Some clarifications regarding power and Type I error control for pairwise comparisons of three groups

A previous study in this journal used Monte Carlo simulations to compare the power and familywise Type I error rates of ten multiple-testing procedures in the context of pairwise comparisons in balanced three-group designs. The authors concluded that the Benjamini–Hochberg procedure was the "best."' However, they did not compare the Benjamini–Hochberg procedure to commonly used multiple-testing procedures that were developed specifically for pairwise comparisons, such as Fisher's protected least significant difference and Tukey's honest significant difference. Simulations in the present study show that in the three-group case, Fisher's method is more powerful than both Tukey's method and the Benjamini–Hochberg procedure. Compared to the Benjamini–Hochberg procedure, Tukey's method is shown to be less powerful in terms of per-pair power (average probability of significance across the tests of false null hypotheses), but more powerful in terms of any-pair power (probability of significance in at least one test of a false null hypothesis). Additionally, the present study shows that small deviations from normality in the population distributions have little effect on the power of pairwise comparisons, and that the previous study's finding to the contrary was based on a methodological inconsistency.