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Improved Fisher z estimators for univariate random‐effects meta‐analysis of correlations
Author(s) -
Hafdahl Adam R.
Publication year - 2009
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711008x281633
Subject(s) - estimator , mathematics , pearson product moment correlation coefficient , statistics , confidence interval , univariate , mean squared error , point estimation , correlation , multivariate statistics , geometry
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.