I'm interested in exploring whether responses to a series of attitudinal questions differ across various countries. I could check significant difference in mean scores but am more interested in the difference between the relationships (i.e. correlations) between attitudes, if there happens to be any noticeable difference in the correlation structure across the different countries.
I was wondering if there were any formal test(s) for this?
One unorthodox (or perhaps orthodox, I don’t know) idea I had was to take the correlations for each country and then calculate the sum of squared difference between all the correlations. A small sum of squared difference value would suggest high similarity between the two correlation matrices. Conversely a high sum of squared value would suggest differing correlation values between the two countries.
This could be used as a yard stick but could this sum of squared difference be significant tested also (after normalizing for size of correlation matrix)? Or is this completely wrong to do…
Best Answer
I'm looking at the same issue - I just came across the functions
cortest.normalandcortest.jennrich, in the excellentpsychpackage for R by William Revelle (see http://www.personality-project.org/r/html/cortest.mat.html). That page also contains references to articles on these tests. In you (our) case, the Jennrich test seems most appropriate (a quick scan of the Steiger paper (see http://ww.w.statpower.net/Steiger%20Biblio/Steiger80b.pdf) gives me the impression that that test,cortest.normal, also tests whether all correlations are zero - but I haven't looked into it more thoroughly yet).