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Publication bias is a substantial problem for the credibility of research in general and of meta-analyses in particular, as it yields overestimated effects and may suggest the existence of non-existing effects. Although there is consensus that publication bias exists, how strongly it affects different scientific literatures is currently less well-known. We examined evidence of publication bias in a large-scale data set of primary studies that were included in 83 meta-analyses published in Psychological Bulletin (representing meta-analyses from psychology) and 499 systematic reviews from the Cochrane Database of Systematic Reviews (CDSR; representing meta-analyses from medicine). Publication bias was assessed on all homogeneous subsets (3.8% of all subsets of meta-analyses published in Psychological Bulletin) of primary studies included in meta-analyses, because publication bias methods do not have good statistical properties if the true effect size is heterogeneous. Publication bias tests did not reveal evidence for bias in the homogeneous subsets. Overestimation was minimal but statistically significant, providing evidence of publication bias that appeared to be similar in both fields. However, a Monte-Carlo simulation study revealed that the creation of homogeneous subsets resulted in challenging conditions for publication bias methods since the number of effect sizes in a subset was rather small (median number of effect sizes equaled 6). Our findings are in line with, in its most extreme case, publication bias ranging from no bias until only 5% statistically nonsignificant effect sizes being published. These and other findings, in combination with the small percentages of statistically significant primary effect sizes (28.9% and 18.9% for subsets published in Psychological Bulletin and CDSR), led to the conclusion that evidence for publication bias in the studied homogeneous subsets is weak, but suggestive of mild publication bias in both psychology and medicine., Competing Interests: I have read the journal's policy and the authors of this manuscript have the following competing interests: Jelte M. Wicherts is a PLOS ONE Editorial Board member. This does not alter the authors’ adherence to PLOS ONE Editorial policies and criteria.

One of the main goals of meta-analysis is to test for and estimate the heterogeneity of effect sizes. We examined the effect of publication bias on the Q test and assessments of heterogeneity as a function of true heterogeneity, publication bias, true effect size, number of studies, and variation of sample sizes. The present study has two main contributions and is relevant to all researchers conducting meta-analysis. First, we show when and how publication bias affects the assessment of heterogeneity. The expected values of heterogeneity measures H ² and I ² were analytically derived, and the power and Type I error rate of the Q test were examined in a Monte Carlo simulation study. Our results show that the effect of publication bias on the Q test and assessment of heterogeneity is large, complex, and nonlinear. Publication bias can both dramatically decrease and increase heterogeneity in true effect size, particularly if the number of studies is large and population effect size is small. We therefore conclude that the Q test of homogeneity and heterogeneity measures H ² and I ² are generally not valid when publication bias is present. Our second contribution is that we introduce a web application, Q-sense, which can be used to determine the impact of publication bias on the assessment of heterogeneity within a certain meta-analysis and to assess the robustness of the meta-analytic estimate to publication bias. Furthermore, we apply Q-sense to 2 published meta-analyses, showing how publication bias can result in invalid estimates of effect size and heterogeneity. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

The unrealistically high rate of positive results within psychology has increased the attention to replication research. However, researchers who conduct a replication and want to statistically combine the results of their replication with a statistically significant original study encounter problems when using traditional meta-analysis techniques. The original study's effect size is most probably overestimated because it is statistically significant, and this bias is not taken into consideration in traditional meta-analysis. We have developed a hybrid method that does take the statistical significance of an original study into account and enables (a) accurate effect size estimation, (b) estimation of a confidence interval, and (c) testing of the null hypothesis of no effect. We analytically approximate the performance of the hybrid method and describe its statistical properties. By applying the hybrid method to data from the Reproducibility Project: Psychology (Open Science Collaboration, 2015), we demonstrate that the conclusions based on the hybrid method are often in line with those of the replication, suggesting that many published psychological studies have smaller effect sizes than those reported in the original study, and that some effects may even be absent. We offer hands-on guidelines for how to statistically combine an original study and replication, and have developed a Web-based application ( https://rvanaert.shinyapps.io/hybrid ) for applying the hybrid method.

Because of overwhelming evidence of publication bias in psychology, techniques to correct meta-analytic estimates for such bias are greatly needed. The methodology on which the p-uniform and p-curve methods are based has great promise for providing accurate meta-analytic estimates in the presence of publication bias. However, in this article, we show that in some situations, p-curve behaves erratically, whereas p-uniform may yield implausible estimates of negative effect size. Moreover, we show that (and explain why) p-curve and p-uniform result in overestimation of effect size under moderate-to-large heterogeneity and may yield unpredictable bias when researchers employ p-hacking. We offer hands-on recommendations on applying and interpreting results of meta-analyses in general and p-uniform and p-curve in particular. Both methods as well as traditional methods are applied to a meta-analysis on the effect of weight on judgments of importance. We offer guidance for applying p-uniform or p-curve using R and a user-friendly web application for applying p-uniform., Competing Interests: The authors declared that they had no conflicts of interest with respect to their authorship or the publication of this article., (© The Author(s) 2016.)

Publication bias threatens the validity of meta-analytic results and leads to overestimation of the effect size in traditional meta-analysis. This particularly applies to meta-analyses that feature small studies, which are ubiquitous in psychology. Here we develop a new method for meta-analysis that deals with publication bias. This method, p-uniform, enables (a) testing of publication bias, (b) effect size estimation, and (c) testing of the null-hypothesis of no effect. No current method for meta-analysis possesses all 3 qualities. Application of p-uniform is straightforward because no additional data on missing studies are needed and no sophisticated assumptions or choices need to be made before applying it. Simulations show that p-uniform generally outperforms the trim-and-fill method and the test of excess significance (TES; Ioannidis & Trikalinos, 2007b) if publication bias exists and population effect size is homogenous or heterogeneity is slight. For illustration, p-uniform and other publication bias analyses are applied to the meta-analysis of McCall and Carriger (1993) examining the association between infants' habituation to a stimulus and their later cognitive ability (IQ). We conclude that p-uniform is a valuable technique for examining publication bias and estimating population effects in fixed-effect meta-analyses, and as sensitivity analysis to draw inferences about publication bias., ((c) 2015 APA, all rights reserved).)