# Kruskal-Wallis Test for H0: ranks differ between groups and H1: ranks do not differ

The traditional Kruskal-Wallis Test tests null hypothesis $H_A$: ranks do not differ between groups against the alternative hypothesis $H_B$ in which the ranks differ between groups. However, what if we are interested in rejecting $H_B$ instead of $H_A$. What will the distribution of the test statistic look like?

I'm interested in analytic solutions. Possibly, an analytic solution requires further information and assumptions about the mechanism that generates unequal means. Please, list the assumptions.

My guess is that this is not a simple problem, since I couldn't find any analytic formulas for the calculation of power of the traditional Kruskal-Wallis test.