# What is the difference between test to check homogenity of variance and ANOVA?

I found many tests like: Fligner, Levene etc etc to check homogeneity of variances, my question is: What is the difference between those tests and ANOVA ?

Thank you

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You may also want to read this: why-levene-test-of-equality-of-variances-rather-than-f-ratio/. –  gung Sep 7 '12 at 3:45

Fligner-Killeen's and Levene's tests are two ways to test the ANOVA assumption of "equal variances in the population" before conducting the ANOVA test. Levene's is widely used and is typically the default in programs like SPSS, but either test (or even Brown-Forsythe) is acceptable. ANOVA is the omnibus test of mean differences among groups. While, in name, ANOVA analyzes the variance (between, within, and overall) among three or more groups, its hypotheses actually make statements about the equality of means versus there being "at least two means different."

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i have a doubt regarding "ANOVA is the omnibus test of mean differences among groups" AND "ANOVA analyzes the variance (between, within, and overall) among three or more groups" I really do not understand this aspect. ANOVA will test if the means are different OR if the variances are different? Thank you for the clarificatio –  Dail Nov 9 '11 at 14:28
ANOVA tests for differences between means. It will tell you if the means are different overall, but you typically have to use a post-hoc test (e.g., Tukey Honestly Significant Difference) to determine which of your three or more groups are different from each other. Mathematically, ANOVA "analyzes the variance" by computing sums of squares and mean squares values in the background (that are like variances), but it is still a test about mean differences in the end. –  Garrett Nov 9 '11 at 14:36
ok perfect, so what is the test to check if the VARIANCES are different from each other? –  Dail Nov 9 '11 at 14:37
You can take your pick among Levene's, Fligner-Killeen's or Brown-Forsythe. Levene's is pretty straightforward and easy to run. –  Garrett Nov 9 '11 at 14:39
To compare mean differences between/among groups by, let's say, just subtracting the averages is not sufficient to establish statistical significance. Rather, it is important to capture the variability of each of your groups that you're comparing, as well. To do this, ANOVA compares the raw data of each group to corresponding group means and an overall (total) mean. These comparisons yield "sums of squares" that when divided by degrees of freedom give you "mean squares." These mean squares are, for all intents and purposes, variances. In the end, you compared means but you analyzed variances. –  Garrett Nov 9 '11 at 16:52
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Don't know about Fligner, but Levene's test is actually an ANOVA of absolute deviations from group means (or group medians, this would be Brown-Forsythe test).

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so what is more accurate Levene or ANOVA? –  Dail Nov 9 '11 at 13:43
? Don't understand you. ANOVA checks deviations from the mean. Levene checks deviations from the mean of absolute deviations about the mean. –  ttnphns Nov 9 '11 at 15:43