# Averaging correlation coefficients

I am calculating Spearman correlations multiple times between individual data vectors that are not necessarily of the same length. So for example, X1=[1,2,3], Y1=[2,3,1] and X2=[10,2,3,4,5], Y2=[2,3,1,1,1], correlating X1 with Y1 and X2 with Y2. I now want to retrieve an average correlation coefficient.

I am aware that a common approach is a Fisher transformation on the individual coefficients; averaging the transformed values; and a back transformation.

However, I have two issues:

1. Some of my correlation coefficients are 1 where the Fisher transformation is not defined. Is there some common way of handling that case?

2. Do I need to cope somehow with the different vector lengths? I found some short information about that in the following paper, but wonder whether this is necessary or there is another approach.

• With heterogeneity I do not mean that there is heterogeneity in correlation, but rather a general clustering effect that warrants to not treat the whole data as equal. Having something like X1=[100,100] and X2=[1,2] and correlate both with a vector like Y1=[1,1] should be treated independently, not pooled. After some thinking, I think a mixed effect model is suitable. – fsociety Jun 21 '16 at 6:52