In order to address publication bias, we computed the fail-safe N (Rosenthal, 1991; Rosenthal & Rubin, 1988) using the following formula: X=K(KZ‒2−2.706)2.706. In this formula, K is the number of studies in the meta-analysis and Z̄ is the mean Z obtained from the K studies. The effect size can be considered robust if the required number of studies (X) to reduce the overall effect size to a non-significant level exceeds 5K + 10 (Rosenthal, 1991). In addition, we constructed a funnel plot to examine the publication bias. No publication bias results in a funnel plot that is symmetrical around the mean effect size. The Trim and Fill method examines whether negative or positive trials are over or under-represented, accounting for the sample size (i.e., where the missing studies would need to fall to make the plot symmetrical). This information can then be used to re-calculate the effect size estimate.
