Comparing 2 correlations

http://psych.unl.edu/psycrs/statpage/biv_corr_comp_eg.pdf

Comparing bivariate correlations across populations Another common question is whether two variables are equally correlated in two different populations. In this example we will ask if the correlation between depression (BDI) and family social support (FASS) is the same for males and females. To do this in SPSS we must first split the file into two subfiles (males and females) and obtain the desired correlation from each subfile. Data  Split File Move the variable or variables into the “Groups Based on:” window and click “OK”. All subsequent analyses we request will be performed and presented separately for each of the resulting groups.

A significance test will require that we find the difference between these two correlations, relative to the expected variability in correlations for this sample size. The common Z-test is useful for this, but assumes that the values being compared are normally distributed, and we know that r is not normally distributed. Fisher, however, determined a way to transform r-values so that they will be normally distributed -- called Fisher's Z-transformation. Z1 - Z2 Z-critical is 1.96 for p < .05 The Z-test is computed as Z = ---------- 2.58 for p < .01 SEZD SEZD =  [1 / (n1-3) + 1 / (n2-3)] On the right is the portion of the FZT program used for Fisher’s Z-test, with the values for this group comparison shown. As with other correlation comparisons, you must decide if you want to test for “correlation differences” (including the sign of the correlations) or the “predictive utility differences’ (using |r| for both correlations). In this case, the results from comparing the “utility” of the predictor for this criterion in the two groups was Z=1.258, p > .05. Remember, the tests are equivalent if the signs of the two correlations are the same. Family social support was correlated with depression for females, r (168) = - .289, p < .001, for women, but not for men, r(64) = .111. The difference between these correlations was statistically significant, Z = 2.776, p < .01.