Egger’s test is a regression test for funnel-plot asymmetry, the tell-tale pattern of small-study effects that can point to publication bias. It regresses each study’s standard normal deviate on its precision and checks whether the intercept differs from zero. This calculator runs that test on the studies you paste, puts ratio measures on the log scale first, and reports the p-value with the intercept, its standard error, the t statistic, and the degrees of freedom. A small p-value suggests asymmetry, not proof that results were suppressed.
Publication bias calculator (Egger's test)
Paste your studies' effect estimates and run Egger's regression test for funnel-plot asymmetry, the formal counterpart to eyeballing a funnel plot for small-study effects.
Drag and drop or click. CSV, TSV, Excel; header row with columns like study, label, author, trial, estimate.
Egger's test p-value
0.4083
The intercept is not clearly different from zero (p of 0.05 or above), so there is no strong evidence of funnel-plot asymmetry from this test.
Egger's regression intercept test
Intercept2.1738
Standard error of intercept2.3555
95% CI for the intercept-4.3661 to 8.7137
t statistic0.9229
Degrees of freedom4
Slope-0.0540
Number of studies6
Begg and Mazumdar rank correlation test
Kendall's tau0.2000
z statistic0.5636
p-value0.5730
Begg's rank correlation test has low power with few studies, so a non-significant result does not rule out asymmetry.
With fewer than ten studies both tests are unreliable; treat these results as exploratory.
Report-ready text
Egger's regression test found no significant funnel-plot asymmetry (intercept = 2.17, 95% CI -4.37 to 8.71, t(4) = 0.92, p = 0.4083). Begg's rank correlation test agreed (Kendall's tau = 0.20, p = 0.5730).
What Egger's test is really detecting
Egger’s test does not measure publication bias directly. What it measures is funnel-plot asymmetry, the statistical fingerprint of small-study effects. The idea is straightforward. Large, precise studies cluster near the true effect, while small, imprecise studies scatter widely around it. Plot every study’s effect against its precision and, if nothing is amiss, the cloud forms a symmetric inverted funnel. If small studies systematically report larger effects than large ones, the funnel tilts, and that tilt is what the test quantifies. It regresses each study’s standard normal deviate on its precision and asks whether the intercept differs from zero; under symmetry the intercept should be zero. The visual half of this pairing is covered in our guide to reading a funnel plot, and the test is the number that backs up the eye.
Why asymmetry is not proof of suppression
Publication bias, where studies with disappointing results never reach print, is one cause of funnel-plot asymmetry, but it is far from the only one. Smaller trials are often of poorer methodological quality and genuinely overstate effects; the true effect may differ between the small and large studies for clinical reasons; the choice of effect measure can induce a spurious correlation between effect and precision; and with few studies, chance alone produces tilt. A low p-value from Egger’s test is therefore a prompt to investigate, not a verdict. The wider set of explanations and remedies is laid out in our explainer on publication bias in systematic reviews.
Interpreting the output, with a worked example
The test reports an intercept, its standard error, a t statistic, the degrees of freedom (the number of studies minus two), and a p-value. Read the p-value first, but read it in context. Suppose you pool twelve studies and the test returns an intercept of 1.8 with a p-value of 0.03. That is evidence of asymmetry: smaller studies are pulling the effect in one direction, and you should not report the pooled estimate without discussing it. Now suppose the same intercept came from only five studies with a p-value of 0.21. Here the test is essentially uninformative, because with so few studies it has almost no power to detect asymmetry and a non-significant result rules nothing out. This is why the standard advice is to apply tests for funnel-plot asymmetry only when there are at least ten studies; below that, the test can neither confirm nor exclude a problem, a caution that sits alongside the broader sensitivity analyses you run to probe a pooled result.
Common mistakes researchers make
The most common error is reading a significant Egger’s test as proof that results were suppressed, then discarding the meta-analysis; investigate the asymmetry instead and let it temper how you grade confidence under the GRADE approach, where publication bias is an explicit downgrading domain. A second error is running the test on a handful of studies and trusting the number. A third is applying it to raw ratio measures rather than the log scale, or ignoring that high heterogeneity can masquerade as asymmetry, so always check the heterogeneity statistics alongside it. A fourth is treating the test as a substitute for the plot; use both, since the plot reveals the pattern the single p-value cannot. Built into a full review, a defensible read on small-study effects is part of our meta-analysis service.
How it works
Each study is placed on the analysis scale, with ratio measures (odds ratios, risk ratios, hazard ratios) logged first, then summarised by its estimate and standard error. Egger’s test regresses the standard normal deviate on the precision and tests the intercept.
SND_i = y_i / SE_i
precision_i = 1 / SE_i
SND = intercept + slope × precision
Under symmetry the intercept is zero. The test statistic is the intercept divided by its standard error, compared with a t distribution on the number of studies minus two.
t = intercept / SE(intercept), df = k - 2
The test needs at least three studies and is unreliable below about ten, so read the p-value alongside the funnel plot and the number of studies rather than on its own.
Frequently asked questions
- What does Egger's test actually test?
- Egger's test regresses each study's standard normal deviate on its precision and examines the intercept. If small studies report systematically larger or smaller effects than large studies, the funnel plot is asymmetric and the intercept moves away from zero. A p-value below 0.05 for that intercept signals funnel-plot asymmetry, which is one possible sign of small-study effects.
- Does a significant Egger's test prove publication bias?
- No. Funnel-plot asymmetry has several possible causes besides publication bias, including genuine differences between small and large studies, poor methodological quality in smaller trials, chance, and the choice of effect measure. A low p-value should prompt investigation, not a firm conclusion that results were suppressed.
- How many studies do I need for Egger's test?
- The test needs at least three studies to run, but it has very low power with few studies and unstable results when effects are large or sample sizes vary little. A common recommendation is to apply tests for funnel-plot asymmetry only when there are at least ten studies, otherwise the test can neither reliably detect nor rule out asymmetry.
- What is the difference between Egger's test and a funnel plot?
- A funnel plot is the visual display: effect estimates against their precision, expected to form a symmetric inverted funnel under no small-study effects. Egger's test is the formal statistical counterpart that quantifies the asymmetry with a regression intercept and a p-value. They are used together, with the plot showing the pattern and the test putting a number on it.
- What should I do if Egger's test is significant?
- Treat it as a prompt to investigate, not a conclusion. Inspect the funnel plot for the source of asymmetry, check whether small studies differ in design or quality, and consider sensitivity analyses such as trim-and-fill or a contour-enhanced funnel plot. Report the asymmetry honestly and let it inform how cautiously you grade the certainty of the pooled effect rather than discarding the result outright.
- Is Egger's test suitable for ratio measures?
- Yes, provided the effects are analysed on the log scale, which this calculator does automatically for odds ratios, risk ratios, and hazard ratios. Running the test on raw ratios would distort the regression because ratio measures are not symmetric on the natural scale. For binary outcomes with rare events some methodologists prefer an alternative test, such as the one by Harbord or Peters, that is less prone to false positives.
The guides behind this tool
More review and meta-analysis tools
Meta-analysisPool study effect estimates with fixed-effect and random-effects models, with the heterogeneity statistics shown.Open tool Heterogeneity (I-squared)Quantify how much your studies disagree: Cochran's Q, I-squared, H, and the between-study variance tau-squared.Open tool Odds ratio / risk ratioTurn a 2x2 table of events into an odds ratio, risk ratio, and risk difference, each with a 95% confidence interval.Open tool