On the Relative Power of the Paired Samples t Test and Wilcoxon's Signed-Ranks Test.

Monte Carlo methods were employed 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: (1) each of the two statistics was more powerful than the other in given situations; (2) the power advantages of the t test under normal theory were small; (3) in the nonnormal situation the t test never attained more than modest advantages over the Wilcoxon test; (4) 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 (5) 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. (Author)