Can ANOVA Be Used with Unequal Variances?

[TheRobster]

I know that one of the key conditions of performing an ANOVA test is that the variances of the groups has to be broadly similar. I have some data sets that I need to compare and the variance of some of them is very different to the rest. Surely this in itself proves (indicates?) that the samples are taken from different populations so I don't need to go any further?

Could I perform some type of test on the difference in variances and get a p value for likelihood that the variances are actually different? If p is significant then wouldn't this show that the groups are actually different anyway, regardless of whether or not their means are similar?

Thanks
-Rob

 

[chiro]

I know that one of the key conditions of performing an ANOVA test is that the variances of the groups has to be broadly similar. I have some data sets that I need to compare and the variance of some of them is very different to the rest. Surely this in itself proves (indicates?) that the samples are taken from different populations so I don't need to go any further?

Could I perform some type of test on the difference in variances and get a p value for likelihood that the variances are actually different? If p is significant then wouldn't this show that the groups are actually different anyway, regardless of whether or not their means are similar?

Thanks
-Rob

Hey TheRobster and welcome to the forums.

For testing unequal variances, you can resort to what are known as F-tests in the frequentist paradigm for testing if they are equal or not with some statistical significance.

Are you aware of the F-distribution and its use for frequentist hypothesis testing for unequal/equal variances under some significance?

 

[TheRobster]

Aren't F-tests part of ANOVA? Seem to remember it's the score that compares variance within groups with variance between groups?

I have statistical software that gives F scores from ANOVA tests.

 

[chiro]

Aren't F-tests part of ANOVA? Seem to remember it's the score that compares variance within groups with variance between groups?

I have statistical software that gives F scores from ANOVA tests.

They should be part of ANOVA. The point is though, that the F-test is a general test for hypothesis testing with respect to whether two population variances (under frequentist statistical assumptions, based on the CLT) are statistically significantly 'equal' or 'not equal' under some measure of significance.

If you can get an F-test for two general distributions, then use this and look at the statistic and p-value (probability value) to see if you get evidence to say if they are equal or not-equal under some statistical significance.