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[R-meta] Comparing dependent, overlapping correlation coefficients

Dear all,

I want to run a meta-analysis that compares dependent, overlapping
correlation coefficients (i.e., I want to see if X correlates more
strongly with Y than it does with Z). I already ran a meta-analysis
separately for both of these correlations and would now like to compare
those two pooled effect sizes statistically. Confidence intervals of the
two correlations do not overlap (r1 = .18 [.12; .24]; r2 = .32 [.25;
.39]), but I wonder if there may be a more elegant way to compare these
correlations than just based on CIs.

I wonder, for example, if a factorial variable could be used to identify
those correlations in a "long" data format style, and if I could test
for a significant interaction between variable type (Y vs. Z) and the
correlation in a meta-analysis:

    Study??? Variable??? r
    1??? Y??? .20
    1??? Z??? .30
    2??? Y??? .34
    2??? Z??? .43


I would greatly appreciate if anyone could tell me if that's a good idea
or could recommend other approaches. Thanks in advance for any offers of
help!

Best,
Anna-Lena