Randomization tests are often recommended when parametric assumptions may be violated because they require no distributional or random sampling assumptions in order to be valid. In addition to being exact, a randomization test may also be more powerful than its parametric counterpart. This was demonstrated in a simulation study which examined the conditional power of three nondirectional tests: the randomization "t" test, the Wilcoxon-Mann-Whitney (WMW) test, and the parametric "t" test. When the treatment effect was skewed, with degree of skewness correlated with the size of the effect, the randomization "t" test was systematically more powerful than the parametric "t" test. The relative power of the WMW test under the skewed treatment effect condition depended on the sample size ratio.