Brown-Forsythe and Welch f-ratios in two-way ANOVAs? 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
 A: 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.
A: 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)
