Pairwise Comparisons Using Ranks in the One-Way Model

Abstract

The Wilcoxon rank sum test for two independent samples and the Kruskal–Wallis rank test for the one-way model with k independent samples are very competitive robust alternatives to the two-sample t-test and k-sample F-test when the underlying data have tails longer than the normal distribution. However, these positives for rank methods do not extend as readily to methods for making all pairwise comparisons used to reveal where the differences in location may exist. Here, we show that the closed method of Marcus et al. applied to ranks is quite powerful for both small and large samples and better than any methods suggested in the list of applied nonparametric texts found in the recent study by Richardson. In addition, we show that the closed method applied to means is even more powerful than the classical Tukey–Kramer method applied to means, which itself is very competitive for nonnormal data with moderately long tails and small samples.

KEYWORDS:

• Bonferroni method
• Closed testing method
• Familywise error rate
• Joint ranking
• Multiple comparisons
• Pairwise ranking
• Tukey–Kramer method

Supplementary Materials

supp2.7z7-Zip file of computer code and expanded Monte Carlo results not included in the article.

Acknowledgments

We are grateful to Peter Westfall for suggesting use of the closed method with ranks.