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This work has its origin in the Fellowship thesis for the Royal College of Veterinary Surgeons of one of us. We would like to thank the thesis supervisor Peter Lee for his invariably prompt and helpful criticisms of this work. We would like to thank Niclas Sjogren (latterly of AstraZeneca Statistics Department) for the fruitful discussions of the ideas from which this work came. Mr. Christopher Holland is a graduate medical student in the clinical portion of his training. 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.

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