# Brown-Forsythe F* Test for Two-way ANOVA

The Brown-Forsythe F* test is useful when the variances across the different groups are not equal. When the sample sizes are equal, we can use an extension of the Brown-Forsythe F* Test for One-way ANOVA.  Since the sample sizes are equal, F* = F and the individual df (dfA, dfB, etc.) are the same as for ANOVA. We only need to calculate the overall df as follows:

where

This df can be used for testing factor A, factor B or interaction effects. The test is

### 3 Responses to Brown-Forsythe F* Test for Two-way ANOVA

1. Colin says:

Sir

Could you give us an example about this topic? I don’t understand why the F test for A,B, and interaction factor has exactly the same 1st df and 2nd df.

Colin

• Charles says:

Colin,
Although I have described the Brown-Forsythe F* test for one-way Anova (and have included a function to carry out the test in the Real Statistics Resource Pack), I have not really given an adequate description for two-way Anova. Perhaps I should remove this webpage for now. I plan to provide a more complete description of the two-way test eventually, but have not yet given it a high enough priority. I am currently working on how to better handle missing data in regression (e.g. using FIML).
Charles

• Colin says:

Sir

I think I can wait. Your website is cool.

Colin