Post-hoc analysis

If the Kruskal-Wallis test is significant one probably wants to know which of the groups are different. BrightStat offers two different methods for post-hoc analysis:

The critical difference of the mean ranks after Conover (1971, 1980, 1999):

whereas

= critical difference of mean ranks of group i and j
= critical t-value with N-k degrees of freedom
n_i = sample size of group i
n_j = sample size of group j

The critical difference of the mean ranks after Schaich and Hamerle (1984):

whereas

= critical difference of mean ranks of group i and j
= critical Chi-Square-value with k-1 degrees of freedom
n_i = sample size of group i
n_j = sample size of group j

The method after Schaich and Hamerle is exact but lacks a bit of power, whereas the method of Conover is approximative and more liberal.