The nonparametric Wilcoxon Rank Sum (also known as the Mann-Whitney U) and the permutation t-tests are robust with respect to Type I error for departures from population normality, and both are powerful alternatives to the independent samples Student’s t-test for detecting shift in location. The question remains regarding their comparative statistical power for small samples, particularly for non-normal distributions. Monte Carlo simulations indicated the rank-based Wilcoxon test was found to be more powerful than both the t and the permutation t-tests.
Weber, Michèle and Sawilowsky, Shlomo
"Comparative Power Of The Independent t, Permutation t, and WilcoxonTests,"
Journal of Modern Applied Statistical Methods:
1, Article 3.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss1/3