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Fig. 6. | BMC Biology

Fig. 6.

From: Meta-evaluation of meta-analysis: ten appraisal questions for biologists

Fig. 6.

Graphical assessment tools for testing for publication bias. a A funnel plot showing greater variance among effects that have larger standard errors (SE) and that are thus more susceptible to sampling variability. Some studies in the lower right corner of the plot, opposite to most major findings, with large SE (less likely to detect significant results) are potentially missing (not shown), suggesting publication bias. b Often funnel plots are depicted using precision (1/SE), giving a different perspective of publication bias, where studies with low precision (or large SE) are expected to show greater sampling variability compared to studies with high precision (or low SE). Note that the data in panel b are the same as in panel a, except that a trim-and-fill analysis has been performed in b. A trim-and-fill analysis estimates the number of studies missing from the meta-analysis and creates ‘mirrored’ studies on the opposite side of the funnel (unfilled dots) to estimate how the overall effect size estimate is impacted by these missing studies. c Radial (Galbraith) plot in which the slope should be close to zero, if little publication bias exists, indicating little asymmetry in a corresponding funnel plot (compare it with b); radial plots are closely associated with Egger’s tests. d Cumulative meta-analysis showing how the effect size changes as the number of studies on a particular topic increases. In this situation, the addition of effect size estimates led to convergence on an overall estimate of 0.36, and the confidence intervals decrease as the precision of the estimate increases. e Bubble plot showing a temporal trend in effect size (Zr) across years. Here effect sizes are weighted by their precision; larger bubbles indicate more precise estimates and smaller bubbles less precise. f Bubble plot of the relationship between effect size and impact factors of journals, indicating that larger magnitudes of effect sizes (the absolute values of Zr) tend to be published in higher impact journals

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