Comparing correlations between groups is not the same as comparing slopes of regressions. Two groups may have very similar slopes and very different correlations, or they may have very different slopes, but very similar correlations.
Assuming you really want to compare the strength of correlation between groups, the standard test uses Fisher's r-to-Z transformation (also known as Fisher's Z' transformation). Note that this test is only appropriate for testing correlations between groups.
As I understand it, there are three different tests for comparing correlations, depending on the relationship between the variables being correlated:
1. Independent correlations
E.g. comparing the correlation of X and Y in group A, with the correlation of X and Y in group B.
For this, use Fisher's r-to-Z transformation (Fisher, 1921, Metron).
2. Correlated non-overlapping correlations
E.g. comparing the correlation of X1 and Y1 in group A, with the correlation of X2 and Y2 in the same group.
For this use the Pearson-Filon statistic modified to use Fisher's r-to-Z transformation (ZPF) (Raghunathan, Rosenthal, & Rubin, 1996, Psychological Methods).
3. Correlated overlapping correlations
E.g. comparing the correlation of X1 and Y in group A, with the correlation of X2 and Y in the same group.
For this use Steiger's Z (Meng, Rosenthal, & Rubin, 1992, Quantitative Methods in Psychology).
I've never applied any of these tests on a voxel-by-voxel basis in SPM (for one thing, SPM doesn't provide "r maps" as far as I know), but I have extracted values from ROIs, calculated the correlations, and then applied these tests.
On Wed, 26 May 2010 23:17:51 +0100, Amit Etkin <[log in to unmask]> wrote:
>I would like to compare the strength of the correlation of brain activation with a behavioral variable in two groups of subjects (ie group A's activation with their behavioral scores vs group B's activation with their behavioral scores). I can see two ways this may be doable, and would love input/thoughts etc.
>1. Run an independent sample t-test including covariates for each group (behavioral measure) and then in the GLM contrast covariate for A minus covariate for B. Problem is that this would be looking at different correlation strengths after accounting for group main effects, which isn't necessarily what I want.
>2. Separately normalize the behavioral scores for each group and then run a multiple regression model with all scans put in, and then two regressors, corresponding to group A's normalized behavioral scores followed by zeros for group B, and zeros for group A followed by group B's normalized behavioral scores.