Significance test for the difference of two correlation coefficients Okay, I have two different data sets, A and B, both of which correspond to a third data set, C.  I have run least-squares regression on both A with C and B with C.  The correlation coefficient of A with C is 72.9%, compared to 66.5% for B with C.  How do I know or how do I test that that 6.5% difference is significant?
 A: Correlation coefficients aren't expressed in percentages, except maybe when squared to represent a shared percentage of variance. It also sounds as though you're referring to three variables within one dataset. If so, you're looking to test the difference of dependent correlations. Jeromy Anglim's blog has some useful links on this. Steiger's Z-test is described in Cal Garbin's "Bivariate Correlation Comparisons (PDF), which I'll paraphrase as a four-step calculation:
$$rm^2=\frac{\big(r_{AC}^2+r_{BC}^2\big)}{2}\\f=\frac{1-r_{AB}}{2(1-rm^2)}\\h=\frac{1-(f\cdot rm^2)}{1-rm^2}\\Z_\text{difference}=(Z_{AC}-Z_{BC})\cdot\frac{\sqrt{N-3}}{\sqrt{2(1-r_{AB})h}}$$
You can find the p value of Zdifference very easily – it's from the z distribution!
If all this is a pain (it is), you can use the paired.r function in the psych package in r as described on another of Jeromy's blog posts (linked in the previous). All you'll need are the three bivariate correlations and the total number of cases (trios of observations for each variable).
