Why is the Mann-Whitney significant when the medians are equal?
A client has sent us the following question: Q. I ran a Mann-Whitney test on two independent groups that have equal medians, the results were significant. I thought that the Mann-Whitney tested differences in medians. Why is the Mann-Whitney test be significant when the medians are equal? A. The answer is that the Mann-Whitney and the equivalent Wilcoxen test (hereafter called the Mann-Whitney-Wilcoxen test) are rank sum tests and not median tests. Basically, the Mann-Whitney-Wilcoxen test ranks all of the observations from both groups and then sums the ranks from one of the groups which is compared with the expected rank sum. It is possible, although not very common, for groups to have different rank sums and yet have equal or nearly equal medians. An example is given below. Consider the following example dataset of 120 observation (60 in each group) that has equal medians and a significant Mann-Whitney-Wilcoxen test. +—————–+ | y grp freq | |—————–| | -2 1 20 |
