Academic Journal
Practical Guidance on Fisher's z Transformation for Meta-Analysis of Pearson's Correlation Coefficients.
| Title: | Practical Guidance on Fisher's z Transformation for Meta-Analysis of Pearson's Correlation Coefficients. |
|---|---|
| Authors: | Chen J; Department of Statistics, Florida State University, Tallahassee, USA., Wang Y; Eli Lilly and Company, Indianapolis, USA., Lin L; Department of Epidemiology and Biostatistics, University of Arizona, Tucson, USA. |
| Source: | Journal of evidence-based medicine [J Evid Based Med] 2026 Sep; Vol. 19 (3), pp. e70165. Date of Electronic Publication: 2026 Jul 22. |
| Publication Type: | Journal Article |
| Language: | English |
| Journal Info: | Publisher: Wiley-Blackwell Country of Publication: England NLM ID: 101497477 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1756-5391 (Electronic) Linking ISSN: 17565391 NLM ISO Abbreviation: J Evid Based Med Subsets: MEDLINE |
| Imprint Name(s): | Original Publication: Oxford : Wiley-Blackwell |
| MeSH Terms: | Meta-Analysis as Topic* , Software*, Data Interpretation, Statistical ; Humans |
| Abstract: | Meta-analyses of correlation coefficients are widely used to synthesize evidence on associations among variables in psychology, medicine, education, and the social sciences, yet practical guidance on how to implement these analyses in standard software remains limited. In this article, we provide a step-by-step introduction to conducting meta-analyses of correlation coefficients in Stata and R, with focus on the use of Fisher's INLINEMATH transformation for valid estimation, weighting, and interpretation. We first provide a brief review of Fisher's INLINEMATH transformation as a statistical foundation for synthesizing correlation coefficients. Using a simple toy dataset consisting of seven artificial studies, we then illustrate how to properly implement correlation meta-analyses in Stata, highlighting the behavior of forest and funnel plots when Fisher's INLINEMATH transformation is applied and when it is omitted. Parallel workflows are demonstrated in R using the "meta" and "metafor" packages, including effect size specification, fitting under the random-effects model, and generation of forest and funnel plots. We compare the results and visualizations produced by the different software tools and outline their respective functionalities. Sample code and practical recommendations are provided to help researchers avoid common pitfalls and to conduct correlation-based meta-analyses that are statistically sound and readily interpretable. (© 2026 Chinese Cochrane Center, West China Hospital of Sichuan University and John Wiley & Sons Australia, Ltd.) |
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| Grant Information: | R03 AG093555 United States AG NIA NIH HHS; R21 LM014533 United States LM NLM NIH HHS; RFGA2023-008-11 Arizona Biomedical Research Centre; R03 AG093555 US National Institute on Aging; R21 LM014533 US National Library of Medicine |
| Contributed Indexing: | Keywords: R software; Stata; correlation; data transformation; forest plot; funnel plot; meta‐analysis |
| Entry Date(s): | Date Created: 20260722 Date Completed: 20260925 Latest Revision: 20260930 |
| Update Code: | 20260930 |
| PubMed Central ID: | PMC13403996 |
| DOI: | 10.1111/jebm.70165 |
| PMID: | 42482605 |
| Database: | MEDLINE |
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