Kruskal-Wallis "Analysis of Variance" by Ranks. We have k groups of observations. Pool all N observations and arrange them in order of size, then rank them, assigning ties the same rank.

Now, after regrouping the observations, find the sum of the ranks in each group. Compute H as shown:

The value of H can be referred to a table of the chi-square distribution with k-1 degrees of freedom, for a test of the hypothesis that all k population distributions are identical.