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Bioinformatics Advance Access published online on July 26, 2006
Bioinformatics, doi:10.1093/bioinformatics/btl383
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© The Author (2006). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received December 9, 2005
Revised June 14, 2006
Accepted July 6, 2006

Article

To permute or not to permute

Yifan Huang 1, Haiyan Xu 2, Violeta Calian 3, and Jason C. Hsu 4

1 H. Lee Moffitt Cancer Center & Research Institute, The University of South Florida, Tampa FL 33612, USA
2 Department of Clinical Biostatistics, Johnson & Johnson Pharmaceutical Research & Development, L.L.C., USA
3 Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland
4 Department of Statistics, The Ohio State University, Columbus OH 43210, USA


  Abstract

Permutation test is a popular technique for testing a hypothesis of no effect, when the distribution of the test statistic is unknown. To test the equality of two means, a permutation test might use a test statistic which is the difference of the two sample means in the univariate case. In the multivariate case, it might use a test statistic which is the maximum of the univariate test statistics. A permutation test then estimates the null distribution of the test statistic by permuting the observations between the two samples.

We will show that, for such tests, if the two distributions are not identical (as for example when they have unequal variances, correlations, or skewness), then a permutation test for equality of means based on difference of sample means can have an inflated Type I error rate even when the means are equal. Our results illustrate permutation testing should be confined to testing for non-identical distributions.

Associate Editor: Joaquin Dopazo
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