F-Test for equality of variances- effect size scale?

#1
The effect size for equality of variances is Ratio=variance1/variance2

I didn't find any "common" scale for this effect size. (although you may say the ratio explains itself...)

I know that these definitions are not absolute, and may depend on the specific field.
Do you know of a scale for the ratio? like Cohen's d is (0.2-small, 0.5-medium, 0.8-large) but if he would come with (0.15,0.4,0.7) probably we all would use today (0.15,0.4,0.7)

I thought for ratio it should be something like 1.02, 1.15, 1.35 (similar to regression f^2 , small 0.02, medium 0.15, large 0.35.)
Do you know if there any general agreement?
This is a general question, not for a specific field.
 

staassis

Active Member
#2
To the best of my knowledge, there is no generally accepted effect size for discrepancies in variances. Metric [variance 1] / [variance 2] seems arbitrary. Why is it better than [variance 2] / [variance 1], which is not the same? The following metric has nice invariance property:

| log(variance 1) - log(variance 2) |.

The topic becomes more "convoluted" once we consider discrepancies among 3 or more groups... You can also exploit the ideas of GARCH, which draws parallels between squared shock ε(t)^2 and shock ε(t). In the same fashion you can consider R-square in regression

ε(t)^2 ~ Group.

This will capture the variability of sample variance due to switching from one group to another.
 
#3
Thanks Staassis!

Why is it better than [variance 2] / [variance 1], which is not the same?
When calculating the power of the F test for variances we use the ratio as an expected effect size.
And yes, for equal samples, the power of ratio=0.5 or ratio=2 is equal.

So I thought of max(ratio, 1/ratio) or maybe max(ratio, 1/ratio)-1

I find it nice when you use the same method to calculate the test's power to achieve a specific effect and the testing effect. (but of course, you can translate the difference of log to ratio to calculate the test power)

Anyway, the ratio is more tangible than the difference of logs, but the difference of logs is also very nice
And I thought there should be some agreement on the scale ...