Table 1.
Summary of publication bias methods to assess publication bias and estimate effect sizes corrected for publication bias.
The penultimate column lists principal references of the different methods and the final column indicates whether a method is included in the analyses of this paper.
Fig 1.
Funnel plot showing the relationship between the observed effect size (Hedges’ g; solid circles) and its standard error in a meta-analysis by Jürgens and Graudal [42] on the effect of sodium intake on Noradrenaline (left panel).
The funnel plot in the right panel also includes the Hedges’ g effect sizes that are imputed by the trim and fill method (open circles).
Fig 2.
Flowchart illustrating the extraction procedure of data from meta-analyses published in Psychological Bulletin between 2004 and 2014.
Table 2.
Hypotheses between predictors and effect size estimate based on random-effects model, p-uniform, and overestimation in effect size when comparing estimate of the random-effects model with p-uniform (Y).
Table 3.
Percentage of statistically significant effect size estimates, median number of effect sizes and median of average sample size per homogeneous subset, and mean and median of effect size estimates when the subsets were analyzed with random-effects meta-analysis, p-uniform, and random-effects meta-analysis based on the 10% most precise observed effect sizes.
Table 4.
Results of applying Egger’s regression test, rank-correlation test, p-uniform’s publication bias test, and test of excess significance (TES) to examine the prevalence of publication bias in meta-analyses from Psychological Bulletin and Cochrane Database of Systematic Reviews.
Table 5.
Results of meta-meta regression on the absolute value of the random-effects meta-analysis effect size estimate with predictors discipline, I2-statistic, harmonic mean of the standard error (standard error), and number of effect sizes in a subset.
Table 6.
Results of meta-meta-regression on the absolute value of p-uniform’s effect size estimate with predictors discipline, I2-statistic, harmonic mean of the standard error (standard error), proportion of statistically significant effect sizes in a subset (Prop. sig. effect sizes), and number of effect sizes in a subset.
Table 7.
Mean, standard deviation (SD), 95% confidence interval (CI), and median of the Y variable computed with p-uniform and the 10% most precise observed effect sizes.
Table 8.
Results of meta-meta-regression on the effect size overestimation in random-effects meta-analysis when compared to p-uniform (Y) and predictors discipline, I2-statistic, harmonic mean of the standard error (standard error), proportion of statistically significant effect sizes in a subset (Prop. sig. effect sizes), and number of effect sizes in a subset.
Fig 3.
Type-I error rate and statistical power of the rank-correlation test (open bullets), Egger’s test (triangles), test of excess significance (TES; diamonds), and p-uniform’s publication bias test (solid bullets) in the Monte-Carlo simulation study.
pub and μ are the extent of publication bias and the average true effect size, respectively.
Fig 4.
Overestimation (Y) of the random-effects model when compared with the 10% most precise observed effect sizes for simulated data based on characteristics of subsets from meta-analyses published in Psychological Bulletin (left panel) and Cochrane Database of Systematic Reviews (CDSR; right panel).
pub refers to the extent of publication bias and open bullets, triangles, and diamonds indicate no, small, and medium average true effect size. The solid line indicates the mean of the Y-variable observed in the homogeneous subsets and the dashed lines are the upper and lower bound of a 95% confidence interval (CI) around the mean of the Y-variable.