An Exact and a Monte Carlo Proposal to the Fisher–Pitman Permutation Tests for Paired Replicates and for Independent Samples

This article concerns the nonparametric Fisher–Pitman tests for paired replicates and independent samples. After outlining the theory of exact tests, I derive Monte Carlo simulations for both of them. Simulations can be useful if one deals with many observations because of the complexity of the algorithms in regard to sample sizes. The tests are designed to be a more powerful alternative to the Wilcoxon signed-rank test and the Wilcoxon–Mann–Whitney rank-sum test if the observations are given on at least an interval scale. The results gained by Monte Carlo versions of the tests are accurate enough in comparison to the exact versions. Finally, I give examples for using both supplemented tests.