Fewer permutations, more accurate P-values.

Abstract

Permutation tests have become a standard tool to assess the statistical significance of an event under investigation. The statistical significance, as expressed in a P-value, is calculated as the fraction of permutation values that are at least as extreme as the original statistic, which was derived from non-permuted data. This empirical method directly couples both the minimal obtainable P-value and the resolution of the P-value to the number of permutations. Thereby, it imposes upon itself the need for a very large number of permutations when small P-values are to be accurately estimated. This is computationally expensive and often infeasible. A method of computing P-values based on tail approximation is presented. The tail of the distribution of permutation values is approximated by a generalized Pareto distribution. A good fit and thus accurate P-value estimates can be obtained with a drastically reduced number of permutations when compared with the standard empirical way of computing P-values. The Matlab code can be obtained from the corresponding author on request. Supplementary data are available at Bioinformatics online.