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
Hello,
maybe someone could help me with my concern.
I woukd like to use a two-way ANOVA to assess the intersection between two factors.
Since the variance between the groups isnt equal, I wanted to use the Brown- Forsythe Test. It just doesn’t work for me, using the program R.
Maybe someone here knows the right package and code, that I would have to use?
Would be much appreciated!
Thanks in advance, Franzi.
Franziska,
I need to look into whether this version of the Brown-Forsythe test really works.
In any case, I believe that two approaches that might be useful for you are:
– Mixed Linear models. I am looking into this now
– Bootstrapping. The following webpage may be useful https://www.sciencedirect.com/science/article/pii/S0047259X12002394
Charles
Hi Charles, thank you for your reply!
I would prefer to use 2-way anova, but as part of my design I believe the brown-forsythe the test is more appropriate due to my data being heteroscedastic. I came to this conclusion after comparing variances of factors and looking at a homoscedasticity plot and using Spearman’s test for heteroscedasticity where they appear heteroscedastic. Reading much literature on this topic it is likely that
So for my experiments, I have set out to use 2-way anova when the data fit the assumptions, but when it doesn’t I have planned to use one-way Anova using the Brown-Forsythe F* test mainly in the case of heteroscedasticity (which is the only violation I have observed).
However, I am worried that using one way ANOVA will make it more difficult to assert the impact of factors on the experiment. Your feedback on this would be very much appreciated.
Thank you!
Brandon
Hello Brandon,
The main advantage of Two-way ANOVA is it ability to assess the intersection between the two factors. If you are not interested in this then you can safely use one-way ANOVA.
If the homogeneity of variances assumption is violated then I prefer using Welch’ ANOVA test over the Brown-Forsythe F* test. In either case, you can follow up with Games-Howell if you get a significant result. To test for homogeneity of variances, I usually use Levene’s test.
Charles
I have read that in particular, this case is predominantly suited for the 2×2 case for two-way anova. So if I was to set a 2×2 two-way anova design as a one-way anova with instead 4 independent variables and one dependent variable, using the brown-forsythe F* test for one-way anova I can compute a representative statistic for the two-way anova case with normal software? Or would I have to take into account the differences in how df is computed?
In the case one can, how would one perform a posthoc test. Would you use the Dunnet T3 like in normal Brown-Forsythe anova, or would you use Tukey’s test for two-way anova?
Hello Brandon,
You can one-way Anova (or the Forsythe F* test) instead of two-way Anova as you describe. You don’t need to adjust the df.
Why don’t you simply use two-way Anova? Is some assumption not met? If so, which one?
The post-hoc test depends on what omnibus test you choose.
Charles