To permute or not to permute.
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.


BACKGROUND
calian@raunvis.hi.is.
Huang
Yifan
Y
H. Lee Moffitt Cancer Center & Research Institute, The University of South Florida Tampa, FL 33612, USA.
Xu
Haiyan
H
Calian
Violeta
V
Hsu
Jason C
JC
D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D020869:Gene Expression Profiling / Q000379:methods*; D008957:Models, Genetic; D015233:Models, Statistical; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D016008:Statistical Distributions