Comparing multiple dependant correlation coefficients

#1
Hello,

I am new to this site but I'm glad I discovered it. I have a question for an apparently unusual analysis that I would like to do. I could not find a validated approach to do so but maybe it is simple...

I have a repeated-measure design with two within-subject factors: F1, 10 levels; F2, 2 levels.

I am looking at the effects of these two factors on two dependent variables, DV1 and DV2.

I know that DV1 and DV2 are associated and partly vary together across the 10 levels of F1. If I look at the correlation coefficients within-subject for F1, DV1 and DV2 are associated with a Pearson r value ranging between 0.4 and 0.9 depending on the subject.

Now, I can do this twice for each subject because I have F2 with 2 levels: this gives me two sets of within-subject correlation coefficents that I would like to compare, because my hyposthesis is that the association between DV1 and DV2 will change between level 1 and 2 of F2.

You understand that correlation coefficients are within-subject and that the two sets of correlation coefficients that I would like to compare are dependent.

My question: is it possible to test the change in the association between DV1 and DV2 between level 1 and 2 of F2? If so, how can I do that?

I had the silly idea of doing this with a paired t-test, which seems wrong from the beginning, but I cannot find anyone to tell me why I can or cannot do it, or what valid test I could use.

Please help!

Thanks

Mathieu