Implications of random cut‐points theory for the Mann‐Whitney and binomial tests

Through random cut‐points theory, the author extends inference for ordered categorical data to the unspecified continuum underlying the ordered categories. He shows that a random cut‐point Mann‐Whitney test yields slightly smaller p ‐values than the conventional test for most data. However, when at least P % of the data lie in one of the k categories (with P = 80 for k = 2, P = 67 for k = 3,…, P = 18 for k = 30), he also shows that the conventional test can yield much smaller p ‐values, and hence misleadingly liberal inference for the underlying continuum. The author derives formulas for exact tests; for k = 2, the Mann‐Whitney test is but a binomial test.