It is well-known that for normally distributed errors parametric tests are optimal statistically, but perhaps less well-known is that when normality does not hold, nonparametric tests frequently possess greater statistical power than parametric tests, while controlling Type I error rate. However, the use of nonparametric procedures has been limited by the absence of easily performed tests for complex experimental designs and analyses and by limited information about their statistical behavior for realistic conditions. A Monte Carlo study of tests of predictor subsets in multiple regression analysis indicates that various nonparametric tests show greater power than the F test for skewed and heavy-tailed data. These nonparametric tests can be computed with available software.