I have two matrices, A and B, of the same size. Each row of A corresponds to a row of B. Theory predicts that some rows of A will negatively correlate with corresponding rows of B.
I am interested in testing the general relationship between these matrices. That is to say, I want to know to what extent the theory is correct.
One way I thought of approaching this problem was as follows: calculate the row-wise correlation coefficients for the two matrices, and compare it with a similar vector of correlation coefficients calculated for randomly sampled rows from the two matrices. Compare the distributions with Kolmogorov-Smirnov test.
I have over 80000 correlation coefficients. K-S shows a significant difference between the real and sampled distribution, but the effect is small. On the other hand, I have clear outliers with almost perfect negative correlation in the former test, while not so in the sampled distribution.
What do you think?