A Two and More Independent Factor Form of the Wilcoxon-Mann-Witney Test, Extendable to Other Permutation-Based Tests

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Abstract
The Wilcoxon-Mann-Witney test is extended to account for a second independent factor. The new test statistic’s probability mass function and normal approximation are derived. Critical-values for balanced, unbalanced and large sample designs are given. The immediate extension of this method to a wide range of non-parametric tests is explained.