[R-meta] Can z-transformed R-squared be used as an effect size?
m@tthew@y@te@ @end|ng |rom out|ook@com
Thu Mar 17 18:47:16 CET 2022
Hello SIG-meta folks,
I have (what I think is) a pretty quick question. I'm currently conducting a peer-review of a meta-analysis in my field.
The authors of this manuscript elected to use fisher-Z-transformed R-squared values (note: NOT Pearson correlation coefficients, but their squared-values) as their 'effect size' statistic, and then calculated variance for the z-transformed R-squared values as for a typical Pearson correlation coefficient (r).
Is this a valid statistical effect size? The z-transformation, as I understand it, was developed specifically for Pearson correlation coefficients, so this strikes me as potentially problematic - the z-transformation, itself, is meant for variables that can span -1 to 1, so the underlying distribution of the transformed variables (0 to 1 for r-squared values) are inherently different. Similarly, estimating the variances based on the sample size (n) of the z-transformed R-squared values again strikes me as potentially problematic as well.
As far as I can tell, I think pretty much all of the studies being analysed were bivariate linear regressions, so there isn't an issue with non-linear relationships, covariates, etc (I saw another post on here asking that question....). I've just never seen this done before in a meta-analysis, or read of it in any literature, guides, etc. on how to conduct a meta-analysis. Most people typically just use the z-transformed Pearson correlation coefficients, rather than the R-squared values!
I've done a few meta-analyses myself, so am familiar with general techniques but would not consider myself an expert/specialist (most of mine were pretty basic). However, this strikes me as potentially problematic, and I was wondering what others with more statistical expertise in meta-analytic techniques might think of this issue.
Any input would be appreciated.
Dr. Matthew C. Yates
Great Lakes Institute for Environmental Research (GLIER)
University of Windsor
2990 Riverside Dr W,
Windsor, ON N9C 1A2
(514) 919 5613
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