The Kruskal-Wallis test compares several populations on the basis of independent random samples from each population. This is the one-way analysis of variance setting.
The null hypothesis for the Kruskal-Wallis test is that the distribution of the response variable is the same in all the populations. The alternative hypothesis is that responses are systematically larger in some populations than in others.
The Kruskal-Wallis statisticH can be viewed in two ways. It is essentially the result of applying one-way ANOVA to the ranks of the observations. It is also a comparison of the sums of the ranks for the several samples.
When the sample sizes are not too small and the null hypothesis is true, H for comparing I populations has approximately the chi-square distribution with I−1 degrees of freedom. We use this approximate distribution to obtain P-values.