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.
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References
1.
BlairR. C., & HigginsJ. J. (1980a) A comparison of the power of the t test and the Wilcoxon statistics when samples are drawn from a certain mixed normal distribution. Evaluation Review, 4, 645–656.
2.
BlairR. C., & HigginsJ. J. (1980b) A comparison of the power of Wilcoxon's rank-sum statistic to that of Student's t statistic under various non-normal populations. Journal of Educational Statistics, 5, 309–335.
3.
MicceriT. (1986) A futile search for that statistical chimera of normality. Paper presented at the annual meeting of the Florida Educational Research Association, Tampa, FL.
4.
MicceriT. (1989) The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156–166.
5.
SawilowskyS. S., & BlairR. C. (1992) A more realistic look at the robustness and Type II error properties of the t test to departures from population normality. Psychological Bulletin, 111, 352–360.
6.
SawilowskyS. S., & BrownM. T. (1991) On using the t test on ranks as an alternative to the Wilcoxon test. Perceptual and Motor Skills, 72, 860–862.
7.
SawilowskyS. S., & HillmanS. B. (1992) Power of the independent samples t test under a prevalent psychometric measure distribution. Journal of Consulting and Clinical Psychology, 60, 240–243.
8.
ZimmermanD. W., & ZumboB. D. (1990) Effects of outliers on the relative power of parametric and nonparametric statistical tests. Perceptual and Motor Skills, 71, 339–349.
