Exact Permutation/Randomization Tests Algorithms

Abstract

Fisher (The design of experiments, Oliver & Boyd, London, 1935) described the exact permutation and randomization tests for comparative experiments without assuming normality or any particular probability distribution. While having this as an attractive feature, the computational challenge was a disadvantage at that time but not now with modern computers. This paper introduces a permutation/randomization data algorithm to generate the permutation/randomization distributions under the null hypotheses for calculating the P-values. The properties of permutation/randomization data matrices developed by algorithms following the proposed mathematical processes are derived. Two illustrative examples demonstrate the usefulness of the proposed computational methods.