The Kruskal Wallis test can not be recommended
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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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