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!
Best Answer
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.