| Random-Effects Model (k = 6) | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Estimate | se | Z | p | CI Lower Bound | CI Upper Bound | ||||||||
| Intercept | -0.66 | 0.19 | -3.57 | < .001 | -1.02 | -0.30 | |||||||
| . | . | . | . | . | . | ||||||||
| Note. Tau² Estimator: Restricted Maximum-Likelihood | |||||||||||||
| [3] | |||||||||||||
| Heterogeneity Statistics | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Tau | Tau² | I² | H² | R² | df | Q | p | ||||||||
| 0.00 | 0 (SE= 0.1253 ) | 0% | 1.00 | . | 5.00 | 8.95 | 0.111 | ||||||||
The analysis was carried out using the log odds ratio as the outcome measure. A random-effects model was fitted to the data. The amount of heterogeneity (i.e., tau²), was estimated using the restricted maximum-likelihood estimator (Viechtbauer 2005). In addition to the estimate of tau², the Q-test for heterogeneity (Cochran 1954) and the I² statistic are reported. In case any amount of heterogeneity is detected (i.e., tau² > 0, regardless of the results of the Q-test), a prediction interval for the true outcomes is also provided. Studentized residuals and Cook's distances are used to examine whether studies may be outliers and/or influential in the context of the model. Studies with a studentized residual larger than the 100 x (1 - 0.05/(2 X k))th percentile of a standard normal distribution are considered potential outliers (i.e., using a Bonferroni correction with two-sided alpha = 0.05 for k studies included in the meta-analysis). Studies with a Cook's distance larger than the median plus six times the interquartile range of the Cook's distances are considered to be influential. The rank correlation test and the regression test, using the standard error of the observed outcomes as predictor, are used to check for funnel plot asymmetry. A total of k=6 studies were included in the analysis. The observed log odds ratios ranged from -4.2646 to 0.0927, with the majority of estimates being negative (83%). The estimated average log odds ratio based on the random-effects model was \hat{\mu} = -0.6608 (95% CI: -1.0238 to -0.2979). Therefore, the average outcome differed significantly from zero (z = -3.5687, p = 0.0004). According to the Q-test, there was no significant amount of heterogeneity in the true outcomes (Q(5) = 8.9462, p = 0.1112, tau² = 0.0000, I² = 0.0026%). A 95% prediction interval for the true outcomes is given by -1.0238 to -0.2979. Hence, even though there may be some heterogeneity, the true outcomes of the studies are generally in the same direction as the estimated average outcome. One study (Dinleyici 2015) had a relatively large weight compared to the rest of the studies (i.e., \mbox{weight} \ge 3/k, so a weight at least 3 times as large as having equal weights across studies). An examination of the studentized residuals revealed that none of the studies had a value larger than ± 2.6383 and hence there was no indication of outliers in the context of this model. According to the Cook's distances, none of the studies could be considered to be overly influential. Neither the rank correlation nor the regression test indicated any funnel plot asymmetry (p = 0.7194 and p = 0.0925, respectively).
| Fail-Safe N Analysis (File Drawer Analysis) | |||
|---|---|---|---|
| Fail-safe N | p | ||
| 28.00 | < .001 | ||
| Note. Fail-safe N Calculation Using the Rosenthal Approach | |||
| Rank Correlation Test for Funnel Plot Asymmetry | |||
|---|---|---|---|
| Kendall's Tau | p | ||
| -0.20 | 0.719 | ||
| Regression Test for Funnel Plot Asymmetry | |||
|---|---|---|---|
| Z | p | ||
| -1.68 | 0.092 | ||
[1] The jamovi project (2022). jamovi. (Version 2.3) [Computer Software]. Retrieved from https://www.jamovi.org.
[2] R Core Team (2021). R: A Language and environment for statistical computing. (Version 4.1) [Computer software]. Retrieved from https://cran.r-project.org. (R packages retrieved from MRAN snapshot 2022-01-01).
[3] Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software. link, 36, 1-48.