Combinations, Probabilities and Sample Size. Investigations into the Mann–Whitney U test

The Mann–Whitney U test is often used by students studying geography, sports science or psychology, yet it rarely appears in A-level mathematics syllabuses. This is a pity, because it provides considerable scope for thought and investigation by the student with a more mathematical background. As a non-parametric test, it is widely used to test whether two samples are “different” (for data that are unlikely to have come from a population that can be modelled by a normal distribution). This article shows how the test can be explained from “first principles”, using simple ideas of combinations and probabilities of equally likely outcomes. The mathematics student can understand the logic behind the test and can determine the minimum sample sizes required for a test of significance.