Simulations were performed to compare the power of the approximate permutation test with the power of t test and Wilcoxon's test for the two‐sample location problem under a shift model. The approximate permutation test is sometimes suggested as a panacea for non‐normality. However, for the distributions and sample sizes used in this study, the power of the approximate permutation test and the t test are nearly equal. Under non‐normality Wilcoxon does have better power characteristics than the other tests. So it can be concluded, that in this study Wilcoxon, a permutation test on ranks, does perform better under non‐normality than the approximate permutation test that uses the measurements themselves.
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Brink et al. (1989) studied this question.