Title: Fisher-z based Confidence Intervals of Correlations in Fixed and
Random-Effects Meta-Analysis

Author: Thilo Welz

Affiliation: TU Dortmund

Abstract:  
In the fields of Psychology and Sociology investigators often consider
meta-analyses with Pearson correlation coefficients as effect measure of
interest. A classical approach to construct confidence intervals for the main
effect is the Hedges-Olkin-Vevea Fisher-z (HOVz) approach, which is based on
the Fisher-z transformation. This approach has been analyzed in various
papers, such as (Field, 2005) and (Hafdahl and Williams, 2009). Their results
indicate that in random-effects models with substantial amounts of
heterogeneity the performance of the HOVz confidence interval can be
unsatisfactory. We propose improvements to the HOVz approach, which are based
on enhanced variance estimators for the main effect estimate. In order to
study the coverage of the new confidence intervals in both fixed- and
random-effects meta-analysis models, we perform an extensive simulation study,
comparing them to established approaches.