Bayesian vs Frequentist Power Functions to Determine the Optimal Sample Size: Testing One Sample Binomial Proportion Using Exact Methods

In order to avoid the drawbacks of sample size determination procedures based on classical power analysis, it is possible to define analogous criteria based on ‘hybrid classical-Bayesian’ or ‘fully Bayesian’ approaches. We review these conditional and predictive procedures and provide an application, when the focus is on a binomial model and the analysis is performed through exact methods. The distinction between analysis and design prior distributions is essential for the practical implementation of the criteria: some guidelines for choosing these priors are discussed, and their impact on the required sample size is examined.