33 Review of social network intervention studies 2 For statistical analyses we used the function “rma.mv” of the metafor package in R (version 4.0.2; R Core Team, 2021; Viechtbauer, 2010) and Statistical Package for the Social Sciences (IBM SPSS Statistics, 2019), version 26. First, to obtain mean Cohen’s d estimates of the effectiveness of social network interventions on themain outcome categories, a three-level random effects model was used (Assink & Wibbelink, 2016; van den Noortgate, López-López, Marín-Martínez, & Sánchez-Meca, 2013). In addition, mean effect sizes for outcome subcategories were estimated with empty (intercept-only) three-level models if the subcategory was filled with at least three studies. We intended to achieve maximum statistical power by using all available effect sizes in the analyses. However, multiple effect sizes extracted from the same study are expected to be more similar than effect sizes from different studies, resulting in dependency of effect sizes. With the three-level random effects model it was possible to account for dependency due to multiple effect sizes within studies. To account for dependency of effect sizes, three sources of variance were modelled: sampling variance of the observed effect sizes (level 1), variance between effect sizes from the same study (level 2), and variance between studies (level 3) (Cheung, 2014; López‐López, Marín‐Martínez, Sánchez‐Meca, van den Noortgate, & Viechtbauer, 2014; van den Noortgate et al., 2013). Furthermore, a likelihood ratio test was used to examine variation between effect sizes from the same study (i.e., within-study heterogeneity) or between studies (i.e., between-study heterogeneity) (Raudenbush & Bryk, 2002). In order to visualize the variability of effect sizes within and between studies, we used an extended three-level forest plot (Fernández-Castilla et al., 2020). Second, to further analyze the heterogeneity, moderator analyses were conducted by extending the models with the predefined categorical and continuous outcome, sample, intervention, and study characteristics. Moderator analyses using categorical moderators were only conducted if categories were filled with at least three studies. An omnibus test of the fixed-model parameters was used for these extended models to test the null hypothesis of equal mean group effect sizes. Subsequently, if multiple significant moderators were found, we conducted an additional moderator analysis by adding all significant moderators to one model to examine the unique contribution of each significant moderator in explaining effect size over and above the contribution of the other moderators. Adjustments were applied to control for type I error rates (Knapp & Hartung, 2003). We addressed potential publication bias and selective outcome reporting bias by using multiple methods, including visual inspection of funnel plots with individual effect sizes as well as study effect sizes (Fernández-Castilla et al., 2021b; Fernández-Castilla et al., 2020),
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