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I understand that in One-Way ANOVA two alternative F-Ratios have been derived to be robust when homogeneity of variance has been violated. Tomarkin and Serlin (1986) review amongst other techniques the Brown-Forsythe and Welch F-Ratios and conclude that both control the type I error rate well.

So far I have only come across W and B-Fs F Ratios in One-Way ANOVAS. Am I able to use them in ANOVAS with two factors? And if no, why not?

Thanks

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2 Answers 2

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I found this article by Algina & Olejnik (1984).

The abstract:

The Welch-James procedure may be used to test hypotheses on means, when independent samples from populations with heterogeneous variances are available. Until recently the complexity of the available presentations of this procedure limited the application of this procedure. To resolve this state of affairs, summation formulas for the Welch-James procedure are presented for the 2 x 2 design. In addition, matrix formulas that permit routine application of the procedure to crossed factorial designs are presented.

It frankly looks a little hairy, but I thought it might be a start.

Citation

Algina, J., & Olejnik, S. F. (1984). Implementing the Welch-James procedure with factorial designs. Educational and psychological measurement, 44(1), 39-48.

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  • $\begingroup$ Looks like a great contribution to a topic that had many of us puzzled for a quite a while. $\endgroup$
    – rolando2
    Mar 26, 2011 at 17:58
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The Brown-Forsythe F* can be used even in two-way ANOVAs. From what I can tell the F statistic is the same as for classic two-way ANOVA, the only difference is in how the degrees of freedom are calculated. Of course it gets more complicated for unbalanced factorial designs. (the original Brown & Forsythe's paper is available at http://www.jstor.org/stable/2529238)

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