Esther Mertens

120 | Chapter 6 Publication Bias As commonly known, studies with nonsignificant or negative results are less likely to be published than studies with significant or positive results. The risk of publication bias was tested using a funnel plot. When the funnel plot was asymmetrical according to Egger’s regression test (Egger, Schmidt, Schneider, & Minder, 1997) the trim-and-fill analysis (Duval & Tweedie, 2000a; 2000b) was used to adjust the effect for possible publication bias. This analysis estimates howmany studies fall outside the symmetric part of the funnel plot and trims this outlying part. With the remaining symmetric funnel plot the true center of the funnel is estimated. The trimmed studies and their missing counterparts are replaced in the funnel representing imputed ‘missing’ effect sizes. Based on this filled funnel plot, the corrected mean is estimated resulting in an adjusted effect size. Tests to visualize and examine publication bias assume independence of effect sizes, which is not the case in multilevel meta-analyses. We took this violation into account by using the variance of the effect sizes as a moderator in Egger’s regression test. Analyses We calculated an effect size for each reported measure of the intra- or interpersonal domain. To account for the clustering of effect sizes within a trial, we used multilevel meta-analytical models with three levels: Sampling variance around each effect size (level 1), variance between effect sizes within studies (level 2), and variance between studies (level 3; Assink & Wibbelink, 2016; Van den Noortgate, López-López, Marín- Martínez, & Sánchez-Meca, 2013). The unit of analyses were the interventions rather than the publications, since we are interested in the effectiveness of the intervention compared to the control condition. When one publication reported on two interventions, both interventions were included and analyzed separately. When multiple publications reported on the same intervention, evaluated in different studies with different samples, their effect sizes were analyzed together, clustered within the same intervention. When multiple publications reported on the same intervention, evaluated in the same study with the same sample, we coded the most comprehensive publication; the less comprehensive publicationwas checked for additional information and their effect sizes were analyzed together, clustered within the same intervention. The multilevel analyses were conducted in R using the metaphor package (Viechtbauer, 2010). First, the overall effects of universal school-based interventions on students’ intrapersonal and interpersonal domains were estimated in separate models. Methodological rigor was assessed to examine how well the overall effect sizes reflected the effects of the intervention rather than methodological influences or biases (Lipsey & Wilson, 2001). Based on the Cochrane Risk of Bias 2.0 tool for