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:
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.