Editverse Free Calculator
Publication Bias Calculator (Funnel Plot & Egger’s Test)
Check a meta-analysis for small-study effects — build a funnel plot and run Egger’s regression test — with the exact R command behind the result. A full interpretation guide follows below. Validated against R 4.3.3.
In Simple Words
Publication bias arises when studies with small or non-significant results are less likely to be published, so the studies you can find overstate the true effect. A funnel plot displays each study’s effect against its precision; without bias the points form a symmetric inverted funnel.
Egger’s test turns that visual check into a number by regressing the standardised effect on its precision. A significant intercept signals funnel-plot asymmetry, which may reflect publication bias — though it can also arise from true heterogeneity or chance, so the result is a flag, not a verdict.
When to Use Publication-Bias Tests
Assess publication bias whenever you pool studies in a meta-analysis, especially if the included studies are mostly small. Asymmetry suggests the pooled estimate may be inflated by missing negative studies, which matters most when the summary effect drives a clinical or policy conclusion.
Interpret these tests cautiously and never in isolation. With fewer than about ten studies they have little power and unreliable results. Pair the funnel plot and Egger’s test with sensitivity analyses, and read them alongside the pooled effect size and study heterogeneity. Unsure which checks your review needs? Our Test Selector can help.
Expected: one row per record, label, effect, standard error
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected: one row per record, label, effect, standard error
library(meta)
studlab <- c({funnel_studlab})
TE <- c({funnel_te})
seTE <- c({funnel_se})
m <- metagen(TE, seTE, studlab = studlab, common = TRUE, random = FALSE)
summary(m) # fixed-effect pooled estimate and 95% CI, as the calculator reports
funnel(m)
metabias(m, method.bias = "linreg", k.min = 3) # Egger's regression test: intercept, t, pUser guide
When to use. Detect funnel-plot asymmetry (a marker of possible publication bias) via Egger’s regression test.
Assumptions. At least ~10 studies for a well-powered Egger test; effect sizes and standard errors per study.
Common mistakes. Asymmetry can also reflect genuine heterogeneity or small-study effects, not only bias.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Egger M, Davey Smith G, Schneider M, Minder C. Bias in meta-analysis detected by a simple, graphical test. BMJ. 1997;315:629-634.
Worked Examples
Example 1 — A symmetric funnel
Ten studies of varying size scatter evenly around the pooled effect, with small studies spread wider at the base and large studies clustered near the top. Egger’s test returns a non-significant intercept. There is no evidence of small-study effects, and the pooled estimate is not obviously distorted by missing studies.
Example 2 — Asymmetry detected
Small studies sit predominantly on the side of a larger effect, leaving a gap where small negative studies would be. Egger’s test is significant. This pattern is consistent with publication bias, so you would report the asymmetry and explore its impact with sensitivity analysis before trusting the summary.
Assumptions to Check
Enough studies. Funnel plots and Egger’s test need a reasonable number of studies — commonly at least ten — to give meaningful results. With fewer, asymmetry cannot be assessed reliably.
A spread of study sizes. The methods rely on contrast between small, imprecise studies and large, precise ones. If all studies are similar in size, the funnel has no shape to interpret.
Asymmetry has several possible causes. Funnel asymmetry is not proof of publication bias; true between-study heterogeneity, poor methodological quality in small studies, or chance can all produce it.
Common Mistakes
Running the test on too few studies
With under about ten studies, Egger’s test has very low power and the funnel plot is hard to read. Reporting a “non-significant” result here gives false reassurance.
Equating asymmetry with publication bias
Asymmetry is consistent with bias but does not prove it. State it as a small-study effect with several possible explanations rather than a confirmed bias.
Choosing the wrong test for the effect measure
Egger’s regression test was developed for certain effect metrics; alternative tests suit binary outcomes with rare events. Match the test to your data rather than defaulting to one.
Ignoring the magnitude of the implied bias
Even real asymmetry may shift the pooled estimate only slightly. Use trim-and-fill or sensitivity analysis to gauge how much the conclusion would actually change.
Frequently Asked Questions
What does a funnel plot show?
It plots each study’s effect estimate against its precision; a symmetric inverted funnel suggests no small-study effects, while a gap or lopsided spread suggests possible bias.
Is a significant Egger’s test proof of publication bias?
No. It indicates funnel-plot asymmetry, which is consistent with publication bias but can also arise from heterogeneity, study quality, or chance.
How many studies do I need?
As a rule of thumb, at least ten. Below that, both the plot and the formal test are unreliable and should be interpreted with great caution or not at all.
Does the result match R and Stata?
Yes. The calculator uses the standard Egger linear-regression test of funnel asymmetry and shows the exact R command so you can reproduce the intercept and p-value.
Related Calculators
References
- Egger M, Davey Smith G, Schneider M, Minder C. Bias in meta-analysis detected by a simple, graphical test. BMJ. 1997;315(7109):629–634. PMID 9310563.
- Sterne JAC, Sutton AJ, Ioannidis JPA, et al. Recommendations for examining and interpreting funnel plot asymmetry in meta-analyses of randomised controlled trials. BMJ. 2011;343:d4002. PMID 21784880.
- Duval S, Tweedie R. Trim and fill: a simple funnel-plot-based method of testing and adjusting for publication bias in meta-analysis. Biometrics. 2000;56(2):455–463.
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