Different group size average comparisons I have 3800 stocks for which I calculate their return correlations. So I end up with a 3800 by 3800 matrix. Each stocks is related in some way to all the other 3799 stocks. For each stock, I create seven groups out of 3799 stocks based on their relatedness. So say for stock A, group 1 (closest in relatedness - based on a pre-specified knowledge based linkage of like-industries) will have 60 stocks, group 2 will have 300 stocks, and group 3 700 stocks and so on up to seven groups. I then average for each group their correlations with stock A. I want to see if there is a decay in the correlation when we move from group 1 to group 7. But the group size varies... can this be a serious issue? 
I then take an average across all groups for each stock and see if the decay holds cross-sectionally? Now the issue is that for each stock, say stock A and stock B the size of each group is different. There may be 60 stocks in group 1 for stock A while there is 40 in group 1 for stock B. How problematic can this be?
 A: You should take account of the fact that there are uneven numbers of stocks in each tiered "relatedness" group. Say our stock is BP. Suppose for simplicity that we had only two groups. Group 1: All petrol companies then Group 2: petrol, automotive, agriculture, and aerospace. I assume they are clustered within subsequent groups.
If you are interested in the question: are group 1 stocks more closely correlated with our target stock (BP) than group 2? Stated as a hypothesis, you would actually split out the overlapping stocks in group 1 from group 2 (telescoping) and use a t-test treating individual level correlations. This infers the same trend for a difference in correlations.
Using the telescoping approach, you can subsequent stocks from each group and code a group level indicator as a continuous numeric variable, then use a scatterplot to show distributions of correlations from proximal groups. Then any regression method will be suited to test the hypothesis whether there's a trend in the level of correlation between groups.
