# How do I compare population variances using the f distribution?

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• #654

Hi,

I am looking to see whether 2 groups differ only in the amount of variance (not the actual scores).

For example, I am hypothesising that group B has a significantly larger variance than group A (all participants takes part in both condition). I have made up some data below:

A = 6, 7, 6, 5, 7, 7, 7, 8, 4, 6 (Mean = 6.3, SD = 1.2)

B = 9, 4, 4, 9, 3, 10, 10, 7, 6, 3 (Mean = 6.5, SD = 2.9)

So group B has a greater amount of variance than group A, but how do I determine if this is statistically significant (p<0.05). – I am not looking at whether group A scores more than group B (otherwise, I know that I could just do a paired t-test) – only if group B has greater variability.

I hope that makes sense, but if not I’ll try and explain things a bit better. Please, please, any help would be appreciated. I have been stuck on this for a while.

Thanks

Graham

#657

Hi,

the test of Levene is done for that. Using the median instead of the mean is more robust.

In R, it is quite easy to fnd the function :

library(car)

leveneTest(A, B, center=median)

Hope it helps.

Nicolas

#656

Hi,

I agree with Nicolas.

You can see the statistics of Levene test if you perform a t-test (in SPSS). It produces a table that will show the following. If sig is greater than 0,05 then the two groups’  variance is considered the “same”

In order to do this you must have the data in one variable and another variable that groups them into group A and group B.

Wishing you well!

 Levene’s Test for Equality of Variances F Sig. 18,189 ,000
#655

Another way to do this is to based on a method developed by Gorsuch (2005). Standardize the scores and square them. That gives you individual estimates of the variance. Then you can run a two sample t test or try to predict conditional relations on variance by setting the variable as the outcome in a regression or ANOVA (GLM).

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