When to use Brown-Forsythe Test? I have been researching the differences between Welch ANOVA and Brown-Forsythe Test.  I know that Welch ANOVA is used for more than two groups comparing whether there is statistically meaningful difference in their means when variance of homogenity assumption is not held. 
My  question is, is Brown-Forsythe Test an alternative to Welch ANOVA when homogenity of variances assumption is not met, or is it an alternative test for Levene Test for comparing homogenity of variances when normality assumption is not met?
Many sources say different things about this test. Nearly half of the sources approve that Brown-Forsythe Test is used for testing equality of means, and the other part approves that it is used for testing equality of variances.
Any help would be greatly appreciated.
Thanks in advance!   
 A: Levene's test for homogeneity of variance involves determining an absolute deviation score from group means for each of the n, while Brown-Forsythe's test for homogeneity of variance involves determining an absolute deviation score from group medians for each of the n. 
From there, both use a single-factor between-subjects analysis of variance to contrast the means of the deviation scores.
Both are robust against normality assumption violations.  However Hartley's F max Test, another popular homogeneity of variance test, is not.
From:
Sheskin, D. (2011). Handbook of parametric and nonparametric statistical procedures: 11th edition. Boca Raton: Chapman & Hall/CRC.
A: Struggling with this myself.  It's a very late answer, but in case anyone comes across this thread maybe it'll help.
Levene's test always comes up as a variance comparison test.
A modification to Leven's test is Brown-Forsythe (the whole mean vs median thing) so it also appears under the name Levene's modified test = Brown-Forsthe variance comparison test.
There is also a a Brown-Forsthe test for equality of means that is the next step when variance assumptions are violated.  The result here is not the same as the results of a Brown-Forsythe test of variance.
I'm struggling to make these comparisons myself since I don't have all the related software, but so far it looks like:
In SPSS, ANOVA with the Brown-Forsythe option selected gives you the equality of means test
For Brown-Forsythe variance test the following programs do this:
In SAS; hovtest
The HH library in R; hovBF, 
The lawstat library you can specify using median or mean;
levene.test(measurements,category,location="median") = Brown-Forsythe variance 
levene.test(measurements,category,location="mean") for straight up Levene's variance.
UPDATE 
Just found an SPSS script that provides both Levene's as well as Brown-Forsythe tests of variance
EXAMINE VARIABLES=ZCu BY Location
  /PLOT BOXPLOT STEMLEAF SPREADLEVEL(1)
  /COMPARE GROUPS
  /STATISTICS DESCRIPTIVES
  /CINTERVAL 95
  /MISSING LISTWISE
  /NOTOTAL

-Output table for Test of Homogeneity of Variance -
means is Levene and median is Brown-Forsythe test
Confirmed using GraphPad Prism Brown-Forsythe test (which is also for variance)                 
A: Just found an SPSS script that provides Levene as wells as Brown-Forsythe tests of variance
EXAMINE VARIABLES=ZCu BY Location
  /PLOT BOXPLOT STEMLEAF SPREADLEVEL(1)
  /COMPARE GROUPS
  /STATISTICS DESCRIPTIVES
  /CINTERVAL 95
  /MISSING LISTWISE
  /NOTOTAL

-Output table for Test of Homogeneity of Variance -
means is Levene and median is Brown-Forsythe test
Confirmed using GraphPad Prism Brown-Forsythe test (which is for variance)              
