Improved bonferroni procedures for testing overall and pairwise homogeneity hypotheses

Abstract

Simes' (1986) improved Bonferroni test is verified by simulations ^∗to control the α-level when testing the overall homogeneity hypothesis with all pairwise t statistics in a balanced parallel group design. Similarly, this result was found to hold (for practical purposes) in various underlying distributions other than the normal and in some unbalanced designs. To allow the use of step-up procedures based on pairwise t statistics, simulations were used to verify that Simes' test, when applied to testing multiple subset homogeneity hypotheses with pairwise t statistics also keeps the level ♣ α. Some robustness as above was found here too. Tables of the simulation results are provided and an example of a step-up Hommel-Shaffer type procedure with pairwise comparisons is given.

Keywords:

• Dependent comparisons
• Intersection hypothesis
• Multiple hypothesis testing