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Kruskal-Wallis test is a one-way ANOVA ranks developed by William Kruskal and W. Allen Wallis. This is a non-parametric test used to examine whether the given sample originates from the same distribution and compare two or more independent samples of equal or different sample sizes. The one-way analysis of variance is the equivalent of Kruskal-Wallis test.
The stochastic dominance of one sample over the other sample is indicated by the Kruskal-Wallis test. But the test fails to examine where the stochastic dominance take place in the sample or for how many pairs in the sample are stochastically dominated. To understand about the stochastic dominance specifically, some other tests are used.
Assumptions
To apply the Kruskal Wallis test the variables of the study must fulfill the following conditions:
⦿ There should be one independent variable with two or more levels. Generally, Mann Whitney tests are used for two levels of variables, whereas; Kruskal Wallis tests are used commonly with three levels of independent variables.
⦿ This test is applicable to dependent variables with ordinal scale, interval scale or ratio scale.
⦿ According to the assumption of independence, Kruskal Wallis test is applicable when the observations are made independent. That is, there should not be any relationship between the members in each group or between groups.
⦿ All groups must have equal or same distribution.