The Median procedure is designed to test the null hypothesis that groups have the same median. Because the test makes no assumptions about the data other than that the median is a valid measure of center, it can be used in a variety of situations. It is especially appealing when you suspect that the test variable has different distributions by group. One weakness of the test is that it is not designed to take advantage of distance from the median.

If you would like to take advantage of these distances and can assume that the groups have similar distributions on your test variable, then you should consider using the Kruskal-Wallis test. The Kruskal-Wallis test is a popular nonparametric alternative to the standard one-way analysis of variance. It is appropriate when your test variable is ordinal or its distribution does not meet the assumptions of standard ANOVA. The only assumptions made by the test are that the test variable is at least ordinal, and that its distribution is similar in all groups. Like the F test in standard ANOVA, Kruskal-Wallis does not tell you how the groups are different, only that some difference is present. You could consider using the Mann-Whitney U test for pairwise group comparisons.