Power, Type I, and Type III Error Rates of Parametric and Nonparametric Statistical Tests

The author used Monte Carlo methods to assess the relative merits of using the Student t test and the Wilcoxon rank sum test under 4 population distributions and 6 sample-size pairings. The results of the simulation indicated that when the null hypothesis was true, the Student t test and the Wilcoxon rank sum test maintained Type I errors at the nominal level for normally distributed populations, but only the Wilcoxon rank sum test maintained the Type I error rate at a nominal level for nonnormal distributions. When the populations were not normally distributed and the null hypothesis was false, the Wilcoxon rank sum test demonstrated (a) a consistent advantage in statistical power, (b) fewer Type III errors, and (c) proportionally fewer rejections that were in the wrong direction. When sample sizes were unequal, those advantages became even more pronounced.