Abstract:
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The Kruskal-Wallis (KW) test, also known as the one-way analysis of variance (ANOVA) by ranks test, is the most common and routinely used nonparametric alternative to the classical ANOVA F test. The null hypothesis for the KW test is that populations are identical but the in practice the result of the test is interpreted as whether or not there is a difference in the location parameters. This research examines the Type-I error robustness of the KW test under broader and more practical assumptions, where the assumption of identical distribution is violated. The effects of non-normality, unequal variances and unbalanced samples are studied. Based on a wide ranging simulation study, our paper shows that the KW test is lack of robustness in many situations. Other alternatives to KW test, such as ANOVA F test, Mood's median test, and Friedman test are also examined and made comparison.
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