The Wilcoxon-Mann-Whitney test and other nonparametric tests based on rank randomization are distribution-free with respect to the probability of Type I errors; however, they are not distribution-free with respect to the probability of Type II errors and power to detect differences. Various shapes of nonnormal distributions substantially reduce the power of nonparametric tests. However, these densities influence parametric counterparts such as t and F to an even greater extent so nonparametric methods acquire an advantage by comparison.
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