Bayesian meta-analysis of correlation coefficients through power prior

TL;DR

This paper introduces a Bayesian meta-analysis method using power priors to weight studies by reliability, improving the accuracy of overall effect size estimates in organizational research.

Contribution

It presents a novel Bayesian approach with power priors for meta-analysis, allowing differential weighting of studies based on reliability, with an illustrative example and software tools.

Findings

Enhanced accuracy in effect size estimation.

Flexible weighting of studies based on reliability.

Practical application with online software.

Abstract

To answer the call of introducing more Bayesian techniques to organizational research (e.g., Kruschke, Aguinis, & Joo, 2012; Zyphur & Oswald, 2013), we propose a Bayesian approach for meta-analysis with power prior in this article. The primary purpose of this method is to allow meta-analytic researchers to control the contribution of each individual study to an estimated overall effect size though power prior. This is due to the consideration that not all studies included in a meta-analysis should be viewed as equally reliable, and that by assigning more weights to reliable studies with power prior, researchers may obtain an overall effect size that reflects the population effect size more accurately. We use the relationship between high-performance work systems and financial performance as an example to illustrate how to apply this method to organizational research. We also provide free online software that can be used to conduct Bayesian meta-analysis proposed in this study. Research implications and future directions are discussed.