Improved Fisher z estimators for univariate random‐effects meta‐analysis of correlations |
| |
Authors: | Dr Adam R. Hafdahl |
| |
Affiliation: | Department of Mathematics, Washington University in St. Louis, Missouri, USA |
| |
Abstract: | Several authors have studied or used the following estimation strategy for meta‐analysing correlations: obtain a point estimate or confidence interval for the mean Fisher z correlation, and transform this estimate to the Pearson r metric. Using the relationship between Fisher z and Pearson r random variables, I demonstrate the potential discrepancy induced by directly z‐to‐r transforming a mean correlation parameter. Point and interval estimators based on an alternative integral z‐to‐r transformation are proposed. Analytic expressions for the expectation and variance of certain meta‐analytic point estimators are also provided, as are selected moments of correlation parameters; numerical examples are included. In an application of these analytic results, the proposed point estimator outperformed its usual direct z‐to‐r counterpart and compared favourably with an estimator based on Pearson r correlations. Practical implications, extensions of the proposed estimators, and uses for the analytic results are discussed. |
| |
Keywords: | |
|
|