Interval-based versus decision theoretic criteria for the choice of sample size

Abstract

SUMMARY Several different criteria for Bayesian sample size determination have recently been proposed. Bayesian approaches are natural, since at the planning stage of an experiment one is forced to consider prior notions about unknown parameter values that may affect the choice of a final sample size. For this, all the methods consider a prior distribution over the unknown parameters. Differences between the methods have been driven by the type of inferences that will be made, e.g. hypothesis testing or interval estimation, the latter based on posterior means and variances or highest posterior density regions. A more fundamental question, however, is whether to introduce formally a loss or utility function to aid in choosing the sample size. In this paper, we discuss the advantages and disadvantages of taking a fully decision theoretic approach versus one of the simpler approaches, which only implicitly consider utilities in balancing increased precision against the increased costs associated with larger sample sizes. Throughout, we emphasize the practical aspects of sample size estimation, raising issues that would face the consumer of statistics in selecting a sample size in a given experiment.