Effect size on X, precision on Y. Asymmetry suggests publication bias.
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Funnel Plot
A funnel plot displays all studies in a meta-analysis as individual dots. The horizontal axis shows the effect size (relative risk, mean difference, or similar). The vertical axis shows study precision, typically plotted as 1/standard error so that large, precise studies cluster near the top of the chart and small, imprecise studies fall toward the bottom.
The inverted-V funnel shape is drawn around the pooled estimate at the expected spread for each level of precision. In the absence of bias, dots should scatter symmetrically inside the funnel: large studies near the apex, small studies spread more widely below.
A symmetric funnel suggests the literature is unbiased. Asymmetry, where one side of the funnel is emptier than the other, raises the possibility of publication bias: small studies finding null or harmful effects may not have been published, leaving only the positive small studies to appear in the lower right of the chart.
However, asymmetry can also arise from genuine heterogeneity (the treatment works better in contexts that happen to be studied by smaller research groups), outcome reporting bias, or chance. The Egger test and Begg test provide formal statistical tests for asymmetry, but both have limited power when fewer than ten studies are available.
The funnel plot was introduced by Light and Pillemer in their 1984 book on research synthesis and further developed by Egger and colleagues in the late 1990s. Egger's 1997 BMJ paper proposed using the regression of standardized effect on precision as a formal test (Egger's test). Sterne and Egger later published guidelines cautioning against over-reliance on funnel plot interpretation, noting that the interpretation depends heavily on how many studies are available and whether heterogeneity is present.
The Cochrane Handbook recommends funnel plots only when at least ten studies are included in a meta-analysis, as smaller numbers make visual or statistical assessment of asymmetry unreliable.
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Source & accuracy
This funnel plot is an editorial illustration built to represent the concept accurately. Where it shows figures, they are typical or representative values chosen to make the relationship clear, not a single underlying dataset. The diagram and its explainer are reviewed and maintained centrally, and updated over time as understanding improves.
Asymmetry as a sign of publication bias
A funnel plot places effect size on the horizontal axis and precision (often inverse standard error or sample size) on the vertical. In the absence of bias, studies scatter symmetrically around the pooled effect: large, high-precision studies near the top center, small studies spread widely below. The shape resembles an inverted funnel.
When the funnel is asymmetrical, missing small negative studies typically nest on the left, suggesting that small trials showing no effect went unpublished while small trials showing large effect made it into print. This publication bias inflates the apparent overall benefit, and the asymmetric funnel signals that reported effects may be artificially large.
Limitations and alternative explanations
Funnel asymmetry is suggestive, not definitive. Genuine heterogeneity, true variation in effect size by study size, or differences in study methodology can mimic publication bias. Statistical tests for asymmetry (Egger regression) are popular but prone to false positives. Asymmetry observed in a meta-analysis of only five studies should be interpreted cautiously.
Addressing potential publication bias includes searching trial registries for unpublished results, contacting authors for missing data, and repeating analyses under assumptions of missing studies. Cumulative meta-analysis, contour plots, and sensitivity analyses offer additional lenses for assessing whether conclusions rest on reported data alone or withstand adjustment for plausible missing evidence.
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Reference
What this is
A free, embeddable, animated funnel plot for any website.
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