The Kruskal-Wallis test
The KW statistic has the form of SST based on ranks, so a permutation KW test can be based on SST(ranks). Alternatively, we can obtain a large sample approximation to the permutation distribution by using a scaling factor of 1/SR2 , where SR2 = N(N+1)/12 for ranks without ties.
For data sets with ties, SR2 is calculated as the sample variance of the adjusted ranks.
Conditions favoring the K-W test; use of general scores.