Comparative Robustness of Rank-Based Multiple Comparison Procedures under Non-Normality and Heteroscedasticity

Abstract

This study compares the performance of three rank-based nonparametric tests—Brunner–Munzel (BM), Bootstrap Rank Welch (BRW), and Fitted (FT) tests for multiple comparisons across three independent groups under conditions of non-normality and heteroscedasticity. Simulation data were generated using SAS 9.4 under normal, t, and lognormal distributions with three balanced sample sizes (10, 30 and 50 per group) and variance ratios (1:1:1, 1:2:3, and 1:4:7), based on 1,000 replications. The tests were evaluated according to Bradley’s robustness criterion for Type I error control and statistical power. The results show that the BRW test achieves the highest power across t and lognormal distributions while maintaining Type I error control for all sample sizes. Under normality, the FT test demonstrates the strongest power but fails to control the error rate for large samples. The BM test remains stable in most conditions, providing a balance between robustness and efficiency. A practical decision rule is proposed to guide the selection of appropriate nonparametric methods for analyzing multiple comparisons under unequal variances and non-normal distributions.