Overall Anova for More Than Two Groups. The Brown-Forsythe and Welch tests are widely recommended as extensions of overall Anova to handle unequal variance with more than two groups. With normal distributions, they keep α under better control and provide more power than regular F.
Nonnormal distributions, however, undercut both tests. Simulations with the normal and four nonnormal symmetric distributions by Lee and Fung (1983) concluded that the Brown-Forsythe and Welch tests “perform poorly except under normality. Under long-tailed [= heavy-tailed symmetric] distributions, they are conservative and have very low power” (p. 137). c
Accordingly, neither test may be generally useful. This conclusion rests in part on the expectation that unequal variance will usually be accompanied by nonnormality.
Trimming. Trimming may have as much potential, perhaps more, with unequal variance as with equal variance. By decreasing the influence of the tail scores, the trimmed variances may be expected to be more equal.
Trimmed versions of the Brown-Forsythe and Welch tests, both available in BMDP, may deserve consideration, as they seemed to perform fairly well in the cited study. As already suggested, however, two-mean comparisons may be generally preferable to overall Anova between all the means.
Repeated Measures. With repeated measures, two-mean comparisons with unequal variance are handled straightforwardly. Because of likely nonsphericity, each two-mean comparison ordinarily requires its own error term. Each such comparison is equivalent to a test of the corresponding difference score, which automatically takes account of unequal variance.
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Publication information: Book title: Empirical Direction in Design and Analysis. Contributors: Norman H. Anderson - Author. Publisher: Lawrence Erlbaum Associates. Place of publication: Mahwah, NJ. Publication year: 2001. Page number: 373.
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