A Bayesian approach to mitigation of publication bias

The reliability of published research findings in psychology has been a topic of rising concern. Publication bias, or treating positive findings differently from negative findings, is a contributing factor to this “crisis of confidence,” in that it likely inflates the number of false-positive effects in the literature. We demonstrate a Bayesian model averaging approach that takes into account the possibility of publication bias and allows for a better estimate of true underlying effect size. Accounting for the possibility of bias leads to a more conservative interpretation of published studies as well as meta-analyses. We provide mathematical details of the method and examples.