Teaching rank-based tests by emphasizing structural similarities to corresponding parametric tests

Students learn to examine the distributional assumptions implicit in the usual t-tests and associated confidence intervals, but are rarely shown what to do when those assumptions are grossly violated. Three data sets are presented. Each data set involves a different distributional anomaly and each illustrates the use of a different nonparametric test. The problems illustrated are well-known, but the formulations of the nonparametric tests given here are different from the large sample formulas usually presented. We restructure the common rank-based tests to emphasize structural similarities between large sample rank-based tests and their parametric analogs. By presenting large sample nonparametric tests as slight extensions of their parametric counterparts, it is hoped that nonparametric methods receive a wider audience.