Comparison of the Power of the Paired Samples t Test to That of Wilcoxon's Signed-Ranks Test Under Various Population Shapes

Monte Carlo methods were used to assess the relative power of the paired samples t test and Wilcoxon's signed-ranks test under ten population shapes. Results of the study indicated that: (a) Each statistic was more powerful than the other in given situations; (b) the power advantages of the t test under normal theory were small; (c) in the nonnormal situation, the t test never attained more than modest advantages over the Wilcoxon test; (d) the Wilcoxon test was not only more often the more powerful test, but in those situations where it was more powerful, it was often vastly so; and (e) the magnitude of the Wilcoxon's power advantage often increased with increases in sample size. It was concluded that, insofar as these two statistics are concerned, the often-repeated claim that parametric tests are more powerful than nonparametric tests is not justified.