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Combining the t test and Wilcoxon's rank-sum test

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  • Markus Neuh�user

Abstract

In the two-sample location-shift problem, Student's t test or Wilcoxon's rank-sum test are commonly applied. The latter test can be more powerful for non-normal data. Here, we propose to combine the two tests within a maximum test. We show that the constructed maximum test controls the type I error rate and has good power characteristics for a variety of distributions; its power is close to that of the more powerful of the two tests. Thus, irrespective of the distribution, the maximum test stabilizes the power. To carry out the maximum test is a more powerful strategy than selecting one of the single tests. The proposed test is applied to data of a clinical trial.

Suggested Citation

  • Markus Neuh�user, 2015. "Combining the t test and Wilcoxon's rank-sum test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2769-2775, December.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:12:p:2769-2775
    DOI: 10.1080/02664763.2015.1070809
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    References listed on IDEAS

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    1. Hisashi Tanizaki, 1997. "Power comparison of non-parametric tests: Small-sample properties from Monte Carlo experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(5), pages 603-632.
    2. R. Clifford Blair & James J. Higgins, 1980. "A Comparison of the Power of Wilcoxon's Rank-Sum Statistic to that of Student'st Statistic Under Various Nonnormal Distributions," Journal of Educational and Behavioral Statistics, , vol. 5(4), pages 309-335, December.
    3. Erich Lehmann, 2009. "Parametric versus nonparametrics: two alternative methodologies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 397-405.
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