Detect publication bias in your meta-analysis. Enter study effect sizes and standard errors to generate funnel plots with Egger's regression test, Begg's rank correlation, and Duval & Tweedie trim-and-fill analysis.
| Study | Effect Size | Standard Error | |
|---|---|---|---|
Add each study with its name, effect size (e.g., log OR, SMD, mean difference), and standard error. Use the example button to see the format.
The tool plots effect size (x-axis) against standard error (y-axis, inverted), with a pseudo 95% CI triangle around the pooled estimate.
Egger's regression test and Begg's rank correlation test for funnel plot asymmetry. View trim-and-fill imputed studies.
Download the funnel plot as SVG or PNG. Copy test statistics for your methods section.
Funnel plot asymmetry can result from true heterogeneity, methodological differences between small and large studies, chance, or artefacts of the effect measure. Always consider alternative explanations before concluding publication bias.
No single test is definitive. Combine visual funnel plot inspection with Egger's test, Begg's test, and trim-and-fill. Sensitivity analyses (e.g., comparing fixed vs. random effects, or excluding outliers) strengthen your conclusions.
Cochrane and PRISMA guidelines require explicit reporting of publication bias assessment. State the methods used, present the funnel plot, report test statistics and p-values, and discuss implications for the certainty of evidence.
The adjusted pooled estimate from trim-and-fill should be interpreted as 'what the result might look like if bias were present,' not as the true unbiased estimate. If the conclusion does not change materially, the finding is more robust.
Publication bias occurs when studies with statistically significant or favorable results are more likely to be published than studies with null or negative findings. This selective reporting distorts the evidence base and inflates pooled effect estimates in meta-analysis. Beyond classic publication bias, funnel plot asymmetry can also arise from time-lag bias (where studies with positive results are published faster) and language bias (where English-language journals preferentially publish significant findings). The Cochrane Handbook for Systematic Reviews of Interventions (Higgins et al., 2023, Chapter 13) identifies publication bias as one of the most serious threats to the validity of systematic reviews, and PRISMA 2020 reporting guidelines require explicit assessment.
A funnel plot generator creates the primary visual diagnostic for detecting this bias. The funnel plot maps each study's effect size on the horizontal axis against its standard error on the vertical axis (with the most precise studies at the top). In the absence of bias, studies scatter symmetrically around the pooled estimate, forming an inverted funnel shape. The pseudo 95% confidence limits create a triangular boundary — studies falling outside this region may reflect genuine heterogeneity or reporting bias. Contour-enhanced funnel plots (Peters et al., 2008) overlay regions of statistical significance onto the scatter, helping reviewers distinguish asymmetry caused by publication bias from asymmetry driven by true heterogeneity. P-curve analysis provides a complementary approach by examining the distribution of statistically significant p-values to detect whether the literature contains evidential value or shows signs of p-hacking.
Visual inspection alone is subjective, which is why a publication bias test online tool should include formal statistical tests. Egger's regression test (Egger et al., 1997) regresses standardized effects against precision and tests whether the intercept differs from zero. A significant result (p < 0.10, using the conventional threshold for this test) indicates funnel plot asymmetry. The Egger's test calculator in this tool reports the intercept, t-statistic, and exact p-value. Begg and Mazumdar's rank correlation test provides a complementary non-parametric assessment using Kendall's tau.
When asymmetry is detected, the trim and fill calculator implements Duval and Tweedie's (2000) non-parametric method to estimate the number of missing studies and impute them as mirror images of the most extreme observed studies. Modern regression-based alternatives include PET-PEESE (Stanley & Doucouliagos, 2014), which uses precision-effect testing and precision-effect estimate with standard error to provide bias-corrected pooled estimates, and selection models (Vevea & Hedges, 1995), which explicitly model the probability of publication as a function of statistical significance. The adjusted pooled estimate provides a sensitivity analysis: if the conclusion changes materially after imputation, publication bias is a concern that should be discussed when rating the certainty of evidence using the GRADE framework.
Important methodological caveats apply: all three tests have limited statistical power with fewer than 10 studies. Funnel plot asymmetry can arise from sources other than publication bias, including genuine heterogeneity, poor methodological quality of smaller studies, or artefacts of the chosen effect measure (Sterne et al., 2011). Always interpret bias tests alongside visual inspection and clinical context. Before running bias assessment, ensure your individual study effect sizes are correctly computed using our effect size calculator, and visualize the full meta-analysis with our forest plot generator to assess the overall pattern of results. Test the stability of your pooled estimate with our leave-one-out sensitivity analysis.
A funnel plot is a scatter plot used to detect publication bias in meta-analysis. It plots each study's effect size on the x-axis against a measure of precision (typically standard error) on the y-axis, with the most precise studies at the top. In the absence of bias, studies scatter symmetrically around the pooled estimate, forming an inverted funnel shape. Asymmetry suggests that smaller studies with non-significant results may be missing — a hallmark of publication bias.
Egger's test is a statistical test for funnel plot asymmetry. It regresses the standardized effect (effect / SE) against precision (1/SE). If the intercept is significantly different from zero (p < 0.10), this indicates asymmetry consistent with publication bias. The test has adequate power when there are at least 10 studies in the meta-analysis. For fewer studies, visual inspection and other methods should be used alongside Egger's test.
Trim-and-fill is a non-parametric method that estimates the number of missing studies due to publication bias and imputes them. The algorithm iteratively: (1) trims the most extreme small studies from the asymmetric side, (2) re-estimates the pooled effect, and (3) fills in the presumed missing studies as mirror images of the trimmed studies. The adjusted pooled estimate provides a sensitivity analysis — if the conclusion changes substantially, publication bias is a concern.
Begg and Mazumdar's rank correlation test examines the association between effect sizes and their variances using Kendall's tau. A significant correlation (p < 0.10) suggests that larger effects are associated with smaller (less precise) studies, which is a pattern consistent with publication bias. Like Egger's test, Begg's test has limited power with fewer than 10 studies and should be interpreted alongside visual assessment.
Publication bias tests have limited statistical power with fewer than 10 studies. Cochrane Handbook recommends not using funnel plots or statistical tests for asymmetry when there are fewer than 10 studies. With 10-30 studies, both visual inspection and statistical tests are informative. Visual funnel plot assessment remains useful even when statistical tests are underpowered, as clear asymmetry patterns can still be detected.
A minimum of 10 studies is generally recommended for funnel plot visual inspection and formal tests like Egger’s regression. With fewer than 10 studies, the power to detect asymmetry is too low, and both visual assessment and statistical tests become unreliable. The Cochrane Handbook advises against using funnel plots with fewer than 10 studies.
Funnel plot asymmetry can result from several non-publication-bias sources: true heterogeneity (smaller studies conducted in different populations), methodological differences correlated with study size, chance variation with few studies, language bias, or selective outcome reporting within studies. Sterne et al. (2011) emphasized that asymmetry should not be automatically equated with publication bias.
Trim-and-fill (Duval & Tweedie, 2000) is a non-parametric method that estimates the number of missing studies from funnel plot asymmetry, imputes their effect sizes, and recalculates the pooled estimate. It is a sensitivity analysis tool, not a definitive correction — the adjusted estimate shows what the result might look like if bias were removed, but it assumes the asymmetry is entirely due to publication bias.
Visualize individual study estimates with our forest plot generator for meta-analysis with weighted squares, CI lines, and diamond summary. Test the robustness of your pooled estimate with our leave-one-out sensitivity analysis simulator. Calculate individual study effect sizes before plotting with our effect size calculator for SMD, OR, and RR.
Our biostatisticians can conduct complete meta-analyses with rigorous publication bias assessment, produce publication-ready funnel plots and forest plots, and write the statistical methods and results sections for your systematic review.