My question arises from a paper I read. Two groups are compared using the non-parametric Kruskal-Wallis test. Neither group has data that is normally distributed. Group A data is skewed low and has a mean that is lower than the median. Group B data is skewed high and has a mean that is higher than the median. Group A has a lower mean but a higher median than group B. The analysis provided in the paper stated the groups are different (p<0.01) by Kruskal Wallis (which in itself surprised me). But they also stated group B had higher results than group A, but that is based on the mean, but if one used the median value you would assume that A was higher than B. Besides showing that the groups are different, does Kruskal Wallis allow you to state which is the higher of the two?