#### Abstract

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.