The Kruskal Wallis test can not be recommended

TL;DR

This paper critiques the limitations of the Kruskal-Wallis test and proposes a new double maximum test that offers better robustness and flexibility for various statistical analyses.

Contribution

It introduces a novel double maximum test that improves upon Kruskal-Wallis by addressing its limitations and extending applicability to complex experimental designs.

Findings

The new test is more robust to arbitrary alternatives.

It provides better sensitivity for location, scale, and shape effects.

R-code for implementation is provided.

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.