On testing equivalence of three populations

We consider analysis of clinical trials in which the objective is to show that three populations are equivalent. Equivalence is defined in terms of delta, the maximum difference in population means; a one-sided hypothesis test of delta is considered. We provide the distribution of the maximum pairwise difference in sample means, and we use this distribution to find critical values for tests of size 0.100, 0.050, 0.025, and 0.010. When standard errors are not equal among the three treatments, a simple adjustment is proposed to control the type I error rate. These tests are applied to studying the equivalence of three binomial proportions. Test-based confidence intervals are discussed. Two examples illustrate the proposed methods.