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.
Holland, Christopher H. and Holland, Tom
"A Two and More Independent Factor Form of the Wilcoxon-Mann-Witney Test, Extendable to Other Permutation-Based Tests,"
Journal of Modern Applied Statistical Methods:
1, Article 8.
Available at: http://digitalcommons.wayne.edu/jmasm/vol15/iss1/8