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

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