Bayesian Sample Size Calculations for Comparing Two Binomial Proportions

Sample size determination is a popular problem in medical Studies. A new approach to calculate the sample size is developed by combining Bayesian and frequentist views when a hypothesis test between two binomial proportions is conducted. The sample size is calculated according to Bayesian posterior decision function and the power of the most powerful test. Sample sizes for two cases that the two proportions are equal to a fixed or to a random Value are investigated. Two numerical examples are used to Illustrate the proposed methodologies.