This nonparametric is to be used when you have k independent samples, in order to determine if the samples come from a single population or if at least one sample comes from a different population than the others. The Kruskal-Wallis nonparametric test is used to test if k samples (k>2) come from the same population or populations with identical properties as regards a position parameter (the position parameter is conceptually close to the median, but the Kruskal-Wallis test takes into account more information than just the position given by the median). This nonparametric test generalizes the Wilcoxon-Mann-Whitney test, which is used to compare only two groups. In other words, they are valid in a broader range of situations (fewer conditions of validity). They can thus be applied even if parametric conditions of validity are not met. These tests are more robust than parametric tests. Nonparametric tests do not rely on any distribution. The Kruskal-Wallis test is often used as an nonparametricalternative to the one-way analysis of variance (ANOVA) where the assumptions are not met (like the assumption of normality).
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