Students learn to examine the distributional assumptions implicit in the usual t-tests and<br><br>associated confidence intervals, but are rarely shown what to do when those assumptions<br><br>are grossly violated. Three data sets are presented. Each data set involves a different<br><br>distributional anomaly and each illustrates the use of a different nonparametric test. The<br><br>problems illustrated are well-known, but the formulations of the nonparametric tests<br><br>given here are different from the large sample formulas usually presented. We restructure<br><br>the common rank-based tests to emphasize structural similarities between large sample<br><br>rank-based tests and their parametric analogs. By presenting large sample nonparametric<br><br>tests as slight extensions of their parametric counterparts, it is hoped that nonparametric<br><br>methods receive a wider audience.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education