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.
Fatal-Weber, M., & Sawilowsky, S. S. (2009). Comparative statistical power of the independent t, permutation t, and Wilcoxon tests. Journal of Modern Applied Statistical Methods, 8(1), 21-26.