Sample Size Determination for Bayesian Informative Hypothesis Testing

Abstract

This dissertation discusses sample size determination to obtain the desired Bayes factor if the researchers use the Bayes factor to evaluate the null, unconstrained, and informative hypotheses. The informative hypothesis can express the specific expectation of the researchers through (in)equality constraints among parameters of interest in a statistical model. The evidence in favor of one hypothesis compared to another can be quantified by the Bayes factor. If the Bayes factor cannot reach a convincing value in a sample of a particular size, the study would produce an inconclusive result. Thus, Bayesian statisticians may be interested in the determination of sample sizes to obtain the desired Bayes factor. This dissertation develops an R package SSDbain to help applied researchers to plan the sample size if they use the Bayes factor to evaluate hypotheses. This package can be used to calculate the sample size for null, unconstrained, and informative hypotheses for a two-sample t-test, one-way ANOVA, and multiple linear regression. The sample size is determined such that the probability that the Bayes factor exceeds a pre-specified threshold reaches a pre-specified value. With the tool provided, the researchers can easily plan their sample size before data collection.