  Meta-analyses of correlation coefficients are an important technique to
integrate results from many cross-sectional and longitudinal research designs.
Uncertainty in pooled estimates is typically assessed with the help of
confidence intervals, which can double as hypothesis tests for two-sided
hypotheses about the underlying correlation. A standard 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. Results from
previous studies (Field, 2005; Hafdahl and Williams, 2009), however, indicate
that in random-effects models the performance of the HOVz confidence interval
can be unsatisfactory. To this end, we propose improvements of 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. Data were generated
via a truncated normal and beta distribution model. The results show that our
newly proposed confidence intervals based on a Knapp-Hartung-type variance
estimator or robust heteroscedasticity consistent sandwich estimators in
combination with the integral z-to-r transformation (Hafdahl, 2009) provide
more accurate coverage than existing approaches in most scenarios, especially
in the more appropriate beta distribution simulation model.
