Marianne Welmers

Chapter 2 38 In addition, we performed a trim and fill procedure, as described by Duval and Tweedie (2000), to test for indications of overestimation or underestimation of the true overall effect size. By using the trim and fill procedure a funnel plot can be drawn, showing whether studies or effect sizes are missing on the left or right side of the distribution of effect sizes. A funnel plot withmissing effect sizes on the left side of the distribution is an indication that the overall estimate is an overestimation of the true effect. When the funnel plot indicates missing effect sizes on the right side of the distribution, it is expected that the overall effect size is an underestimation of the true effect. These trim and fill analyses were performed for all associations using all available effect sizes in R with the function “trimfill” of the metafor package (Viechtbauer, 2015). Results Correlation between Alliance and Outcomes Table 3 shows the overall effect sizes for the meta-analyses on level of alliance and outcome, split alliances and outcome and alliance change scores and outcome. The effect size for the relation between level of alliance and outcome was significant ( r = .183; 95% CI .100, .265; p < .001), indicating that higher levels of therapeutic alliance are related to better outcomes of family-involved treatment. The estimate was calculated fromdata of 20 independent samples reporting on 329 effect sizes. The effect size for the correlation between split alliance and outcome was not significant ( r = .106; CI -.124, .327; p = .343). This estimate was calculated from5 study samples reporting on 17 effect sizes. The effect size for the correlation between alliance change scores and outcome just failed to reach significance, showing a trend ( r = .281, CI -.023, .538; p = .067), which suggests that alliances that improve during the treatment process might lead to more favorable treatment outcomes. This estimate was calculated from 3 study samples reporting on 15 effect sizes. Moderator Analyses When applying the 75% rule of Hunter and Schmidt (1990), we concluded that for all three meta-analyses less than 75%of the total variance could be attributed to randomsampling error (level 1), and heterogeneity at level 2 and 3 could be considered substantial. We therefor conducted moderator analyses for all three meta-analyses. Moderator analyses on level of alliance and outcome correlation The results of the moderator analyses on the level of alliance and outcome correlation are depicted in Table 4.