Practical Guidance on Fisher's <i>z</i> Transformation for Meta‐Analysis of Pearson's Correlation Coefficients

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 transformation for valid estimation, weighting, and interpretation. We first provide a brief review of Fisher's 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 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.

Authors

Institutions

Publication Details

Journal
Journal of Evidence-Based Medicine
Published
2026-07-22
DOI
https://doi.org/10.1111/jebm.70165
Primary Topic
Meta-analysis and systematic reviews
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Practical Guidance on Fisher's z Transformation for Meta‐Analysis of Pearson's Correlation Coefficients

Y C Wang, Jiayu Chen, Lifeng Lin
Journal of Evidence-Based Medicine
Meta-analysis and systematic reviews
article

Practical Guidance on Fisher's z Transformation for Meta‐Analysis of Pearson's Correlation Coefficients

Y C Wang, Jiayu Chen, Lifeng Lin
article en

Abstract

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 transformation for valid estimation, weighting, and interpretation. We first provide a brief review of Fisher's 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 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.

Journal of Evidence-Based Medicine
Florida State University (US), University of Arizona (US), Eli Lilly (United States) (US)
Openalex Percentile: Top 7%
Meta-analysis and systematic reviews
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.