A Comparison of the Power of Wilcoxon's Rank-Sum Statistic to that of Student'st Statistic Under Various Nonnormal Distributions

Abstract

Computer generated Monte Carlo techniques were used to compare the power of Wilcoxon's rank-sum test to the power of the two independent means t test for situations in which samples were drawn from (1) uniform, (2) Laplace, (3) half-normal, (4) exponential, (5) mixed-normal, and (6) mixed-uniform distributions. Sample sizes studied were ( n1, n2) = (3,9), (6,6), (9,27), (18,18), (27,81), and (54,54). It was concluded that (1) generally speaking, the Wilcoxon statistic held very large power advantages over the t statistic, (2) asymptotic relative efficiencies were reasonably good indicators of the relative power of the two statistics, (3) results obtained from smaller samples were often markedly different from the results obtained from larger samples, and (4) because of the narrow ranges of population shapes and sample sizes investigated in some widely cited previous studies of this type, the conclusions reached in those studies must now be deemed questionable.