Moment approximations as an alternative to the <i>F</i> test in analysis of variance

Abstract

In analysis of variance experimental designs, it is not uncommon to encounter populations where the requirements of normality and/or homogeneity of variance for the use of F or t tests cannot be satisfied. Fisher‐Pitman randomization tests and Monte Carlo randomization tests are two techniques often espoused as alternatives to the F or t tests. The first is impractical in all but the most trivial cases and the second engenders an additional Type I error. Moment approximations provide an attractive and cost‐effective alternative which is free from the normality and homogeneity requirements of the F or t tests and does not add further Type I error.