The Kruskal Wallis test can not be recommended

2023/02/11 by Ludwig A. Hothorn, Hothorn, Ludwig A.
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2302.05647

openalex publication_date 2023/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Although the Kruskal-Wallis (KW) test is widely used, it should not be recommended: it is not robust to arbitrary alternatives, it is only a global test without confidence intervals for the marginal hypotheses, it is inherently defined for two-sided hypotheses, it is not very suitable for pre/post hoc test combinations and hard to modified for factorial designs or the analysis of covariance. As an alternative a double maximum test is proposed: a maximum over multiple contrasts against the grand mean (approximating global power as a linear test statistics) and a maximum over three rank scores, sensitive for location, scale and shape effects. The joint distribution of this new test is achieved by the multiple marginal models approach. Related R-code is provided.

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