To calculate the effect of Reiki therapy for pain and anxiety in randomized clinical trials. Data Sources A systematic search of PubMed, ProQuest, Cochrane, PsychInfo, CINAHL, Web of Science, Global Health, and Medline databases was conducted using the search terms pain, anxiety, and Reiki. The Center for Reiki Research was also examined for articles. Study Selection Studies that used randomization and a control or usual care group, used Reiki therapy in one arm of the study, published in 2000 or later in peer-reviewed journals in English, and measured pain or anxiety were included. Results After removing duplicates, 49 articles were examined and 12 articles received full review. Seven studies met the inclusion criteria: four articles studied cancer patients; one examined post-surgical patients; and two analyzed community dwelling older adults. Effect sizes were calculated for all studies using Cohen’s d statistic. Effect sizes for within group differences ranged from d=0.24 for decrease in anxiety in women undergoing breast biopsy to d=2.08 for decreased pain in community dwelling adults. The between group differences ranged from d=0.32 for decrease of pain in a Reiki versus rest intervention for cancer patients to d=4.5 for decrease in pain in community dwelling adults. Conclusions While the number of studies is limited, based on the size Cohen’s d statistics calculated in this review, there is evidence to suggest that Reiki therapy may be effective for pain and anxiety. Continued research using Reiki therapy with larger sample sizes, consistently randomized groups, and standardized treatment protocols is recommended. PMID:24582620

Influence of sampling rate on the calculated fidelity of an aircraft simulation

NASA Technical Reports Server (NTRS)

Howard, J. C.

1983-01-01

One of the factors that influences the fidelity of an aircraft digital simulation is the sampling rate. As the sampling rate is increased, the calculated response of the discrete representation tends to coincide with the response of the corresponding continuous system. Because of computer limitations, however, the sampling rate cannot be increased indefinitely. Moreover, real-time simulation requirements demand that a finite sampling rate be adopted. In view of these restrictions, a study was undertaken to determine the influence of sampling rate on the response characteristics of a simulated aircraft describing short-period oscillations. Changes in the calculated response characteristics of the simulated aircraft degrade the fidelity of the simulation. In the present context, fidelity degradation is defined as the percentage change in those characteristics that have the greatest influence on pilot opinion: short period frequency omega, short period damping ratio zeta, and the product omega zeta. To determine the influence of the sampling period on these characteristics, the equations describing the response of a DC-8 aircraft to elevator control inputs were used. The results indicate that if the sampling period is too large, the fidelity of the simulation can be degraded.

Electrical and magnetic properties of nano-sized magnesium ferrite

NASA Astrophysics Data System (ADS)

T, Smitha; X, Sheena; J, Binu P.; Mohammed, E. M.

2015-02-01

Nano-sized magnesium ferrite was synthesized using sol-gel techniques. Structural characterization was done using X-ray diffractometer and Fourier Transform Infrared Spectrometer. Vibration Sample Magnetometer was used to record the magnetic measurements. XRD analysis reveals the prepared sample is single phasic without any impurity. Particle size calculation shows the average crystallite size of the sample is 19nm. FTIR analysis confirmed spinel structure of the prepared samples. Magnetic measurement study shows that the sample is ferromagnetic with high degree of isotropy. Hysterisis loop was traced at temperatures 100K and 300K. DC electrical resistivity measurements show semiconducting nature of the sample.

Sample size requirements for indirect association studies of gene-environment interactions (G x E).

PubMed

Hein, Rebecca; Beckmann, Lars; Chang-Claude, Jenny

2008-04-01

Association studies accounting for gene-environment interactions (G x E) may be useful for detecting genetic effects. Although current technology enables very dense marker spacing in genetic association studies, the true disease variants may not be genotyped. Thus, causal genes are searched for by indirect association using genetic markers in linkage disequilibrium (LD) with the true disease variants. Sample sizes needed to detect G x E effects in indirect case-control association studies depend on the true genetic main effects, disease allele frequencies, whether marker and disease allele frequencies match, LD between loci, main effects and prevalence of environmental exposures, and the magnitude of interactions. We explored variables influencing sample sizes needed to detect G x E, compared these sample sizes with those required to detect genetic marginal effects, and provide an algorithm for power and sample size estimations. Required sample sizes may be heavily inflated if LD between marker and disease loci decreases. More than 10,000 case-control pairs may be required to detect G x E. However, given weak true genetic main effects, moderate prevalence of environmental exposures, as well as strong interactions, G x E effects may be detected with smaller sample sizes than those needed for the detection of genetic marginal effects. Moreover, in this scenario, rare disease variants may only be detectable when G x E is included in the analyses. Thus, the analysis of G x E appears to be an attractive option for the detection of weak genetic main effects of rare variants that may not be detectable in the analysis of genetic marginal effects only.

Effect of finite sample size on feature selection and classification: a simulation study.

PubMed

Way, Ted W; Sahiner, Berkman; Hadjiiski, Lubomir M; Chan, Heang-Ping

2010-02-01

The small number of samples available for training and testing is often the limiting factor in finding the most effective features and designing an optimal computer-aided diagnosis (CAD) system. Training on a limited set of samples introduces bias and variance in the performance of a CAD system relative to that trained with an infinite sample size. In this work, the authors conducted a simulation study to evaluate the performances of various combinations of classifiers and feature selection techniques and their dependence on the class distribution, dimensionality, and the training sample size. The understanding of these relationships will facilitate development of effective CAD systems under the constraint of limited available samples. Three feature selection techniques, the stepwise feature selection (SFS), sequential floating forward search (SFFS), and principal component analysis (PCA), and two commonly used classifiers, Fisher's linear discriminant analysis (LDA) and support vector machine (SVM), were investigated. Samples were drawn from multidimensional feature spaces of multivariate Gaussian distributions with equal or unequal covariance matrices and unequal means, and with equal covariance matrices and unequal means estimated from a clinical data set. Classifier performance was quantified by the area under the receiver operating characteristic curve Az. The mean Az values obtained by resubstitution and hold-out methods were evaluated for training sample sizes ranging from 15 to 100 per class. The number of simulated features available for selection was chosen to be 50, 100, and 200. It was found that the relative performance of the different combinations of classifier and feature selection method depends on the feature space distributions, the dimensionality, and the available training sample sizes. The LDA and SVM with radial kernel performed similarly for most of the conditions evaluated in this study, although the SVM classifier showed a slightly higher

Enzymatic Kinetic Isotope Effects from First-Principles Path Sampling Calculations.

PubMed

Varga, Matthew J; Schwartz, Steven D

2016-04-12

In this study, we develop and test a method to determine the rate of particle transfer and kinetic isotope effects in enzymatic reactions, specifically yeast alcohol dehydrogenase (YADH), from first-principles. Transition path sampling (TPS) and normal mode centroid dynamics (CMD) are used to simulate these enzymatic reactions without knowledge of their reaction coordinates and with the inclusion of quantum effects, such as zero-point energy and tunneling, on the transferring particle. Though previous studies have used TPS to calculate reaction rate constants in various model and real systems, it has not been applied to a system as large as YADH. The calculated primary H/D kinetic isotope effect agrees with previously reported experimental results, within experimental error. The kinetic isotope effects calculated with this method correspond to the kinetic isotope effect of the transfer event itself. The results reported here show that the kinetic isotope effects calculated from first-principles, purely for barrier passage, can be used to predict experimental kinetic isotope effects in enzymatic systems.

Enhanced Sampling in Free Energy Calculations: Combining SGLD with the Bennett's Acceptance Ratio and Enveloping Distribution Sampling Methods.

PubMed

König, Gerhard; Miller, Benjamin T; Boresch, Stefan; Wu, Xiongwu; Brooks, Bernard R

2012-10-09

One of the key requirements for the accurate calculation of free energy differences is proper sampling of conformational space. Especially in biological applications, molecular dynamics simulations are often confronted with rugged energy surfaces and high energy barriers, leading to insufficient sampling and, in turn, poor convergence of the free energy results. In this work, we address this problem by employing enhanced sampling methods. We explore the possibility of using self-guided Langevin dynamics (SGLD) to speed up the exploration process in free energy simulations. To obtain improved free energy differences from such simulations, it is necessary to account for the effects of the bias due to the guiding forces. We demonstrate how this can be accomplished for the Bennett's acceptance ratio (BAR) and the enveloping distribution sampling (EDS) methods. While BAR is considered among the most efficient methods available for free energy calculations, the EDS method developed by Christ and van Gunsteren is a promising development that reduces the computational costs of free energy calculations by simulating a single reference state. To evaluate the accuracy of both approaches in connection with enhanced sampling, EDS was implemented in CHARMM. For testing, we employ benchmark systems with analytical reference results and the mutation of alanine to serine. We find that SGLD with reweighting can provide accurate results for BAR and EDS where conventional molecular dynamics simulations fail. In addition, we compare the performance of EDS with other free energy methods. We briefly discuss the implications of our results and provide practical guidelines for conducting free energy simulations with SGLD.

Sample Size and Item Parameter Estimation Precision When Utilizing the One-Parameter "Rasch" Model

ERIC Educational Resources Information Center

Custer, Michael

2015-01-01

This study examines the relationship between sample size and item parameter estimation precision when utilizing the one-parameter model. Item parameter estimates are examined relative to "true" values by evaluating the decline in root mean squared deviation (RMSD) and the number of outliers as sample size increases. This occurs across…

Three-year-olds obey the sample size principle of induction: the influence of evidence presentation and sample size disparity on young children's generalizations.

PubMed

Lawson, Chris A

2014-07-01

Three experiments with 81 3-year-olds (M=3.62years) examined the conditions that enable young children to use the sample size principle (SSP) of induction-the inductive rule that facilitates generalizations from large rather than small samples of evidence. In Experiment 1, children exhibited the SSP when exemplars were presented sequentially but not when exemplars were presented simultaneously. Results from Experiment 3 suggest that the advantage of sequential presentation is not due to the additional time to process the available input from the two samples but instead may be linked to better memory for specific individuals in the large sample. In addition, findings from Experiments 1 and 2 suggest that adherence to the SSP is mediated by the disparity between presented samples. Overall, these results reveal that the SSP appears early in development and is guided by basic cognitive processes triggered during the acquisition of input. Copyright © 2013 Elsevier Inc. All rights reserved.

Sample Size Methods for Estimating HIV Incidence from Cross-Sectional Surveys

PubMed Central

Brookmeyer, Ron

2015-01-01

Summary Understanding HIV incidence, the rate at which new infections occur in populations, is critical for tracking and surveillance of the epidemic. In this paper we derive methods for determining sample sizes for cross-sectional surveys to estimate incidence with sufficient precision. We further show how to specify sample sizes for two successive cross-sectional surveys to detect changes in incidence with adequate power. In these surveys biomarkers such as CD4 cell count, viral load, and recently developed serological assays are used to determine which individuals are in an early disease stage of infection. The total number of individuals in this stage, divided by the number of people who are uninfected, is used to approximate the incidence rate. Our methods account for uncertainty in the durations of time spent in the biomarker defined early disease stage. We find that failure to account for this uncertainty when designing surveys can lead to imprecise estimates of incidence and underpowered studies. We evaluated our sample size methods in simulations and found that they performed well in a variety of underlying epidemics. Code for implementing our methods in R is available with this paper at the Biometrics website on Wiley Online Library. PMID:26302040

Sample size methods for estimating HIV incidence from cross-sectional surveys.

PubMed

Konikoff, Jacob; Brookmeyer, Ron

2015-12-01

Understanding HIV incidence, the rate at which new infections occur in populations, is critical for tracking and surveillance of the epidemic. In this article, we derive methods for determining sample sizes for cross-sectional surveys to estimate incidence with sufficient precision. We further show how to specify sample sizes for two successive cross-sectional surveys to detect changes in incidence with adequate power. In these surveys biomarkers such as CD4 cell count, viral load, and recently developed serological assays are used to determine which individuals are in an early disease stage of infection. The total number of individuals in this stage, divided by the number of people who are uninfected, is used to approximate the incidence rate. Our methods account for uncertainty in the durations of time spent in the biomarker defined early disease stage. We find that failure to account for this uncertainty when designing surveys can lead to imprecise estimates of incidence and underpowered studies. We evaluated our sample size methods in simulations and found that they performed well in a variety of underlying epidemics. Code for implementing our methods in R is available with this article at the Biometrics website on Wiley Online Library. © 2015, The International Biometric Society.

Parameter Estimation with Small Sample Size: A Higher-Order IRT Model Approach

ERIC Educational Resources Information Center

de la Torre, Jimmy; Hong, Yuan

2010-01-01

Sample size ranks as one of the most important factors that affect the item calibration task. However, due to practical concerns (e.g., item exposure) items are typically calibrated with much smaller samples than what is desired. To address the need for a more flexible framework that can be used in small sample item calibration, this article…

A model-based approach to sample size estimation in recent onset type 1 diabetes.

PubMed

Bundy, Brian N; Krischer, Jeffrey P

2016-11-01

The area under the curve C-peptide following a 2-h mixed meal tolerance test from 498 individuals enrolled on five prior TrialNet studies of recent onset type 1 diabetes from baseline to 12 months after enrolment were modelled to produce estimates of its rate of loss and variance. Age at diagnosis and baseline C-peptide were found to be significant predictors, and adjusting for these in an ANCOVA resulted in estimates with lower variance. Using these results as planning parameters for new studies results in a nearly 50% reduction in the target sample size. The modelling also produces an expected C-peptide that can be used in observed versus expected calculations to estimate the presumption of benefit in ongoing trials. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

An Analytic Solution to the Computation of Power and Sample Size for Genetic Association Studies under a Pleiotropic Mode of Inheritance.

PubMed

Gordon, Derek; Londono, Douglas; Patel, Payal; Kim, Wonkuk; Finch, Stephen J; Heiman, Gary A

2016-01-01

Our motivation here is to calculate the power of 3 statistical tests used when there are genetic traits that operate under a pleiotropic mode of inheritance and when qualitative phenotypes are defined by use of thresholds for the multiple quantitative phenotypes. Specifically, we formulate a multivariate function that provides the probability that an individual has a vector of specific quantitative trait values conditional on having a risk locus genotype, and we apply thresholds to define qualitative phenotypes (affected, unaffected) and compute penetrances and conditional genotype frequencies based on the multivariate function. We extend the analytic power and minimum-sample-size-necessary (MSSN) formulas for 2 categorical data-based tests (genotype, linear trend test [LTT]) of genetic association to the pleiotropic model. We further compare the MSSN of the genotype test and the LTT with that of a multivariate ANOVA (Pillai). We approximate the MSSN for statistics by linear models using a factorial design and ANOVA. With ANOVA decomposition, we determine which factors most significantly change the power/MSSN for all statistics. Finally, we determine which test statistics have the smallest MSSN. In this work, MSSN calculations are for 2 traits (bivariate distributions) only (for illustrative purposes). We note that the calculations may be extended to address any number of traits. Our key findings are that the genotype test usually has lower MSSN requirements than the LTT. More inclusive thresholds (top/bottom 25% vs. top/bottom 10%) have higher sample size requirements. The Pillai test has a much larger MSSN than both the genotype test and the LTT, as a result of sample selection. With these formulas, researchers can specify how many subjects they must collect to localize genes for pleiotropic phenotypes. © 2017 S. Karger AG, Basel.

Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions.

PubMed

Tao, Guohua; Miller, William H

2011-07-14

An efficient time-dependent importance sampling method is developed for the Monte Carlo calculation of time correlation functions via the initial value representation (IVR) of semiclassical (SC) theory. A prefactor-free time-dependent sampling function weights the importance of a trajectory based on the magnitude of its contribution to the time correlation function, and global trial moves are used to facilitate the efficient sampling the phase space of initial conditions. The method can be generally applied to sampling rare events efficiently while avoiding being trapped in a local region of the phase space. Results presented in the paper for two system-bath models demonstrate the efficiency of this new importance sampling method for full SC-IVR calculations.

Mesh-size effects on drift sample composition as determined with a triple net sampler

USGS Publications Warehouse

Slack, K.V.; Tilley, L.J.; Kennelly, S.S.

1991-01-01

Nested nets of three different mesh apertures were used to study mesh-size effects on drift collected in a small mountain stream. The innermost, middle, and outermost nets had, respectively, 425 ??m, 209 ??m and 106 ??m openings, a design that reduced clogging while partitioning collections into three size groups. The open area of mesh in each net, from largest to smallest mesh opening, was 3.7, 5.7 and 8.0 times the area of the net mouth. Volumes of filtered water were determined with a flowmeter. The results are expressed as (1) drift retained by each net, (2) drift that would have been collected by a single net of given mesh size, and (3) the percentage of total drift (the sum of the catches from all three nets) that passed through the 425 ??m and 209 ??m nets. During a two day period in August 1986, Chironomidae larvae were dominant numerically in all 209 ??m and 106 ??m samples and midday 425 ??m samples. Large drifters (Ephemerellidae) occurred only in 425 ??m or 209 ??m nets, but the general pattern was an increase in abundance and number of taxa with decreasing mesh size. Relatively more individuals occurred in the larger mesh nets at night than during the day. The two larger mesh sizes retained 70% of the total sediment/detritus in the drift collections, and this decreased the rate of clogging of the 106 ??m net. If an objective of a sampling program is to compare drift density or drift rate between areas or sampling dates, the same mesh size should be used for all sample collection and processing. The mesh aperture used for drift collection should retain all species and life stages of significance in a study. The nested net design enables an investigator to test the adequacy of drift samples. ?? 1991 Kluwer Academic Publishers.

Thermal conductivity measurements of particulate materials: 3. Natural samples and mixtures of particle sizes

NASA Astrophysics Data System (ADS)

Presley, Marsha A.; Craddock, Robert A.

2006-09-01

A line-heat source apparatus was used to measure thermal conductivities of natural fluvial and eolian particulate sediments under low pressures of a carbon dioxide atmosphere. These measurements were compared to a previous compilation of the dependence of thermal conductivity on particle size to determine a thermal conductivity-derived particle size for each sample. Actual particle-size distributions were determined via physical separation through brass sieves. Comparison of the two analyses indicates that the thermal conductivity reflects the larger particles within the samples. In each sample at least 85-95% of the particles by weight are smaller than or equal to the thermal conductivity-derived particle size. At atmospheric pressures less than about 2-3 torr, samples that contain a large amount of small particles (<=125 μm or 4 Φ) exhibit lower thermal conductivities relative to those for the larger particles within the sample. Nonetheless, 90% of the sample by weight still consists of particles that are smaller than or equal to this lower thermal conductivity-derived particle size. These results allow further refinement in the interpretation of geomorphologic processes acting on the Martian surface. High-energy fluvial environments should produce poorer-sorted and coarser-grained deposits than lower energy eolian environments. Hence these results will provide additional information that may help identify coarser-grained fluvial deposits and may help differentiate whether channel dunes are original fluvial sediments that are at most reworked by wind or whether they represent a later overprint of sediment with a separate origin.

Reduced Sampling Size with Nanopipette for Tapping-Mode Scanning Probe Electrospray Ionization Mass Spectrometry Imaging

PubMed Central

Kohigashi, Tsuyoshi; Otsuka, Yoichi; Shimazu, Ryo; Matsumoto, Takuya; Iwata, Futoshi; Kawasaki, Hideya; Arakawa, Ryuichi

2016-01-01

Mass spectrometry imaging (MSI) with ambient sampling and ionization can rapidly and easily capture the distribution of chemical components in a solid sample. Because the spatial resolution of MSI is limited by the size of the sampling area, reducing sampling size is an important goal for high resolution MSI. Here, we report the first use of a nanopipette for sampling and ionization by tapping-mode scanning probe electrospray ionization (t-SPESI). The spot size of the sampling area of a dye molecular film on a glass substrate was decreased to 6 μm on average by using a nanopipette. On the other hand, ionization efficiency increased with decreasing solvent flow rate. Our results indicate the compatibility between a reduced sampling area and the ionization efficiency using a nanopipette. MSI of micropatterns of ink on a glass and a polymer substrate were also demonstrated. PMID:28101441

Evaluation of Pump Pulsation in Respirable Size-Selective Sampling: Part II. Changes in Sampling Efficiency

PubMed Central

Lee, Eun Gyung; Lee, Taekhee; Kim, Seung Won; Lee, Larry; Flemmer, Michael M.; Harper, Martin

2015-01-01

This second, and concluding, part of this study evaluated changes in sampling efficiency of respirable size-selective samplers due to air pulsations generated by the selected personal sampling pumps characterized in Part I (Lee E, Lee L, Möhlmann C et al. Evaluation of pump pulsation in respirable size-selective sampling: Part I. Pulsation measurements. Ann Occup Hyg 2013). Nine particle sizes of monodisperse ammonium fluorescein (from 1 to 9 μm mass median aerodynamic diameter) were generated individually by a vibrating orifice aerosol generator from dilute solutions of fluorescein in aqueous ammonia and then injected into an environmental chamber. To collect these particles, 10-mm nylon cyclones, also known as Dorr-Oliver (DO) cyclones, were used with five medium volumetric flow rate pumps. Those were the Apex IS, HFS513, GilAir5, Elite5, and Basic5 pumps, which were found in Part I to generate pulsations of 5% (the lowest), 25%, 30%, 56%, and 70% (the highest), respectively. GK2.69 cyclones were used with the Legacy [pump pulsation (PP) = 15%] and Elite12 (PP = 41%) pumps for collection at high flows. The DO cyclone was also used to evaluate changes in sampling efficiency due to pulse shape. The HFS513 pump, which generates a more complex pulse shape, was compared to a single sine wave fluctuation generated by a piston. The luminescent intensity of the fluorescein extracted from each sample was measured with a luminescence spectrometer. Sampling efficiencies were obtained by dividing the intensity of the fluorescein extracted from the filter placed in a cyclone with the intensity obtained from the filter used with a sharp-edged reference sampler. Then, sampling efficiency curves were generated using a sigmoid function with three parameters and each sampling efficiency curve was compared to that of the reference cyclone by constructing bias maps. In general, no change in sampling efficiency (bias under ±10%) was observed until pulsations exceeded 25% for the

Evaluation of pump pulsation in respirable size-selective sampling: part II. Changes in sampling efficiency.

PubMed

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

Guide for Calculating and Interpreting Effect Sizes and Confidence Intervals in Intellectual and Developmental Disability Research Studies

ERIC Educational Resources Information Center

Dunst, Carl J.; Hamby, Deborah W.

2012-01-01

This paper includes a nontechnical description of methods for calculating effect sizes in intellectual and developmental disability studies. Different hypothetical studies are used to illustrate how null hypothesis significance testing (NHST) and effect size findings can result in quite different outcomes and therefore conflicting results. Whereas…

Weighting by Inverse Variance or by Sample Size in Random-Effects Meta-Analysis

ERIC Educational Resources Information Center

Marin-Martinez, Fulgencio; Sanchez-Meca, Julio

2010-01-01

Most of the statistical procedures in meta-analysis are based on the estimation of average effect sizes from a set of primary studies. The optimal weight for averaging a set of independent effect sizes is the inverse variance of each effect size, but in practice these weights have to be estimated, being affected by sampling error. When assuming a…

SU-E-T-454: Impact of Calculation Grid Size On Dosimetry and Radiobiological Parameters for Head and Neck IMRT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Srivastava, S; Das, I; Indiana University Health Methodist Hospital, Indianapolis, IN

2014-06-01

Purpose: IMRT has become standard of care for complex treatments to optimize dose to target and spare normal tissues. However, the impact of calculation grid size is not widely known especially dose distribution, tumor control probability (TCP) and normal tissue complication probability (NTCP) which is investigated in this study. Methods: Ten head and neck IMRT patients treated with 6 MV photons were chosen for this study. Using Eclipse TPS, treatment plans were generated for different grid sizes in the range 1–5 mm for the same optimization criterion with specific dose-volume constraints. The dose volume histogram (DVH) was calculated for allmore » IMRT plans and dosimetric data were compared. ICRU-83 dose points such as D2%, D50%, D98%, as well as the homogeneity and conformity indices (HI, CI) were calculated. In addition, TCP and NTCP were calculated from DVH data. Results: The PTV mean dose and TCP decreases with increasing grid size with an average decrease in mean dose by 2% and TCP by 3% respectively. Increasing grid size from 1–5 mm grid size, the average mean dose and NTCP for left parotid was increased by 6.0% and 8.0% respectively. Similar patterns were observed for other OARs such as cochlea, parotids and spinal cord. The HI increases up to 60% and CI decreases on average by 3.5% between 1 and 5 mm grid that resulted in decreased TCP and increased NTCP values. The number of points meeting the gamma criteria of ±3% dose difference and ±3mm DTA was higher with a 1 mm on average (97.2%) than with a 5 mm grid (91.3%). Conclusion: A smaller calculation grid provides superior dosimetry with improved TCP and reduced NTCP values. The effect is more pronounced for smaller OARs. Thus, the smallest possible grid size should be used for accurate dose calculation especially in H and N planning.« less

Thermal conductivity of graphene mediated by strain and size

DOE PAGES

Kuang, Youdi; Shi, Sanqiang; Wang, Xinjiang; ...

2016-06-09

Based on first-principles calculations and full iterative solution of the linearized Boltzmann–Peierls transport equation for phonons, we systematically investigate effects of strain, size and temperature on the thermal conductivity k of suspended graphene. The calculated size-dependent and temperature-dependent k for finite samples agree well with experimental data. The results show that, contrast to the convergent room-temperature k = 5450 W/m-K of unstrained graphene at a sample size ~8 cm, k of strained graphene diverges with increasing the sample size even at high temperature. Out-of-plane acoustic phonons are responsible for the significant size effect in unstrained and strained graphene due tomore » their ultralong mean free path and acoustic phonons with wavelength smaller than 10 nm contribute 80% to the intrinsic room temperature k of unstrained graphene. Tensile strain hardens the flexural modes and increases their lifetimes, causing interesting dependence of k on sample size and strain due to the competition between boundary scattering and intrinsic phonon–phonon scattering. k of graphene can be tuned within a large range by strain for the size larger than 500 μm. These findings shed light on the nature of thermal transport in two-dimensional materials and may guide predicting and engineering k of graphene by varying strain and size.« less

Forestry inventory based on multistage sampling with probability proportional to size

NASA Technical Reports Server (NTRS)

Lee, D. C. L.; Hernandez, P., Jr.; Shimabukuro, Y. E.

1983-01-01

A multistage sampling technique, with probability proportional to size, is developed for a forest volume inventory using remote sensing data. The LANDSAT data, Panchromatic aerial photographs, and field data are collected. Based on age and homogeneity, pine and eucalyptus classes are identified. Selection of tertiary sampling units is made through aerial photographs to minimize field work. The sampling errors for eucalyptus and pine ranged from 8.34 to 21.89 percent and from 7.18 to 8.60 percent, respectively.

40 CFR 600.211-08 - Sample calculation of fuel economy values for labeling.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 30 2011-07-01 2011-07-01 false Sample calculation of fuel economy... AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Procedures for Calculating Fuel Economy and Carbon-Related Exhaust Emission Values for 1977 and Later Model...

Effect of roll hot press temperature on crystallite size of PVDF film

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hartono, Ambran, E-mail: ambranhartono@yahoo.com; Sanjaya, Edi; Djamal, Mitra

2014-03-24

Fabrication PVDF films have been made using Hot Roll Press. Preparation of samples carried out for nine different temperatures. This condition is carried out to see the effect of Roll Hot Press temperature on the size of the crystallite of PVDF films. To obtain the diffraction pattern of sample characterization is performed using X-Ray Diffraction. Furthermore, from the diffraction pattern is obtained, the calculation to determine the crystallite size of the sample by using the Scherrer equation. From the experimental results and the calculation of crystallite sizes obtained for the samples with temperature 130 °C up to 170 °C respectivelymore » increased from 7.2 nm up to 20.54 nm. These results show that increasing temperatures will also increase the size of the crystallite of the sample. This happens because with the increasing temperature causes the higher the degree of crystallization of PVDF film sample is formed, so that the crystallite size also increases. This condition indicates that the specific volume or size of the crystals depends on the magnitude of the temperature as it has been studied by Nakagawa.« less

Optimal number of features as a function of sample size for various classification rules.

PubMed

Hua, Jianping; Xiong, Zixiang; Lowey, James; Suh, Edward; Dougherty, Edward R

2005-04-15

Given the joint feature-label distribution, increasing the number of features always results in decreased classification error; however, this is not the case when a classifier is designed via a classification rule from sample data. Typically (but not always), for fixed sample size, the error of a designed classifier decreases and then increases as the number of features grows. The potential downside of using too many features is most critical for small samples, which are commonplace for gene-expression-based classifiers for phenotype discrimination. For fixed sample size and feature-label distribution, the issue is to find an optimal number of features. Since only in rare cases is there a known distribution of the error as a function of the number of features and sample size, this study employs simulation for various feature-label distributions and classification rules, and across a wide range of sample and feature-set sizes. To achieve the desired end, finding the optimal number of features as a function of sample size, it employs massively parallel computation. Seven classifiers are treated: 3-nearest-neighbor, Gaussian kernel, linear support vector machine, polynomial support vector machine, perceptron, regular histogram and linear discriminant analysis. Three Gaussian-based models are considered: linear, nonlinear and bimodal. In addition, real patient data from a large breast-cancer study is considered. To mitigate the combinatorial search for finding optimal feature sets, and to model the situation in which subsets of genes are co-regulated and correlation is internal to these subsets, we assume that the covariance matrix of the features is blocked, with each block corresponding to a group of correlated features. Altogether there are a large number of error surfaces for the many cases. These are provided in full on a companion website, which is meant to serve as resource for those working with small-sample classification. For the companion website, please

MUDMASTER: A Program for Calculating Crystalline Size Distributions and Strain from the Shapes of X-Ray Diffraction Peaks

USGS Publications Warehouse

Eberl, D.D.; Drits, V.A.; Środoń, Jan; Nüesch, R.

1996-01-01

Particle size may strongly influence the physical and chemical properties of a substance (e.g. its rheology, surface area, cation exchange capacity, solubility, etc.), and its measurement in rocks may yield geological information about ancient environments (sediment provenance, degree of metamorphism, degree of weathering, current directions, distance to shore, etc.). Therefore mineralogists, geologists, chemists, soil scientists, and others who deal with clay-size material would like to have a convenient method for measuring particle size distributions. Nano-size crystals generally are too fine to be measured by light microscopy. Laser scattering methods give only average particle sizes; therefore particle size can not be measured in a particular crystallographic direction. Also, the particles measured by laser techniques may be composed of several different minerals, and may be agglomerations of individual crystals. Measurement by electron and atomic force microscopy is tedious, expensive, and time consuming. It is difficult to measure more than a few hundred particles per sample by these methods. This many measurements, often taking several days of intensive effort, may yield an accurate mean size for a sample, but may be too few to determine an accurate distribution of sizes. Measurement of size distributions by X-ray diffraction (XRD) solves these shortcomings. An X-ray scan of a sample occurs automatically, taking a few minutes to a few hours. The resulting XRD peaks average diffraction effects from billions of individual nano-size crystals. The size that is measured by XRD may be related to the size of the individual crystals of the mineral in the sample, rather than to the size of particles formed from the agglomeration of these crystals. Therefore one can determine the size of a particular mineral in a mixture of minerals, and the sizes in a particular crystallographic direction of that mineral.

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 III Appendix III to Part 600 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) ENERGY POLICY FUEL ECONOMY AND CARBON-RELATED EXHAUST EMISSIONS OF MOTOR VEHICLES Pt. 600, App. III Appendix III to Part 600—Sample Fuel Economy Label...

Norm Block Sample Sizes: A Review of 17 Individually Administered Intelligence Tests

ERIC Educational Resources Information Center

Norfolk, Philip A.; Farmer, Ryan L.; Floyd, Randy G.; Woods, Isaac L.; Hawkins, Haley K.; Irby, Sarah M.

2015-01-01

The representativeness, recency, and size of norm samples strongly influence the accuracy of inferences drawn from their scores. Inadequate norm samples may lead to inflated or deflated scores for individuals and poorer prediction of developmental and academic outcomes. The purpose of this study was to apply Kranzler and Floyd's method for…

Enhancing sampling design in mist-net bat surveys by accounting for sample size optimization.

PubMed

Trevelin, Leonardo Carreira; Novaes, Roberto Leonan Morim; Colas-Rosas, Paul François; Benathar, Thayse Cristhina Melo; Peres, Carlos A

2017-01-01

The advantages of mist-netting, the main technique used in Neotropical bat community studies to date, include logistical implementation, standardization and sampling representativeness. Nonetheless, study designs still have to deal with issues of detectability related to how different species behave and use the environment. Yet there is considerable sampling heterogeneity across available studies in the literature. Here, we approach the problem of sample size optimization. We evaluated the common sense hypothesis that the first six hours comprise the period of peak night activity for several species, thereby resulting in a representative sample for the whole night. To this end, we combined re-sampling techniques, species accumulation curves, threshold analysis, and community concordance of species compositional data, and applied them to datasets of three different Neotropical biomes (Amazonia, Atlantic Forest and Cerrado). We show that the strategy of restricting sampling to only six hours of the night frequently results in incomplete sampling representation of the entire bat community investigated. From a quantitative standpoint, results corroborated the existence of a major Sample Area effect in all datasets, although for the Amazonia dataset the six-hour strategy was significantly less species-rich after extrapolation, and for the Cerrado dataset it was more efficient. From the qualitative standpoint, however, results demonstrated that, for all three datasets, the identity of species that are effectively sampled will be inherently impacted by choices of sub-sampling schedule. We also propose an alternative six-hour sampling strategy (at the beginning and the end of a sample night) which performed better when resampling Amazonian and Atlantic Forest datasets on bat assemblages. Given the observed magnitude of our results, we propose that sample representativeness has to be carefully weighed against study objectives, and recommend that the trade-off between

Enhancing sampling design in mist-net bat surveys by accounting for sample size optimization

PubMed Central

Trevelin, Leonardo Carreira; Novaes, Roberto Leonan Morim; Colas-Rosas, Paul François; Benathar, Thayse Cristhina Melo; Peres, Carlos A.

2017-01-01

The advantages of mist-netting, the main technique used in Neotropical bat community studies to date, include logistical implementation, standardization and sampling representativeness. Nonetheless, study designs still have to deal with issues of detectability related to how different species behave and use the environment. Yet there is considerable sampling heterogeneity across available studies in the literature. Here, we approach the problem of sample size optimization. We evaluated the common sense hypothesis that the first six hours comprise the period of peak night activity for several species, thereby resulting in a representative sample for the whole night. To this end, we combined re-sampling techniques, species accumulation curves, threshold analysis, and community concordance of species compositional data, and applied them to datasets of three different Neotropical biomes (Amazonia, Atlantic Forest and Cerrado). We show that the strategy of restricting sampling to only six hours of the night frequently results in incomplete sampling representation of the entire bat community investigated. From a quantitative standpoint, results corroborated the existence of a major Sample Area effect in all datasets, although for the Amazonia dataset the six-hour strategy was significantly less species-rich after extrapolation, and for the Cerrado dataset it was more efficient. From the qualitative standpoint, however, results demonstrated that, for all three datasets, the identity of species that are effectively sampled will be inherently impacted by choices of sub-sampling schedule. We also propose an alternative six-hour sampling strategy (at the beginning and the end of a sample night) which performed better when resampling Amazonian and Atlantic Forest datasets on bat assemblages. Given the observed magnitude of our results, we propose that sample representativeness has to be carefully weighed against study objectives, and recommend that the trade-off between

Size Reduction of Hamiltonian Matrix for Large-Scale Energy Band Calculations Using Plane Wave Bases

NASA Astrophysics Data System (ADS)

Morifuji, Masato

2018-01-01

We present a method of reducing the size of a Hamiltonian matrix used in calculations of electronic states. In the electronic states calculations using plane wave basis functions, a large number of plane waves are often required to obtain precise results. Even using state-of-the-art techniques, the Hamiltonian matrix often becomes very large. The large computational time and memory necessary for diagonalization limit the widespread use of band calculations. We show a procedure of deriving a reduced Hamiltonian constructed using a small number of low-energy bases by renormalizing high-energy bases. We demonstrate numerically that the significant speedup of eigenstates evaluation is achieved without losing accuracy.

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…

Convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks

NASA Astrophysics Data System (ADS)

Long, Yin; Zhang, Xiao-Jun; Wang, Kui

2018-05-01

In this paper, convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks (RBDNs) are studied. First, we find and demonstrate that the average degree is convergent in the form of power law. Meanwhile, we discover that the ratios of the back items to front items of convergent reminder are independent of network link number for large network size, and we theoretically prove that the limit of the ratio is a constant. Moreover, since it is difficult to calculate the analytical solution of the average degree for large network sizes, we adopt numerical method to obtain approximate expression of the average degree to approximate its analytical solution. Finally, simulations are presented to verify our theoretical results.

The Impact of Sample Size and Other Factors When Estimating Multilevel Logistic Models

ERIC Educational Resources Information Center

Schoeneberger, Jason A.

2016-01-01

The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying…

Sample Size Requirements for Structural Equation Models: An Evaluation of Power, Bias, and Solution Propriety

ERIC Educational Resources Information Center

Wolf, Erika J.; Harrington, Kelly M.; Clark, Shaunna L.; Miller, Mark W.

2013-01-01

Determining sample size requirements for structural equation modeling (SEM) is a challenge often faced by investigators, peer reviewers, and grant writers. Recent years have seen a large increase in SEMs in the behavioral science literature, but consideration of sample size requirements for applied SEMs often relies on outdated rules-of-thumb.…

Estimation of sample size and testing power (part 6).

PubMed

Hu, Liang-ping; Bao, Xiao-lei; Guan, Xue; Zhou, Shi-guo

2012-03-01

The design of one factor with k levels (k ≥ 3) refers to the research that only involves one experimental factor with k levels (k ≥ 3), and there is no arrangement for other important non-experimental factors. This paper introduces the estimation of sample size and testing power for quantitative data and qualitative data having a binary response variable with the design of one factor with k levels (k ≥ 3).

Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range.

PubMed

Luo, Dehui; Wan, Xiang; Liu, Jiming; Tong, Tiejun

2018-06-01

The era of big data is coming, and evidence-based medicine is attracting increasing attention to improve decision making in medical practice via integrating evidence from well designed and conducted clinical research. Meta-analysis is a statistical technique widely used in evidence-based medicine for analytically combining the findings from independent clinical trials to provide an overall estimation of a treatment effectiveness. The sample mean and standard deviation are two commonly used statistics in meta-analysis but some trials use the median, the minimum and maximum values, or sometimes the first and third quartiles to report the results. Thus, to pool results in a consistent format, researchers need to transform those information back to the sample mean and standard deviation. In this article, we investigate the optimal estimation of the sample mean for meta-analysis from both theoretical and empirical perspectives. A major drawback in the literature is that the sample size, needless to say its importance, is either ignored or used in a stepwise but somewhat arbitrary manner, e.g. the famous method proposed by Hozo et al. We solve this issue by incorporating the sample size in a smoothly changing weight in the estimators to reach the optimal estimation. Our proposed estimators not only improve the existing ones significantly but also share the same virtue of the simplicity. The real data application indicates that our proposed estimators are capable to serve as "rules of thumb" and will be widely applied in evidence-based medicine.

On the Structure of Cortical Microcircuits Inferred from Small Sample Sizes.

PubMed

Vegué, Marina; Perin, Rodrigo; Roxin, Alex

2017-08-30

The structure in cortical microcircuits deviates from what would be expected in a purely random network, which has been seen as evidence of clustering. To address this issue, we sought to reproduce the nonrandom features of cortical circuits by considering several distinct classes of network topology, including clustered networks, networks with distance-dependent connectivity, and those with broad degree distributions. To our surprise, we found that all of these qualitatively distinct topologies could account equally well for all reported nonrandom features despite being easily distinguishable from one another at the network level. This apparent paradox was a consequence of estimating network properties given only small sample sizes. In other words, networks that differ markedly in their global structure can look quite similar locally. This makes inferring network structure from small sample sizes, a necessity given the technical difficulty inherent in simultaneous intracellular recordings, problematic. We found that a network statistic called the sample degree correlation (SDC) overcomes this difficulty. The SDC depends only on parameters that can be estimated reliably given small sample sizes and is an accurate fingerprint of every topological family. We applied the SDC criterion to data from rat visual and somatosensory cortex and discovered that the connectivity was not consistent with any of these main topological classes. However, we were able to fit the experimental data with a more general network class, of which all previous topologies were special cases. The resulting network topology could be interpreted as a combination of physical spatial dependence and nonspatial, hierarchical clustering. SIGNIFICANCE STATEMENT The connectivity of cortical microcircuits exhibits features that are inconsistent with a simple random network. Here, we show that several classes of network models can account for this nonrandom structure despite qualitative differences in

Luminescence isochron dating: a new approach using different grain sizes.

PubMed

Zhao, H; Li, S H

2002-01-01

A new approach to isochron dating is described using different sizes of quartz and K-feldspar grains. The technique can be applied to sites with time-dependent external dose rates. It is assumed that any underestimation of the equivalent dose (De) using K-feldspar is by a factor F, which is independent of grain size (90-350 microm) for a given sample. Calibration of the beta source for different grain sizes is discussed, and then the sample ages are calculated using the differences between quartz and K-feldspar De from grains of similar size. Two aeolian sediment samples from north-eastern China are used to illustrate the application of the new method. It is confirmed that the observed values of De derived using K-feldspar underestimate the expected doses (based on the quartz De) but, nevertheless, these K-feldspar De values correlate linearly with the calculated internal dose rate contribution, supporting the assumption that the underestimation factor F is independent of grain size. The isochron ages are also compared with the results obtained using quartz De and the measured external dose rates.

Sample size estimation for alternating logistic regressions analysis of multilevel randomized community trials of under-age drinking.

PubMed

Reboussin, Beth A; Preisser, John S; Song, Eun-Young; Wolfson, Mark

2012-07-01

Under-age drinking is an enormous public health issue in the USA. Evidence that community level structures may impact on under-age drinking has led to a proliferation of efforts to change the environment surrounding the use of alcohol. Although the focus of these efforts is to reduce drinking by individual youths, environmental interventions are typically implemented at the community level with entire communities randomized to the same intervention condition. A distinct feature of these trials is the tendency of the behaviours of individuals residing in the same community to be more alike than that of others residing in different communities, which is herein called 'clustering'. Statistical analyses and sample size calculations must account for this clustering to avoid type I errors and to ensure an appropriately powered trial. Clustering itself may also be of scientific interest. We consider the alternating logistic regressions procedure within the population-averaged modelling framework to estimate the effect of a law enforcement intervention on the prevalence of under-age drinking behaviours while modelling the clustering at multiple levels, e.g. within communities and within neighbourhoods nested within communities, by using pairwise odds ratios. We then derive sample size formulae for estimating intervention effects when planning a post-test-only or repeated cross-sectional community-randomized trial using the alternating logistic regressions procedure.

Minimizing the Maximum Expected Sample Size in Two-Stage Phase II Clinical Trials with Continuous Outcomes

PubMed Central

Wason, James M. S.; Mander, Adrian P.

2012-01-01

Two-stage designs are commonly used for Phase II trials. Optimal two-stage designs have the lowest expected sample size for a specific treatment effect, for example, the null value, but can perform poorly if the true treatment effect differs. Here we introduce a design for continuous treatment responses that minimizes the maximum expected sample size across all possible treatment effects. The proposed design performs well for a wider range of treatment effects and so is useful for Phase II trials. We compare the design to a previously used optimal design and show it has superior expected sample size properties. PMID:22651118

Estimating the Size of a Large Network and its Communities from a Random Sample

PubMed Central

Chen, Lin; Karbasi, Amin; Crawford, Forrest W.

2017-01-01

Most real-world networks are too large to be measured or studied directly and there is substantial interest in estimating global network properties from smaller sub-samples. One of the most important global properties is the number of vertices/nodes in the network. Estimating the number of vertices in a large network is a major challenge in computer science, epidemiology, demography, and intelligence analysis. In this paper we consider a population random graph G = (V, E) from the stochastic block model (SBM) with K communities/blocks. A sample is obtained by randomly choosing a subset W ⊆ V and letting G(W) be the induced subgraph in G of the vertices in W. In addition to G(W), we observe the total degree of each sampled vertex and its block membership. Given this partial information, we propose an efficient PopULation Size Estimation algorithm, called PULSE, that accurately estimates the size of the whole population as well as the size of each community. To support our theoretical analysis, we perform an exhaustive set of experiments to study the effects of sample size, K, and SBM model parameters on the accuracy of the estimates. The experimental results also demonstrate that PULSE significantly outperforms a widely-used method called the network scale-up estimator in a wide variety of scenarios. PMID:28867924

Estimating the Size of a Large Network and its Communities from a Random Sample.

PubMed

Chen, Lin; Karbasi, Amin; Crawford, Forrest W

2016-01-01

Most real-world networks are too large to be measured or studied directly and there is substantial interest in estimating global network properties from smaller sub-samples. One of the most important global properties is the number of vertices/nodes in the network. Estimating the number of vertices in a large network is a major challenge in computer science, epidemiology, demography, and intelligence analysis. In this paper we consider a population random graph G = ( V, E ) from the stochastic block model (SBM) with K communities/blocks. A sample is obtained by randomly choosing a subset W ⊆ V and letting G ( W ) be the induced subgraph in G of the vertices in W . In addition to G ( W ), we observe the total degree of each sampled vertex and its block membership. Given this partial information, we propose an efficient PopULation Size Estimation algorithm, called PULSE, that accurately estimates the size of the whole population as well as the size of each community. To support our theoretical analysis, we perform an exhaustive set of experiments to study the effects of sample size, K , and SBM model parameters on the accuracy of the estimates. The experimental results also demonstrate that PULSE significantly outperforms a widely-used method called the network scale-up estimator in a wide variety of scenarios.

(Sample) Size Matters: Best Practices for Defining Error in Planktic Foraminiferal Proxy Records

NASA Astrophysics Data System (ADS)

Lowery, C.; Fraass, A. J.

2016-02-01

Paleoceanographic research is a vital tool to extend modern observational datasets and to study the impact of climate events for which there is no modern analog. Foraminifera are one of the most widely used tools for this type of work, both as paleoecological indicators and as carriers for geochemical proxies. However, the use of microfossils as proxies for paleoceanographic conditions brings about a unique set of problems. This is primarily due to the fact that groups of individual foraminifera, which usually live about a month, are used to infer average conditions for time periods ranging from hundreds to tens of thousands of years. Because of this, adequate sample size is very important for generating statistically robust datasets, particularly for stable isotopes. In the early days of stable isotope geochemistry, instrumental limitations required hundreds of individual foraminiferal tests to return a value. This had the fortunate side-effect of smoothing any seasonal to decadal changes within the planktic foram population. With the advent of more sensitive mass spectrometers, smaller sample sizes have now become standard. While this has many advantages, 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 (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

Analysis of variograms with various sample sizes from a multispectral image

USDA-ARS?s Scientific Manuscript database

Variograms play a crucial role in remote sensing application and geostatistics. In this study, the analysis of variograms with various sample sizes of remotely sensed data was conducted. A 100 X 100 pixel subset was chosen from an aerial multispectral image which contained three wavebands, green, ...

On Two-Stage Multiple Comparison Procedures When There Are Unequal Sample Sizes in the First Stage.

ERIC Educational Resources Information Center

Wilcox, Rand R.

1984-01-01

Two stage multiple-comparison procedures give an exact solution to problems of power and Type I errors, but require equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes. (Author/BW)

The effect of machine learning regression algorithms and sample size on individualized behavioral prediction with functional connectivity features.

PubMed

Cui, Zaixu; Gong, Gaolang

2018-06-02

Individualized behavioral/cognitive prediction using machine learning (ML) regression approaches is becoming increasingly applied. The specific ML regression algorithm and sample size are two key factors that non-trivially influence prediction accuracies. However, the effects of the ML regression algorithm and sample size on individualized behavioral/cognitive prediction performance have not been comprehensively assessed. To address this issue, the present study included six commonly used ML regression algorithms: ordinary least squares (OLS) regression, least absolute shrinkage and selection operator (LASSO) regression, ridge regression, elastic-net regression, linear support vector regression (LSVR), and relevance vector regression (RVR), to perform specific behavioral/cognitive predictions based on different sample sizes. Specifically, the publicly available resting-state functional MRI (rs-fMRI) dataset from the Human Connectome Project (HCP) was used, and whole-brain resting-state functional connectivity (rsFC) or rsFC strength (rsFCS) were extracted as prediction features. Twenty-five sample sizes (ranged from 20 to 700) were studied by sub-sampling from the entire HCP cohort. The analyses showed that rsFC-based LASSO regression performed remarkably worse than the other algorithms, and rsFCS-based OLS regression performed markedly worse than the other algorithms. Regardless of the algorithm and feature type, both the prediction accuracy and its stability exponentially increased with increasing sample size. The specific patterns of the observed algorithm and sample size effects were well replicated in the prediction using re-testing fMRI data, data processed by different imaging preprocessing schemes, and different behavioral/cognitive scores, thus indicating excellent robustness/generalization of the effects. The current findings provide critical insight into how the selected ML regression algorithm and sample size influence individualized predictions of

Adaptive beamlet-based finite-size pencil beam dose calculation for independent verification of IMRT and VMAT.

PubMed

Park, Justin C; Li, Jonathan G; Arhjoul, Lahcen; Yan, Guanghua; Lu, Bo; Fan, Qiyong; Liu, Chihray

2015-04-01

The use of sophisticated dose calculation procedure in modern radiation therapy treatment planning is inevitable in order to account for complex treatment fields created by multileaf collimators (MLCs). As a consequence, independent volumetric dose verification is time consuming, which affects the efficiency of clinical workflow. In this study, the authors present an efficient adaptive beamlet-based finite-size pencil beam (AB-FSPB) dose calculation algorithm that minimizes the computational procedure while preserving the accuracy. The computational time of finite-size pencil beam (FSPB) algorithm is proportional to the number of infinitesimal and identical beamlets that constitute an arbitrary field shape. In AB-FSPB, dose distribution from each beamlet is mathematically modeled such that the sizes of beamlets to represent an arbitrary field shape no longer need to be infinitesimal nor identical. As a result, it is possible to represent an arbitrary field shape with combinations of different sized and minimal number of beamlets. In addition, the authors included the model parameters to consider MLC for its rounded edge and transmission. Root mean square error (RMSE) between treatment planning system and conventional FSPB on a 10 × 10 cm(2) square field using 10 × 10, 2.5 × 2.5, and 0.5 × 0.5 cm(2) beamlet sizes were 4.90%, 3.19%, and 2.87%, respectively, compared with RMSE of 1.10%, 1.11%, and 1.14% for AB-FSPB. This finding holds true for a larger square field size of 25 × 25 cm(2), where RMSE for 25 × 25, 2.5 × 2.5, and 0.5 × 0.5 cm(2) beamlet sizes were 5.41%, 4.76%, and 3.54% in FSPB, respectively, compared with RMSE of 0.86%, 0.83%, and 0.88% for AB-FSPB. It was found that AB-FSPB could successfully account for the MLC transmissions without major discrepancy. The algorithm was also graphical processing unit (GPU) compatible to maximize its computational speed. For an intensity modulated radiation therapy (∼12 segments) and a volumetric modulated arc

A cautionary note on Bayesian estimation of population size by removal sampling with diffuse priors.

PubMed

Bord, Séverine; Bioche, Christèle; Druilhet, Pierre

2018-05-01

We consider the problem of estimating a population size by removal sampling when the sampling rate is unknown. Bayesian methods are now widespread and allow to include prior knowledge in the analysis. However, we show that Bayes estimates based on default improper priors lead to improper posteriors or infinite estimates. Similarly, weakly informative priors give unstable estimators that are sensitive to the choice of hyperparameters. By examining the likelihood, we show that population size estimates can be stabilized by penalizing small values of the sampling rate or large value of the population size. Based on theoretical results and simulation studies, we propose some recommendations on the choice of the prior. Then, we applied our results to real datasets. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Grain size of loess and paleosol samples: what are we measuring?

NASA Astrophysics Data System (ADS)

Varga, György; Kovács, János; Szalai, Zoltán; Újvári, Gábor

2017-04-01

Particle size falling into a particularly narrow range is among the most important properties of windblown mineral dust deposits. Therefore, various aspects of aeolian sedimentation and post-depositional alterations can be reconstructed only from precise grain size data. Present study is aimed at (1) reviewing grain size data obtained from different measurements, (2) discussing the major reasons for disagreements between data obtained by frequently applied particle sizing techniques, and (3) assesses the importance of particle shape in particle sizing. Grain size data of terrestrial aeolian dust deposits (loess and paleosoil) were determined by laser scattering instruments (Fritsch Analysette 22 Microtec Plus, Horiba Partica La-950 v2 and Malvern Mastersizer 3000 with a Hydro Lv unit), while particles size and shape distributions were acquired by Malvern Morphologi G3-ID. Laser scattering results reveal that the optical parameter settings of the measurements have significant effects on the grain size distributions, especially for the fine-grained fractions (<5 µm). Significant differences between the Mie and Fraunhofer approaches were found for the finest grain size fractions, while only slight discrepancies were observed for the medium to coarse silt fractions. It should be noted that the different instruments provided different grain size distributions even with the exactly same optical settings. Image analysis-based grain size data indicated underestimation of clay and fine silt fractions compared to laser measurements. The measured circle-equivalent diameter of image analysis is calculated from the acquired two-dimensional image of the particle. It is assumed that the instantaneous pulse of compressed air disperse the sedimentary particles onto the glass slide with a consistent orientation with their largest area facing to the camera. However, this is only one outcome of infinite possible projections of a three-dimensional object and it cannot be regarded as a

Analysis of variograms with various sample sizes from a multispectral image

USDA-ARS?s Scientific Manuscript database

Variogram plays a crucial role in remote sensing application and geostatistics. It is very important to estimate variogram reliably from sufficient data. In this study, the analysis of variograms with various sample sizes of remotely sensed data was conducted. A 100x100-pixel subset was chosen from ...

Does an uneven sample size distribution across settings matter in cross-classified multilevel modeling? Results of a simulation study.

PubMed

Milliren, Carly E; Evans, Clare R; Richmond, Tracy K; Dunn, Erin C

2018-06-06

Recent advances in multilevel modeling allow for modeling non-hierarchical levels (e.g., youth in non-nested schools and neighborhoods) using cross-classified multilevel models (CCMM). Current practice is to cluster samples from one context (e.g., schools) and utilize the observations however they are distributed from the second context (e.g., neighborhoods). However, it is unknown whether an uneven distribution of sample size across these contexts leads to incorrect estimates of random effects in CCMMs. Using the school and neighborhood data structure in Add Health, we examined the effect of neighborhood sample size imbalance on the estimation of variance parameters in models predicting BMI. We differentially assigned students from a given school to neighborhoods within that school's catchment area using three scenarios of (im)balance. 1000 random datasets were simulated for each of five combinations of school- and neighborhood-level variance and imbalance scenarios, for a total of 15,000 simulated data sets. For each simulation, we calculated 95% CIs for the variance parameters to determine whether the true simulated variance fell within the interval. Across all simulations, the "true" school and neighborhood variance parameters were estimated 93-96% of the time. Only 5% of models failed to capture neighborhood variance; 6% failed to capture school variance. These results suggest that there is no systematic bias in the ability of CCMM to capture the true variance parameters regardless of the distribution of students across neighborhoods. Ongoing efforts to use CCMM are warranted and can proceed without concern for the sample imbalance across contexts. Copyright © 2018 Elsevier Ltd. All rights reserved.

Maximum type I error rate inflation from sample size reassessment when investigators are blind to treatment labels.

PubMed

Żebrowska, Magdalena; Posch, Martin; Magirr, Dominic

2016-05-30

Consider a parallel group trial for the comparison of an experimental treatment to a control, where the second-stage sample size may depend on the blinded primary endpoint data as well as on additional blinded data from a secondary endpoint. For the setting of normally distributed endpoints, we demonstrate that this may lead to an inflation of the type I error rate if the null hypothesis holds for the primary but not the secondary endpoint. We derive upper bounds for the inflation of the type I error rate, both for trials that employ random allocation and for those that use block randomization. We illustrate the worst-case sample size reassessment rule in a case study. For both randomization strategies, the maximum type I error rate increases with the effect size in the secondary endpoint and the correlation between endpoints. The maximum inflation increases with smaller block sizes if information on the block size is used in the reassessment rule. Based on our findings, we do not question the well-established use of blinded sample size reassessment methods with nuisance parameter estimates computed from the blinded interim data of the primary endpoint. However, we demonstrate that the type I error rate control of these methods relies on the application of specific, binding, pre-planned and fully algorithmic sample size reassessment rules and does not extend to general or unplanned sample size adjustments based on blinded data. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.