This article considers a J by K ANOVA design where all JK groups are dependent and where groups are to be compared based on medians. Two general approaches are considered. The first is based on an omnibus test for no main effects and no interactions and the other tests each member of a collection of relevant linear contrasts. Based on an earlier paper dealing with multiple comparisons, an obvious speculation is that a particular bootstrap method should be used. One of the main points here is that, in general, this is not the case for the problem at hand. The second main result is that, in terms of Type I errors, the second approach, where multiple hypotheses are tested based on relevant linear contrasts, performs about as well or better than the omnibus method, and in some cases it offers a distinct advantage.