Bayesian sample size determination for normal means and differences between normal means

Abstract

Several criteria for Bayesian sample size determination based on lengths and coverages of posterior credible intervals have recently appeared in the literature. Some but not all of these have been applied to estimating sample sizes for normal distributions. In this paper, these criteria are applied to find sample sizes for single normal means and differences between two normal means, both when the variances are known and when they are unknown. Fully Bayesian approaches as well as mixed Bayesian-- likelihood approaches are considered. In the case of the difference between two normal means, situations with equal and unequal variances of the two distributions are considered. In addition to the rule that assumes equally sized groups, optimal solutions are determined which allow the sizes drawn from the two populations to differ while minimizing their sum. Exact closed form solutions are available for many of the situations, whereas numerical algorithms are described for others.