Sample Sizes Using Hochberg's Procedure for Two Comparisons with Three Different Study Designs

When simultaneous comparisons are performed, a procedure must be employed to control the overall level (also known as the Type I Error rate). Hochberg's stepwise testing procedure is often used and here determination of the sample size needed to achieve a specified power for two pairwise comparisons when observations follow a normal distribution is addressed. Three different scenarios are considered: subsets defined by a baseline criterion, two treatments compared to a control, or one set of subjects nested within the other. The solutions for these three scenarios differ and are examined. The sample sizes for the differences in success probabilities for binomial distributions are presented using the asymptotic normality. The sample sizes and power using Hochberg's procedure are compared to the corresponding results using the Bonferroni approach.