[R-meta] Can z-transformed R-squared be used as an effect size?

Matthew Yates 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.

Thanks,

Dr. Matthew C. Yates

Post-doctoral Researcher

Great Lakes Institute for Environmental Research (GLIER)
University of Windsor
2990 Riverside Dr W,
Windsor, ON N9C 1A2

(514) 919 5613

Website: https://matthewyates6.wixsite.com/ecologist

[[alternative HTML version deleted]]

```