ANOVA and different 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.

 

[blue_raver22]

ert

Hello Robert,

I understand your concern about the difference in variances among your data sets and its impact on ANOVA testing. It is true that one of the assumptions of ANOVA is that the variances of the groups being compared should be similar. This is because ANOVA assumes that the variation within each group is representative of the overall variation in the population. However, this assumption can be relaxed to some extent if the sample sizes are equal among the groups.

In terms of your question about performing a test on the difference in variances and getting a p-value, there are actually tests available specifically for this purpose, such as the Levene's test or the Bartlett's test. These tests compare the variances among groups and provide a p-value that can be used to determine if the differences in variances are statistically significant. If the p-value is significant, it indicates that the variances are indeed different among the groups.

However, it is important to note that even if the variances are significantly different, this does not necessarily mean that the groups are taken from different populations. It could just be due to random variation or other factors. Therefore, it is still necessary to perform the ANOVA test to determine if the means of the groups are significantly different.

In summary, while the assumption of equal variances is important in ANOVA testing, it can be relaxed to some extent if sample sizes are equal. Additionally, there are tests available to assess the significance of differences in variances among groups. However, it is still necessary to perform the ANOVA test to determine if the means of the groups are significantly different. I hope this helps to clarify your concerns. Best of luck with your research.