Say for example I calculated two sets of cross-correlation matrices, one that compared time series A1 and A2 for 10 test subjects and another that compared time series B1 and B2 for the same 10 test subjects. If I took the average of each of these cross-correlation sets, I would have the average matrix A for all cross-correlations between A1 and A2, and the average matrix B for all cross-correlations between B1 and B2:
Lag = [ -3 lag; -2 lag; -1 lag; 0 lag; +1 lag; +2 lag; +3 lag]
A = [0.003100173; 0.042535000; 0.140213224; 0.256917007; 0.17103877; 0.095175853; 0.062051573]
B = [0.030890086; 0.023768139; 0.025463862; 0.086639792; 0.03560601; 0.012300708; 0.019001531]
Is there a way to then compare the similarity of these two average cross-correlation matrices? I essentially want to say something about whether the cross-correlation is statistically stronger between time series A1 and A2 versus time series B1 and B2 at a time lag of 0 (which would be 0.256917007 for A and 0.086639792 for B).
I thought about just doing a dependent-samples t-test to check for differences between A and B since I have variance and standard error around these averages, but that feels almost too simple? Should I be looking into chi-square to see whether the number of people who had maximum cross-correlation at 0 were different between A and B? Or are there more sophisticated analyses that would be better here? I would love any help or advice or resources that would be good for understanding what I can do here!
