Funnel Plot

Definition

A funnel plot is a scatter plot of effect-size estimates from multiple studies against a measure of study precision (typically the standard error or sample size). In the absence of bias, the plot should resemble a symmetrical inverted funnel, with small studies scattered widely at the bottom and large studies clustered tightly at the top. Asymmetry suggests publication bias or other systematic distortions.

Why It Matters

Publication bias occurs when studies with statistically significant or positive results are more likely to be published than null or negative findings. This distorts the evidence base and can lead to overestimated treatment effects in meta-analyses. Funnel plots provide a visual diagnostic for this problem. When asymmetry is detected, researchers should use statistical adjustments such as trim-and-fill or selection models, or conduct sensitivity analyses.

Example

A meta-analysis of 20 drug trials reports a pooled odds ratio of 0.60 favouring the experimental treatment. The funnel plot shows a gap in the bottom-left quadrant: small studies with null or negative results are missing. Egger's test for funnel-plot asymmetry is significant (p = 0.03). The researcher applies the trim-and-fill method, which imputes four missing studies and revises the pooled odds ratio to 0.75 — a smaller but more realistic treatment effect.

Related Terms

• Meta-Analysis
• Forest Plot
• Effect Size
• Publication Bias (not a separate page on staging)

Software Notes

• SPSS: Funnel plots are not available natively. Use RevMan, Comprehensive Meta-Analysis, or R.
• R: metafor::funnel(rma_model) draws a funnel plot. metafor::trimfill(rma_model) applies the trim-and-fill adjustment. metafor::regtest(rma_model) performs Egger's regression test for asymmetry.
• Stata: metafunnel effect se draws a funnel plot. metabias effect se, egger performs Egger's test. metatrim effect se applies the trim-and-fill method.