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I am building a hierarchical model for prediction purposes, and I am considering modeling the variances of each group in addition to the means. This is a graphical depiction of what I would like to do:

enter image description here

Before I march on do that, however I would like to determine whether it is worth modeling the variances rather than assuming homogenity in the variances across groups.

I can simply compare the variances within each group, either by eyeballing or graphing, but I was wondering whether there is a statistical test that does this?

I would use the F-test, but that seems tailored for two populations...maybe I could compare each variance to the other variances?

So yeah, imagine I have data like this, where 1 - 6 are the 6 groups, sd is the standard deviation, var is the variance, and count is the # of obs / group:

 head(Var_df[,2:4])
         sd       var  count
1 2.4598859 6.0510387     60
2 2.9044591 8.4358827  18169
3 2.2603269 5.1090775  14621
4 2.2817452 5.2063610 116397
5 0.6260919 0.3919910    266
6 0.7845818 0.6155686    372

How would I tell whether the variances are meaningfully different in the different groups and therefore worth modeling? I should also note that I am assuming that the different groups are normally distributed.

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For that particular data, you could tell just by looking at them! The difference between any of groups 1-4 and 5-6 couldn't possibly be due to chance at that sample size.

More generally, though, a fairly robust option that works on 3+ groups is the Brown-Forsythe test. (For instance, in R this lives in the lawstat package in levene.test. The standard Levene test may have more power if your data don't deviate significantly from normality.)

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