This paper describes the comparison of the anova and the Kruskal-Wallis test by means of the power when violating the assumption about normally distributed populations. The permutation method is used as a simulation method to determine the power of the test. It appears that in the case of asymmetric populations the non-parametric Kruskal-Wallis test performs better than the parametric equivalent anova method.
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Tanja Van Hecke (2012) studied this question.
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