# Test for equal variance

I need to test for equal variance. I tried to read up and it mentioned there are a few tests I can use to test for equality of variance such as F Test (F ratio?), Levene Test, Bartlett Test etc.

I was wondering if there is a qualitative method of telling whether there is equal variance by using the SD and the mean of the two data sets (both normally distributed) My lecturer was saying I can assume equal variance by just looking the mean and the SD?

I do not know how to tell... can anyone help?

• I'm not sure I follow the motivation for this question. If you want to test if the variances are equal, then you have discovered some (that you listed), what would be the point of the qualitative method? Oct 23, 2012 at 13:35
• +1 I would be interested in learning how anyone can learn about equality of variances (in the usual applications of ANOVA, regression, t-tests, and so on) through consideration of the means! @Gung If we interpret "qualitative" as "exploratory" or "potentially revealing of unexpected data characteristics," it becomes clearer how such a method could supplement--and even be superior to--a formal test.
– whuber
Oct 23, 2012 at 13:36
• There is this saying of the ratio of the two variances should not exceed three. I found many resources using this scheme, but I couldn't find the source. Oct 23, 2012 at 13:45

Note that all the tests for equal variances are rule out tests. They test the null hypothesis that the 2 variances (standard deviations) are equal, so if you reject the null hypothesis then you can be fairly sure that they are not equal, but if you get a non-significant result that does not mean that they are equal, they could be equal or you may just not have enough power to find the difference.

The rules of thumb are often more useful because if the variances are not equal, but still similar then your other tests are still reasonable.

What is the most important is an understanding of the science that produces the data and the question of interest. There are cases where the distributions have different enough variance that you would not want to use methods that assume equal variances, but many of the samples from the distributions would not reject the equal variances

I wonder if your lecturer was referring to a common rule of thumb: analyses like ANOVA are fairly robust to heterogeneity and can often withstand differing variances between groups by up to a ratio of four times. You can get a sense of that by just looking at the variances.

Another possibility is that your lecturer was warning about the possibility that there is a constant coefficient of variation (the variance is a constant function of the mean), which would make sense of the suggestion to look at the mean also. This phenomenon can be common in some cases, such as when working with counts.

I wrote a little about the various tests for homogeneity of variance here: why-levene-test-of-equality-of-variances-rather-than-f-ratio, it it helps.

• Thanks for the replies. The reason why I am keen to explore qualitative method of testing variance because my lecturer mentioned it and I am very curious. About the ratio of variance, Can I use the big variance over the small variance to determine whether they have equal variance? Penguin knight has mentioned the ratio must not exceed 3 to assume equal variance. Do you have a name for this simple test? Thanks... Oct 24, 2012 at 15:18
• Ratios of 3 & 4 are just rules of thumb--the main point is that it's actually hard to break the ANOVA (the universe is kind to us in this case). As for using the ratio as a formal test, read my answer that I linked above. Note that it is hard to give you any more info about this w/o knowing more about the context. Oct 24, 2012 at 15:27