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Zimmerman DW, Zumbo BD. The Relative Power of the Wilcoxon-Mann-Whitney Test and Student t Test Under Simple Bounded Transformations. J Gen Psychol. 1990;117(4):425-436doi: 10.1080/00221309.1990.9921148.
Zimmerman, D. W., & Zumbo, B. D. (1990). The Relative Power of the Wilcoxon-Mann-Whitney Test and Student t Test Under Simple Bounded Transformations. The Journal of general psychology, 117(4), 425-436. https://doi.org/10.1080/00221309.1990.9921148
Zimmerman, Donald W, and Zumbo, Bruno D. "The Relative Power of the Wilcoxon-Mann-Whitney Test and Student t Test Under Simple Bounded Transformations." The Journal of general psychology vol. 117,4 (1990): 425-436. doi: https://doi.org/10.1080/00221309.1990.9921148
Zimmerman DW, Zumbo BD. The Relative Power of the Wilcoxon-Mann-Whitney Test and Student t Test Under Simple Bounded Transformations. J Gen Psychol. 1990 Oct;117(4):425-436. doi: 10.1080/00221309.1990.9921148. PMID: 28142339.
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J Gen Psychol. 1990 Oct;117(4):425-436. doi: 10.1080/00221309.1990.9921148.

The Relative Power of the Wilcoxon-Mann-Whitney Test and Student t Test Under Simple Bounded Transformations.

The Journal of general psychology

Donald W Zimmerman, Bruno D Zumbo

Affiliations

  1. a Department of Psychology , Carleton University , Ottawa , Ontario , Canada.

PMID: 28142339 DOI: 10.1080/00221309.1990.9921148

Abstract

The Wilcoxon-Mann-Whitney test and related nonparametric statistical methods based on ranks have been found to be more powerful than parametric tests such as the Student t test for various heavy-tailed distributions, including the exponential, Cauchy, and mixed-normal distributions, both in the asymptotic limit and for relatively small sample sizes. The present computer simulation study provided evidence that this power advantage results from reduction of the influence of outliers by transformation of measures to ranks. Random samples were obtained from these heavy-tailed distributions, and the initial sample values were mapped onto several bounded sets of numbers that are not ranks, including a set having a random component in which order was not preserved. An ordinary Student t test performed on the transformed values in most cases was considerably more powerful than one performed on the original values and also as powerful as the Wilcoxon-Mann-Whitney test.

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