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Detecting Treatment Effects with Small Samples: The Power of Some Tests Under the Randomization Model

Published online by Cambridge University Press:  01 January 2025

Bryan Keller
Bryan Keller*
Affiliation:
University of Wisconsin–Madison
*
Requests for reprints should be sent to Bryan Keller, University of Wisconsin–Madison, Madison, WI, USA. E-mail: bskeller@wisc.edu
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Abstract

Randomization tests are often recommended when parametric assumptions may be violated because they require no distributional or random sampling assumptions in order to be valid. In addition to being exact, a randomization test may also be more powerful than its parametric counterpart. This was demonstrated in a simulation study which examined the conditional power of three nondirectional tests: the randomization t test, the Wilcoxon–Mann–Whitney (WMW) test, and the parametric t test. When the treatment effect was skewed, with degree of skewness correlated with the size of the effect, the randomization t test was systematically more powerful than the parametric t test. The relative power of the WMW test under the skewed treatment effect condition depended on the sample size ratio.

Keywords

randomization testpermutation testWilcoxon–Mann–Whitney testnonparametricexact Type I error rateconditional power
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 2 , April 2012 , pp. 324 - 338
Copyright
Copyright © 2012 The Psychometric Society

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