My data is not normal, and have unequal sample sizes. But I am getting different results for Variance upon calculations with these tests. Levene is saying that variances are equal, but B-F is saying that it is not equal. Which one to believe???
Look at your data and if it has outliers, the Brown Forsythe test may be more reliable.
Akshay Kumar When comparing variances with unequal sample sizes and non-normal data, Levene’s test and the Brown-Forsythe (B-F) test may give different results due to how they handle deviations from assumptions.
Levene's test is sensitive to deviations from normality, whereas the Brown-Forsythe test adjusts by using the median instead of the mean, making it more robust in the presence of non-normal data. Given your scenario, where the data is non-normal, it would be advisable to rely on the Brown-Forsythe test as it provides a more accurate assessment under these conditions.
According to Nordstokke and Zumbo the Levene test isn't really a single procedure. It's a strategy for assessing variation in groups of data points. It is just a one-way ANOVA of the absolute differences from each of the group averages. You can use the mean average, the median or some other average value. (It used to be that SPSS implemented the mean and median version in different functions but didn't really make it clear what they did - but maybe its changed). It follows that the mean version will be less sensitive to extreme values.
Article A Cautionary Tale About Levene's Tests for Equal Variances.
So it turns out the B-F test is really a modified Levene test that uses the median in place of the mean originally used.
In practice I'd use neither and just look at the SDs or if being cautious use a corrected version of the ANOVA as a default (corrections like Welch and B-F are essentially the same as the uncorrected test if the SDs aren't different so they are pretty safe as a default).
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