REVISITING THE t TEST ON RANKS AS AN ALTERNATIVE TO THE WILCOXON RANK-SUM TEST

Abstract

Summary.-In comparison with the Student t test, the test on the ranks of scores has been shown to be slightly less powerful than the Wilcoxon Rank-Sum test conducted on the original scores For real smooth and symmetric data sets because it does not provide a correction for ties or continuity. Here it is demonstrated that the t test on ranks is nonetheless superior to the usual t test for real data that are skewed or otherwise severely nonnormally distributed. The advice to use the nonparametric Wilcoxon Rank-sum test in applied data analysis is based on studies of its statistical power in comparison with the parametric t test on data sampled from theoretical nonnormal distributions (Blair & Higgins, 1980a, 1980b). The Wilcoxon test has been - shown to be as much as three or four times more powerful than the t test when data are highly skewed or come from populations with heavy tails (Sawdowsky & Blair, 1992). When data are normally hstributed, the Wilcoxon test is typically only slightly less powerful (e.g., about 0.02) than its parametric counterpart. Therefore, there is much to gain if the population is nonnormdy distributed and little to lose in using the Wilcoxon test when the data come from a normal distribution. Given the prevalence of nonnormality in applied psychological and educational data (Ahcceri, 1989), researchers should give serious consideration to performing the nonparametric Wilcoxon test instead of the classic t test. Zirnmerman and Zurnbo (199O),.among others, noted that an analog to the Wilcoxon test can easily be computed by simply ranking the original scores, and then applying the t test on those ranks. This technique also has the advantage of using the critical values of the t test, which are found in many textbooks and computer statistics packages. They referred to this procedure as being alpha equivalent, meaning that whatever statistical conclusion would be obtained by the Wilcoxon Rank-Sum test on the original scores WLU be the same as that obtained by computing the t test on the ranks of the original scores. Sadowsky and Brown (1991) investigated the comparative power properties of the two procedures for a real data set identified by Micceri (1989)