Power of the F-Test for Nonnormal Distributions and Unequal Error Variances

摘要

An empirical investigation was made of the power of the F-test when the underlying distribution is nonnormal and the within-cell variances are not homogeneous. It is shown that even for small samples the analysis-of-variance F-test is valid, although the usual assumptions of normal distribution and homogeneous error variances are seriously violated. The test is shown to be valid for both Type I and Type II error. An analysis of the correlation between the numerator and denominator of the null hypothesis F-ratio demonstrates that the distribution of F is little affected by the shape of the underlying distribution. (Author)