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Publication bias and questionable research practices in primary research can lead to badly overestimated effects in meta-analysis. Methodologists have proposed a variety of statistical approaches to correct for such overestimation. However, much of this work has not been tailored specifically to psychology, so it is not clear which methods work best for data typically seen in our field. Here, we present a comprehensive simulation study to examine how some of the most promising meta-analytic methods perform on data that might realistically be produced by research in psychology. We created such scenarios by simulating several levels of questionable research practices, publication bias, heterogeneity, and using study sample sizes empirically derived from the literature. Our results clearly indicated that no single meta-analytic method consistently outperformed all others. Therefore, we recommend that meta-analysts in psychology focus on sensitivity analyses—that is, report on a variety of methods, consider the conditions under which these methods fail (as indicated by simulation studies such as ours), and then report how conclusions might change based on which conditions are most plausible. Moreover, given the dependence of meta-analytic methods on untestable assumptions, we strongly recommend that researchers in psychology continue their efforts on improving the primary literature and conducting large-scale, pre-registered replications. We provide detailed results and simulation code at https://osf.io/rf3ys and interactive figures at http://www.shinyapps.org/apps/metaExplorer/.
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