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A Hybrid Method for Combining a Statistically Significant Original Study and a Replication Tilburg University Examining reproducibility in psychology Van Aert, R.C.M.; Van Assen, M.A.L.M. Published in: Behavior Research Methods DOI: 10.3758/s13428-017-0967-6 Publication date: 2018 Document Version Publisher's PDF, also known as Version of record Link to publication in Tilburg University Research Portal Citation for published version (APA): Van Aert, R. C. M., & Van Assen, M. A. L. M. (2018). Examining reproducibility in psychology: A hybrid method for combining a statistically significant original study and a replication. Behavior Research Methods, 50(4), 1515- 1539. https://doi.org/10.3758/s13428-017-0967-6 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 27. sep. 2021 Behav Res DOI 10.3758/s13428-017-0967-6 Examining reproducibility in psychology: A hybrid method for combining a statistically significant original study and a replication Robbie C. M. van Aert1 & Marcel A. L. M. van Assen1,2 # The Author(s) 2017. This article is an open access publication Abstract The unrealistically high rate of positive results within replication, and have developed a Web-based application psychology has increased the attention to replication research. (https://rvanaert.shinyapps.io/hybrid) for applying the hybrid However, researchers who conduct a replication and want to method. statistically combine the results of their replication with a statis- tically significant original study encounter problems when using Keywords Replication . Meta-analysis . p-Uniform . ’ traditional meta-analysis techniques. The original study s effect Reproducibility size is most probably overestimated because it is statistically significant, and this bias is not taken into consideration in tradi- tional meta-analysis. We have developed a hybrid method that Increased attention is being paid to replication research in does take the statistical significance of an original study into psychology, mainly due to the unrealistic high rate of positive account and enables (a) accurate effect size estimation, (b) esti- results within the published psychological literature. mation of a confidence interval, and (c) testing of the null hy- Approximately 95% of the published psychological research pothesis of no effect. We analytically approximate the perfor- contains statistically significant results in the predicted direc- mance of the hybrid method and describe its statistical proper- tion (Fanelli, 2012; Sterling, Rosenbaum, & Weinkam, 1995). ties. By applying the hybrid method to data from the This is not in line with the average amount of statistical power, Reproducibility Project: Psychology (Open Science which has been estimated at .35 (Bakker, van Dijk, & Collaboration, 2015), we demonstrate that the conclusions based Wicherts, 2012) or .47 (Cohen, 1990) in psychological re- on the hybrid method are often in line with those of the replica- search and .21 in neuroscience (Button et al., 2013), indicating tion, suggesting that many published psychological studies have that statistically nonsignificant results often do not get pub- smaller effect sizes than those reported in the original study, and lished. This suppression of statistically nonsignificant results that some effects may even be absent. We offer hands-on guide- from being published is called publication bias (Rothstein, lines for how to statistically combine an original study and Sutton, & Borenstein, 2005). Publication bias causes the pop- ulation effect size to be overestimated (e.g., Lane & Dunlap, 1978; van Assen, van Aert, & Wicherts, 2015) and raises the Electronic supplementary material The online version of this article question whether a particular effect reported in the literature (https://doi.org/10.3758/s13428-017-0967-6) contains supplementary actually exists. Other research fields have also shown an ex- material, which is available to authorized users. cess of positive results (e.g., Ioannidis, 2011; Kavvoura et al., 2008; Renkewitz, Fuchs, & Fiedler, 2011;Tsilidis, * Robbie C. M. van Aert Papatheodorou, Evangelou, & Ioannidis, 2012), so publica- [email protected] tion bias and the overestimation of effect size by published research is not only an issue within psychology. 1 Department of Methodology and Statistics, Tilburg University, Replication research can help to identify whether a particular P.O. Box 90153, 5000 LE Tilburg, The Netherlands effect in the literature is probably a false positive (Murayama, 2 Department of Sociology, Utrecht University, Pekrun, & Fiedler, 2014), and to increase accuracy and precision Utrecht, The Netherlands of effect size estimation. The Open Science Collaboration Behav Res carried out a large-scale replication study to examine the repro- a replication and want to aggregate the results of the original ducibility of psychological research (Open Science study and their own replication. Cumming (2012,p.184)em- Collaboration, 2015). In this so-called Reproducibility Project: phasized that combining two studies by means of a meta- Psychology (RPP), articles were sampled from the 2008 issues analysis has added value over interpreting two studies in isola- of three prominent and high-impact psychology journals and a tion. Moreover, researchers in the field of psychology have also key effect of each article was replicated according to a structured started to use meta-analysis to combine the studies within a protocol. The results of the replications were not in line with the single article, in what is called an internal meta-analysis results of the original studies for the majority of replicated ef- (Ueno, Fastrich, & Murayama, 2016). Additionally, the propor- fects. For instance, 97% of the original studies reported a statis- tion of published replication studies will increase in the near tically significant effect for a key hypothesis, whereas only 36% future due to the widespread attention to the replicability of of the replicated effects were statistically significant (Open psychological research nowadays. Finally, we must note that Science Collaboration, 2015). Moreover, the average effect size the Makel, Plucker, and Hegarty’s(2012)estimateof1%of of the replication studies was substantially smaller (r = .197) published studies in psychology being replications is a gross than those of original studies (r = .403). Hence, the results of underestimation. They merely searched for the word the RPP confirm both the excess of significant findings and Breplication^ and variants thereof in psychological articles. overestimation of published effects within psychology. However, researchers often do not label studies as replications, The larger effect size estimates in the original studies than in to increase the likelihood of publication (Neuliep & Crandall, their replications can be explained by the expected value of a 1993), even though many of them carry out a replication before statistically significant original study being larger than the true starting their own variation of the study. To conclude, making mean (i.e., overestimation). The observed effect size of a repli- sense of and combining the results of an original study and a cation, which has not (yet) been subjected to selection for sta- replication is a common and important problem. tistical significance, will usually be smaller. This statistical prin- The main difficulty with combining an original study and a ciple of an extreme score on a variable (in this case a statistically replication is how to aggregate a likely overestimated effect size significant effect size) being followed by a score closer to the in the published original study with the unpublished and prob- true mean is also known as regression to the mean (e.g., Straits ably unbiased replication. For instance, what should a research- & Singleton, 2011, chap. 5). Regression to the mean occurs if er conclude when the original study is statistically significant simultaneously (i) selection occurs on the first measure (in our and the replication is not? This situation often arises—for ex- case, only statistically significant effects), and (ii) both of the ample, of the 100 effects examined in the RPP, in 62% of the measures are subject to error (in our case, sampling error). cases the original study was statistically significant, whereas the It is crucial to realize that the expected value of statistically replication was not. To examine the main problem in more significant observed effects of the original studies will be larger detail, consider the following hypothetical situation. Both the than the true effect size irrespective of the presence of publica- original study and replication consist of two independent groups tion bias. That is, conditional on being statistically significant, of equal size, with the total sample size in the replication being the expected
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