The Kruskal-Wallis test (H-test) is a hypothesis test for multiple independent samples, which is used when the requirements for a one factor analysis of variance are not met.
Since the Kruskal-Wallis test is a nonparametric test (also called a distribution-free procedure), the data used do not have to be normally distributed, in contrast to analysis of variance. The only requirement is that the data be ordinal scale.
In the Kruskal-Wallis test, ordinal variables are sufficient because in nonparametric procedures, it is not the differences of the values that are used, but the rank places (which value is larger, which is smaller). Therefore, the Kruskal-Wallis test is also often called rank variance analysis according to Kruskal and Wallis.
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