[R-meta] Calculating effect size of within-subjects design with escalc with different correlation coefficients

[Viechtbauer, Wolfgang (SP)]

Dear Katharina,

For measure SMCR, ri is actually not involved in calculating the effect itself:

yi <- cmi * (m1i - m2i) / sd1i

where 'cmi' is a bias correction, but that's not pertinent to the issue. As you can see, with raw-score standardization, the mean change (which is identical to the difference between the means) is standardized based on sd1i, so this does not depend on ri.

For SMCC, the computation involves ri:

sddi <- sqrt(sd1i^2 + sd2i^2 - 2*ri*sd1i*sd2i)
yi <- cmi * (m1i - m2i) / sddi

So here, the value of ri does influence yi, since the mean change is standardized based on the SD of the change scores (and that depends on ri).

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Katharina Schlingensiepen
Sent: Thursday, 31 January, 2019 16:49
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Calculating effect size of within-subjects design with escalc with different correlation coefficients

Hi,
 
I am trying to calculate the effect sizes of dependent groups (cross-over design) with the escalc function "SMCR" for my meta-analysis. I tried to change the ri in the function as I wondered how the effect sizes are changing when using .0, 0.2 or 0.6 as I am missing these in the papers used for the meta-analysis and need to run a sensitivity analysis. Hereby, trying to calculate the effect sizes of the within groups, only the variance changed but not the effect size when running it with different ri which I can´t understand as ri is part of the formula and what I did wrong. The effect sizes are also higher when usin .0 as when calculating it manually.
 
I hope you can help me out.
 
Best,
Katharina