[R-meta] Can z-transformed R-squared be used as an effect size?
Dear Matthew I share your concerns and doubts about this. I would hesitate to go out on a limb over it but if you are reviewing it for a journal I would suggest politely telling the authors that you find it hard to justify and ask them to provide a reference or other wise justify it. I do not make confidential comments to the editors on principle but if I did I would tell them that unless the authors can justify it the paper demands instant rejection. Michael
On 17/03/2022 17:47, Matthew Yates wrote:
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]]
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