The comparative power of the independent-samples t-test and Wilcoxon Rank Sum test in non-normal distributions of real data sets in education and psychology

摘要

Historically, small samples Monte Carlo studies testing the robustness and comparative power properties of the independent-samples t-test and Wilcoxon Rank Sum test have been restricted to known mathematical distributions. Recently, the prevalence of nonnormally distributed data sets has been recognized in the fields of education and psychology. This, in turn, has generated a need in understanding appropriate test application under these conditions. Using Monte Carlo techniques, the purpose of this study was to assess the Type I error properties and comparative power of the Wilcoxon Rank Sum test (algebraic equivalent: t-test on the ranks of original scores) and the independent samples t-test to violations of normality. The sampling is from eight real distributions in education and psychology which were identified in a study by Micceri (1989). Sample sizes (n1, n2) = (10, 10), (5, 15), (30, 30), and (15, 45) were used, with nominal alpha set at.05. Eight treatment effects ranging from.25$sigma$ to 2.00$sigma$ were used for each distribution and sample size to measure shift in location parameters.;Comparative power results demonstrated that in those distributions considered relatively symmetric, the t-test maintained its reputation as being the Uniformly Most Powerful Unbiased test under normal theory. Yet, the power advantages were extremely modest and in most instances near equivalent to the Wilcoxon Rank Sum test. When the distribution demonstrated extreme skews or heavy tails, the power advantages overwhelmingly favored the Wilcoxon Rank Sum test.;The t-test generated nonrobust results to Type I error in 25% (8 of 32) of the distributions and sample sizes studied, with most occurring in the distributions with extreme skews. In addition, the WRS also demonstrated nonrobust results and obscure power results in a distribution characterizing extreme ties.;It is recommended when the characteristics of a population are known to be relatively symmetric the t-test should be applied. When distributions consist of heavier tails or skews the WRS should be the test of choice. In turn, when population characteristics are unknown, the WRS is recommended because of the magnitude of the power differences in extreme skews, the modest variations in symmetric distributions, and the comparative power and robustness of the WRS to Type I and Type II errors in small, medium, and large effect sizes.