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Cited by 725Meta-analysis and systematic reviewsPsychology Research and BibliometricsReliability and Agreement in Measurement

Meta-analysis of correlation coefficients: A Monte Carlo comparison of fixed- and random-effects methods.

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Field, Andy P.·2001·Psychological Methods
DOI 10.1037/1082-989x.6.2.161
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Abstract

The efficacy of the Hedges and colleagues, Rosenthal-Rubin, and Hunter-Schmidt methods for combining correlation coefficients was tested for cases in which population effect sizes were both fixed and variable. After a brief tutorial on these meta-analytic methods, the author presents two Monte Carlo simulations that compare these methods for cases in which the number of studies in the meta-analysis and the average sample size of studies were varied. In the fixed case the methods produced comparable estimates of the average effect size; however, the Hunter-Schmidt method failed to control the Type I error rate for the associated significance tests. In the variable case, for both the Hedges and colleagues and Hunter-Schmidt methods, Type I error rates were not controlled for meta-analyses including 15 or fewer studies and the probability of detecting small effects was less than .3. Some practical recommendations are made about the use of meta-analysis.

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  • Eight studies involving 444 participants reported correlation sizes; meta-analytically combined, the average r = .02, which did not differ significantly from zero, z = .29, p > .70.

    “Eight studies in Table 3 involving a total of 444 participants reported actual correlation sizes and these were combined meta-analytically (Field, 2001; Hunter & Schmidt, 1990). Where more than one effect was reported separately within a single study, their average was used. This yielded an average r = .02, which did not differ significantly from zero, z = .29, p > .70.”

    From Episodic memory, perceptual memory, and their interaction: Foundations for a theory of posttraumatic stress disorder. (2014) · cites this paper as Field, 2001

  • Field (2001) shows that using the Fisher z transformation for heterogeneous effect sizes overestimates the true effect size by about 15% to 45%.

    “Moreover, Field (2001) shows that using the Fisher z transformation for heterogeneous effect sizes overestimates the true effect size by about 15 % to 45 % .”

    From A Meta-Analysis of Organizational Complaint Handling and Customer Responses (2011) · cites this paper as Field (2001)

  • Fisher z-transformation was not applied because it would underestimate the actual variance and overestimate the effect size of heterogeneous correlations typical in marketing studies by 15% to 45%.

    “we did not apply a Fisher z-transformation when integrating effect sizes, because these correlations would underestimate the coefficients' actual variance and overestimate the effect size of heterogeneous correlations (as are typical in marketing studies) by 15% to 45%.”

    From Understanding and managing customer relational benefits in services: a meta-analysis (2020) · cites this paper as Field 2001

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Authors
Field, A. P.
Affiliations
University of Sussex (GB)
Corresponding author
Field, Andy P.
ORCID
Field, Andy P.
Venue
Psychological Methods
Publisher
American Psychological Association (APA)
Published
2001
Volume
6
Issue
2
Pages
161-180
ISSN
  • 1082-989X (ISSN-L)
  • 1939-1463
DOI
10.1037/1082-989x.6.2.161
OpenAlex
W2103027218
Cited by
725
References
6
Citations by year
2026: 13 · 2025: 29 · 2024: 25 · 2023: 34 · 2022: 41 · 2021: 36 · 2020: 36 · 2019: 33 · 2018: 33 · 2017: 37 · 2016: 35 · 2015: 43 · 2014: 41 · 2013: 41 · 2012: 37
FWCI
2.10
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Psychological Methods (publishedVersion)
  • PubMed (publishedVersion)
  • Sussex Research Online (University of Sussex) (submittedVersion)
  • Figshare (submittedVersion, cc-by)
Topics
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Reliability and Agreement in Measurement
Keywords
fixed effects model, random effects models, type I error rate, sample size, Monte Carlo simulation
MeSH terms
Humans, Monte Carlo Method, Psychometrics, Meta-Analysis as Topic, Reproducibility of Results

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