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Quantifying and Incorporating Sources of Variability and Uncertainty in Statistical Analyses with Very Small Sample Sizes (303561)

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Keywords: Applied statistics, frequentist methods, Bayesian methods, small sample size

Statisticians sometimes have to conduct analyses comparing concentrations of chemicals based on data sets with very small sample sizes of 5 or less. Traditional approaches for estimating mean differences and variability in concentrations of these chemicals may not provide meaningful results. We present an example illustrating and comparing one frequentist and two Bayesian approaches used to estimate the difference in concentrations between two products and the variability of this difference. In addition, we discuss the use of a Form 1 null hypothesis if the analytic goal is to demonstrate that concentrations for two products are equivalent. In this case, equality of population means must be the burden of proof (i.e., the alternative hypothesis) and a Form 2 null hypothesis (H0 = population means are different) should be considered. Otherwise, insufficient power greatly increases the likelihood of incorrectly claiming equality of the concentrations of two products which are, in truth, different. This presentation is geared toward a broad audience; no prior experience with Bayesian methods is required.