Kruskal-Wallis Test

The Kruskal-Wallis Test is a generalized U-Test for more than two groups. It tests H0 that data from k populations are not different.

Requirements:

Data must be ordinal (rank-order) scaled.

Distribution is free

Idea:

The test works like the Mann-Whintey U-Test. The data from all groups are brought together in one rank order. For each group the sum of ranks T_i and mean rank is then computed. Whereas the total sum of ranks is:

with

The test value H is computed as follows:

whereas

n_i = sample size of group i

H is Chi-Square distributed with k-1 degrees of freedom

If there are tied ranks H is corrected as follows:

whereas

t_i = Number of subjects sharing rank i
p = number of tied ranks

and