Compare and contrast the MannWhitney aka Wilcoxon Rank Sum T

Compare and contrast the Mann-Whitney (aka Wilcoxon Rank Sum) Test with the Median test. Discuss their similarities/differences.

Solution

the Mann-Whitney and the equivalent Wilcoxon test (hereafter called the Mann-Whitney-Wilcoxon test) are rank sum tests and not median tests. Basically, the Mann-Whitney-Wilcoxon 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.