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Bioinformatics Advance Access originally published online on July 26, 2006
Bioinformatics 2006 22(18):2244-2248; 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

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

*To whom correspondence should be addressed.

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.

Contact: calian{at}raunvis.hi.is

Received on December 9, 2005; revised on June 14, 2006; accepted on July 6, 2006

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