[R-meta] Comparing dependent, overlapping correlation coefficients

[Viechtbauer, Wolfgang (SP)]

Hi Anna-Lena,

Do you have cor(Y,Z)? Then this allows you to compute the covariance between cor(X,Y) and cor(X,Z) -- which is what you need to do a proper test. Indeed, you want the data in long format as you have them, but you also need the 2x2 var-cov matrix for each study. You can compute this with:

https://gist.github.com/wviechtb/700983ab0bde94bed7c645fce770f8e9

See also this thread in the archives:

https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-January/000483.html

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Anna-Lena Schubert
Sent: Friday, 10 August, 2018 16:21
To: r-sig-meta-analysis using r-project.org
Subject: [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