Step-Down Multiple Comparison Procedures Using Medians and Permutation Tests

Richter and McCann (2007) presented a median-based multiple comparison procedure for assessing evidence of group location differences. The sampling distribution was based on the permutation distribution of the maximum median difference among all pairs, and provides strong control of the FWE. This idea is extended to develop a step-down procedure for comparing group locations. The new step-down procedure exploits logical dependencies between pairwise hypotheses and provides greater power than the single-step procedure, while still maintaining strong FWE control. The new procedure can also be a more powerful alternative to existing methods based on means, especially for heavy-tailed distributions