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A Kruskal-Wallis test is used to compare a continuous outcome in matched samples where there are...

A Kruskal-Wallis test is used to compare a continuous outcome in matched samples where there are greater than two matches.

Math   Statistics-And-Probability   
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The Kruskal-Wallis test is a nonparametric test, that is used when the assumptions of one-way ANOVA do not meet. Both the Kruskal-Wallis test and one-way ANOVA assess for significant differences on a continuous dependent variable by a categorical independent variable. In the ANOVA, we have to assume that the dependent variable is normally distributed and there is approximately equal variance on the scores across groups. But, when using the Kruskal-Wallis Test, we do not have to make any of these assumptions. Thus, the Kruskal-Wallis test can be used for both continuous and ordinal-level dependent variables. However, like most non-parametric tests, the Kruskal-Wallis Test is not as powerful as the ANOVA.

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