scholarly journals A Note on Inferences About the Probability of Success

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Rand Wilcox
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Small Sample ◽  
Extensive Literature ◽  
Sample Sizes ◽  
Probability Of Success ◽  
Small Sample Sizes ◽  
A Minor ◽  
Sample Case

There is an extensive literature dealing with inferences about the probability of success. A minor goal in this note is to point out when certain recommended methods can be unsatisfactory when the sample size is small. The main goal is to report results on the two-sample case. Extant results suggest using one of four methods. The results indicate when computing a 0.95 confidence interval, two of these methods can be more satisfactory when dealing with small sample sizes.

scholarly journals What can we Learn from Studies Based on Small Sample Sizes? Comment on Regan, Lakhanpal, and Anguiano (2012)

2013 ◽  
Vol 113 (1) ◽  
pp. 221-224 ◽  
Author(s):  
David R. Johnson ◽  
Lauren K. Bachan
Keyword(s):  
Sample Size ◽  
Recent Article ◽  
Small Sample ◽  
Sample Sizes ◽  
Relationship Outcomes ◽  
Small Sample Sizes

In a recent article, Regan, Lakhanpal, and Anguiano (2012) highlighted the lack of evidence for different relationship outcomes between arranged and love-based marriages. Yet the sample size ( n = 58) used in the study is insufficient for making such inferences. This reply discusses and demonstrates how small sample sizes reduce the utility of this research.

scholarly journals Sample Size Determination and Optimal Design of Simple Pretest-Posttest Experimental Designs: Introduction, Software, and Illustrations

2021 ◽  
Author(s):  
Metin Bulus
Keyword(s):  
Optimal Design ◽  
Sample Size ◽  
Small Sample ◽  
Experimental Designs ◽  
Sample Size Determination ◽  
Size Determination ◽  
Sample Sizes ◽  
Control Groups ◽  
Small Sample Sizes ◽  
And Control

A recent systematic review of experimental studies conducted in Turkey between 2010 and 2020 reported that small sample sizes had been a significant drawback (Bulus and Koyuncu, 2021). A small chunk of the studies were small-scale true experiments (subjects randomized into the treatment and control groups). The remaining studies consisted of quasi-experiments (subjects in treatment and control groups were matched on pretest or other covariates) and weak experiments (neither randomized nor matched but had the control group). They had an average sample size below 70 for different domains and outcomes. These small sample sizes imply a strong (and perhaps erroneous) assumption about the minimum relevant effect size (MRES) of intervention before an experiment is conducted; that is, a standardized intervention effect of Cohen’s d < 0.50 is not relevant to education policy or practice. Thus, an introduction to sample size determination for pretest-posttest simple experimental designs is warranted. This study describes nuts and bolts of sample size determination, derives expressions for optimal design under differential cost per treatment and control units, provide convenient tables to guide sample size decisions for MRES values between 0.20 ≤ Cohen’s d ≤ 0.50, and describe the relevant software along with illustrations.

The Relationship Between Sample Sizes and Effect Sizes in Systematic Reviews in Education

2009 ◽  
Vol 31 (4) ◽  
pp. 500-506 ◽  
Author(s):  
Robert Slavin ◽  
Dewi Smith
Keyword(s):  
Sample Size ◽  
Effect Size ◽  
Secondary Mathematics ◽  
Significant Negative Correlation ◽  
Small Sample ◽  
Effect Sizes ◽  
Sample Sizes ◽  
Large Samples ◽  
Small Sample Sizes ◽  
The Relationship

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 the Best Evidence Encyclopedia. As predicted, there was a significant negative correlation between sample size and effect size. The differences in effect sizes between small and large experiments were much greater than those between randomized and matched experiments. Explanations for the effects of sample size on effect size are discussed.

scholarly journals Adequate Sample Sizes for a Three-Level Growth Model

2021 ◽  
Vol 12 ◽  
Author(s):  
Eunsoo Lee ◽  
Sehee Hong
Keyword(s):  
Sample Size ◽  
Growth Model ◽  
Multilevel Models ◽  
Growth Models ◽  
Intraclass Correlation ◽  
Small Sample ◽  
Sample Sizes ◽  
Level 3 ◽  
Unbiased Estimates ◽  
Small Sample Sizes

Multilevel models have been developed for addressing data that come from a hierarchical structure. In particular, due to the increase of longitudinal studies, a three-level growth model is frequently used to measure the change of individuals who are nested in groups. In multilevel modeling, sufficient sample sizes are needed to obtain unbiased estimates and enough power to detect individual or group effects. However, there are few sample size guidelines for three-level growth models. Therefore, it is important that researchers recognize the possibility of unreliable results when sample sizes are small. The purpose of this study is to find adequate sample sizes for a three-level growth model under realistic conditions. A Monte Carlo simulation was performed under 12 conditions: (1) level-2 sample size (10, 30), (2) level-3 sample size (30, 50, 100) (3) intraclass correlation at level-3 (0.05, 0.15). The study examined the following outcomes: convergence rate, relative parameter bias, mean square error (MSE), 95% coverage rate and power. The results indicate that estimates of the regression coefficients are unbiased, but the variance component tends to be inaccurate with small sample sizes.

A novel confidence interval for a single proportion in the presence of clustered binary outcome data

2019 ◽  
Vol 29 (1) ◽  
pp. 111-121
Author(s):  
Meghan I Short ◽  
Howard J Cabral ◽  
Janice M Weinberg ◽  
Michael P LaValley ◽  
Joseph M Massaro
Keyword(s):  
Confidence Interval ◽  
Clustered Data ◽  
Epidemiological Studies ◽  
Outcome Data ◽  
Small Sample ◽  
Interval Methods ◽  
Sample Sizes ◽  
Wide Range ◽  
Small Sample Sizes ◽  
Over Dispersion

Estimating the precision of a single proportion via a 100(1−α)% confidence interval in the presence of clustered data is an important statistical problem. It is necessary to account for possible over-dispersion, for instance, in animal-based teratology studies with within-litter correlation, epidemiological studies that involve clustered sampling, and clinical trial designs with multiple measurements per subject. Several asymptotic confidence interval methods have been developed, which have been found to have inadequate coverage of the true proportion for small-to-moderate sample sizes. In addition, many of the best-performing of these intervals have not been directly compared with regard to the operational characteristics of coverage probability and empirical length. This study uses Monte Carlo simulations to calculate coverage probabilities and empirical lengths of five existing confidence intervals for clustered data across various true correlations, true probabilities of interest, and sample sizes. In addition, we introduce a new score-based confidence interval method, which we find to have better coverage than existing intervals for small sample sizes under a wide range of scenarios.

A quantum leap in the reproducibility, precision, and sensitivity of gene expression profile analysis even when sample size is extremely small

2015 ◽  
Vol 13 (04) ◽  
pp. 1550018 ◽  
Author(s):  
Kevin Lim ◽  
Zhenhua Li ◽  
Kwok Pui Choi ◽  
Limsoon Wong
Keyword(s):  
Gene Expression ◽  
Sample Size ◽  
Small Sample Size ◽  
Statistical Tests ◽  
Transcript Level ◽  
Small Sample ◽  
Sample Sizes ◽  
Quantum Leap ◽  
Two Samples ◽  
Small Sample Sizes

Transcript-level quantification is often measured across two groups of patients to aid the discovery of biomarkers and detection of biological mechanisms involving these biomarkers. Statistical tests lack power and false discovery rate is high when sample size is small. Yet, many experiments have very few samples (≤ 5). This creates the impetus for a method to discover biomarkers and mechanisms under very small sample sizes. We present a powerful method, ESSNet, that is able to identify subnetworks consistently across independent datasets of the same disease phenotypes even under very small sample sizes. The key idea of ESSNet is to fragment large pathways into smaller subnetworks and compute a statistic that discriminates the subnetworks in two phenotypes. We do not greedily select genes to be included based on differential expression but rely on gene-expression-level ranking within a phenotype, which is shown to be stable even under extremely small sample sizes. We test our subnetworks on null distributions obtained by array rotation; this preserves the gene–gene correlation structure and is suitable for datasets with small sample size allowing us to consistently predict relevant subnetworks even when sample size is small. For most other methods, this consistency drops to less than 10% when we test them on datasets with only two samples from each phenotype, whereas ESSNet is able to achieve an average consistency of 58% (72% when we consider genes within the subnetworks) and continues to be superior when sample size is large. We further show that the subnetworks identified by ESSNet are highly correlated to many references in the biological literature. ESSNet and supplementary material are available at: http://compbio.ddns.comp.nus.edu.sg:8080/essnet .

scholarly journals A Pooled Analysis of Pharmacokinetic Variability Information for Common Probe Substrates Used in Drug-Drug Interaction Studies

Pharmacology ◽  
2018 ◽  
Vol 101 (3-4) ◽  
pp. 170-175
Author(s):  
Chunsheng He ◽  
Amber Griffies ◽  
Xuan Liu ◽  
Robert Adamczyk ◽  
Shu-Pang Huang
Keyword(s):  
Drug Interaction ◽  
Sample Size ◽  
Area Under The Curve ◽  
Pooled Analysis ◽  
Small Sample ◽  
Effective Sample Size ◽  
Maximum Plasma ◽  
Sample Sizes ◽  
Drug Drug Interaction ◽  
Small Sample Sizes

Sample size estimates for drug-drug interaction (DDI) studies are often based on variability information from the literature or from historical studies, but small sample sizes in these sources may limit the precision of the estimates obtained. This project aimed to create an intra-subject variability library of the pharmacokinetic (PK) exposure parameters, area under the curve, and maximum plasma concentration, for probes commonly used in DDI studies. Data from 66 individual DDI studies in healthy subjects relating to 18 common probe substrates were pooled to increase the effective sample size for the identified probes by 1.5- to 9-fold, with corresponding improvements in precision of the intra-subject PK variability estimates in this library. These improved variability estimates will allow better assessment of the sample sizes needed for DDI studies in future.

scholarly journals A Fuzzy Evaluation Model Aimed at Smaller-the-Better-Type Quality Characteristics

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2513
Author(s):  
Kuen-Suan Chen ◽  
Tsun-Hung Huang
Keyword(s):  
Confidence Interval ◽  
Quality Index ◽  
Evaluation Model ◽  
Quality Characteristics ◽  
Process Quality ◽  
Small Sample ◽  
Fuzzy Evaluation ◽  
Sample Sizes ◽  
Small Sample Sizes ◽  
Fuzzy Evaluation Model

Numerous key components of tool machines possess critical smaller-the-better-type quality characteristics. Under the assumption of normality, a one-to-one mathematical relationship exists between the process quality index and the process yield. Therefore, this paper utilized the index to produce a quality fuzzy evaluation model aimed at the small-the-better-type quality characteristics and adopted the model as a decision-making basis for improvement. First, we derived the 100(1 −α)% confidence region of the process mean and process standard deviation. Next, we obtained the 100(1 −α)% confidence interval of the quality index using the mathematical programming method. Furthermore, a one-tailed fuzzy testing method based on this confidence interval was proposed, aiming to assess the process quality. In addition, enterprises’ pursuit of rapid response often results in small sample sizes. Since the evaluation model is built on the basis of the confidence interval, not only can it diminish the risk of wrong judgment due to sampling errors, but it also can enhance the accuracy of evaluations for small sample sizes.

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