The imprecise trials report the larger effects. Egger’s intercept is 1.6083 with p = 0.01558 — and I² on the same seven trials is exactly 0.00%. There is no detectable heterogeneity here at all, and the funnel is still asymmetric. The two statistics are answering different questions.
7 studies · 5 degrees of freedom
Intercept 1.6083, p = 0.01558
95% CI 0.4591 to 2.7575, t = 3.5976. A symmetric funnel puts the intercept at zero. I² on the same studies is 0.00%, which is a separate question: this set is asymmetric with no detectable heterogeneity at all.
Egger intercept
1.6083
SE 0.4471
p-value
0.01558
t = 3.598 on 5 df
Regression slope
0.0077
the effect a perfectly precise study would report
Studies
7
below the usual minimum of 10
The regression the test actually runs
The left-hand end of the line is where a study with no precision at all would sit, and that is the intercept: 1.6083. The right-hand end is the effect an infinitely precise study would report, which is the slope: 0.0077.
Every study on both axes
Each study’s precision, z score and fitted value in Egger’s regression
Study
Effect
SE
Precision
z score
Residual
Trial A
0.1700
0.1000
10.000
1.7000
0.0148
Trial B
0.1600
0.1400
7.143
1.1429
-0.5204
Trial C
0.4000
0.1900
5.263
2.1053
0.4565
Trial D
0.5000
0.2200
4.545
2.2727
0.6295
Trial E
0.3600
0.2800
3.571
1.2857
-0.3501
Trial F
0.6200
0.3300
3.030
1.8788
0.2472
Trial G
0.4600
0.4000
2.500
1.1500
-0.4775
The same fit read the other way — regressing the effect on the standard error, weighted by one over the variance — gives a slope of 1.608309 and an intercept of 0.007688. Those are the two numbers above with their roles swapped, which is an algebraic identity rather than a coincidence.
Independent of I² Regression shown, not hidden Underpowered below 10 studies Asymmetry is not proof of bias
What this tool shows
The first preset here is asymmetric — Egger’s p is 0.01558 — and its I² is exactly 0.00%. The second is its mirror: I² of 58.00%, Egger p of 0.88262. Asymmetry and heterogeneity are separate questions, and a set can score high on either with nothing on the other.
Egger’s regression intercept with a standard error, t, df and confidence interval
The regression itself plotted — z score against precision, with the fitted line
I² computed on the same studies, because the two are routinely confused
Every study’s precision, z score and residual, so a single influential point is visible
The identical fit read the other way, as a weighted regression of effect on standard error
An explicit power warning below ten studies, with a preset that demonstrates it
Regression plotted I² beside it Residuals shown Power flagged
Asymmetry has several causes. Publication bias is only one.
Updated 13 September 2026 · Works in any browser, no installation
Egger’s test asks whether imprecise studies report systematically different effects from precise ones. It regresses each study’s z score on its precision and tests whether the intercept is zero. An intercept of zero means a study with no precision at all would report no effect, which is what a symmetric funnel implies. An intercept away from zero means the small studies are pulling in one direction — which may be publication bias, and may be four other things.
At a glance
Formula shown
Regress zᵢ = yᵢ/SEᵢ on precᵢ = 1/SEᵢ by ordinary least squares: z = β₀ + β₁·prec. The test is t = β₀/SE(β₀) on k − 2 degrees of freedom. The identical fit can be written as a weighted regression of the effect on the standard error with weights 1/SEᵢ², which returns the same two numbers with their roles swapped — β₀ becomes the slope and β₁ the intercept. Both are computed here from scratch and printed, because an identity you can check is worth more than one you are told about.
Scenario support
Checking a systematic review for small-study effects before trusting its pooled estimate, deciding whether a funnel plot that looks lopsided is lopsided enough to matter, screening a literature where positive results are easier to publish than null ones, and documenting a publication-bias assessment for a review protocol.
Educational estimate
Planning support from the values you enter — not professional advice.
Asymmetry and heterogeneity are different questions
These two statistics are reported side by side so often that they get read as versions of the same thing. The two shipped presets are built to break that habit.
The first preset: Egger p = 0.01558, I² = 0.00%. Seven trials with no detectable disagreement at all, and a clearly lopsided funnel.
The second preset: Egger p = 0.88262, I² = 58.00%. Seven trials that disagree substantially, in a funnel with no detectable tilt.
I² asks whether the studies disagree. Egger asks whether the disagreement lines up with study size. A literature can do either without the other.
Which is why the two are printed together here. “I² was low so we did not check for publication bias” is a non-sequitur, and the first preset is the counter-example.
Below ten studies the test mostly cannot see
Egger’s own paper recommends at least ten studies. The third preset shows what happens when that is ignored, using data where the answer is already known.
Take four of the seven asymmetric trials, keeping the pattern intact. The intercept is still large at 1.1940.
But p rises from 0.01558 to 0.12849 and the interval runs from −0.85 to 3.24. On 2 degrees of freedom, the t multiplier alone is over four.
The asymmetry did not go away. The ability to certify it did. A non-significant Egger test at k < 10 is close to no information.
Which makes the intercept and its interval more useful than the p-value here, and both are printed for that reason.
Five reasons a funnel tilts, only one of them publication bias
“Egger significant, therefore publication bias” is the standard misreading, and it skips four alternatives that are at least as common.
Smaller trials are often run differently. More selected patients, more intensive delivery, tighter protocols — all of which can produce genuinely larger effects.
Smaller trials are often conducted less carefully. Weaker allocation concealment and unblinded outcome assessment both bias effects upward.
The effect measure itself can create asymmetry. Odds ratios are mathematically linked to their own standard errors, so a funnel of log odds ratios can tilt with no bias present at all.
True heterogeneity correlated with size — for example if small trials tend to study higher-risk populations — produces the same pattern.
And chance. At the k typical of a real review, a lopsided funnel is a common random outcome.
What the plotted line is doing
The regression is drawn rather than summarised, because the geometry is what makes the test intelligible.
The x axis is precision, one over the standard error. Large, precise studies sit at the right; small ones at the left.
The y axis is the z score, effect over standard error. A study with a real effect and lots of precision has a large z; one with the same effect and no precision has a z near zero.
So under symmetry the line must pass through the origin: no precision, no z. The intercept is how far from the origin it actually passes.
And the slope is the effect an infinitely precise study would report, which is a bias-adjusted estimate in its own right — a crude one, but it is the number the test is implicitly comparing everything against.
The same fit, written the other way round
Egger’s test appears in the literature in two forms that look unrelated, and readers reasonably wonder which one a calculator ran.
Form one: regress z on precision, unweighted, and test the intercept. That is what the plot above shows.
Form two: regress the effect on the standard error, weighted by one over the variance, and test the slope. That is the form used in several standard software packages.
They are the same least-squares problem. Multiplying through by the precision turns one objective into the other exactly, so the intercept of the first equals the slope of the second and vice versa.
Both are computed here independently and both are printed, so the identity is visible rather than asserted — and the verification suite asserts it on 300 generated study sets.
When not to use this test
Egger’s test is the default, and there are well-known situations where it is the wrong default.
Fewer than ten studies: do not run it. Report the funnel plot and say the sample is too small to test.
Binary outcomes with rare events: use the Harbord or Peters modification. The structural link between a log odds ratio and its standard error inflates the false-positive rate of the standard test substantially.
Substantial heterogeneity: the test is over-sensitive. With large τ² the residual variance is not what the test assumes, and significance becomes easy to obtain.
Standardised mean differences have the same structural problem as odds ratios, since the effect appears in its own variance formula.
And no version of this test can distinguish bias from a real small-study effect. That is a judgement about the studies, not a statistic.
Reporting the test
Four items, and the first is the one most often left out.
Give k. The test’s behaviour is dominated by the number of studies, and a p-value without k cannot be interpreted.
Give the intercept and its interval, not only p. “1.19, 95% CI −0.85 to 3.24” says what “p = 0.13” hides.
Say which form of the test you ran, and for binary outcomes say whether you used a modification.
And name the candidate explanations. A significant result narrows nothing on its own; naming which of the five causes is plausible for this literature is the actual contribution.
Method. The test is computed as the unweighted ordinary least-squares regression of each study’s z score on its precision, with the intercept tested on k − 2 degrees of freedom, and the plot shows exactly that fit rather than a redrawn approximation of it. The equivalent weighted regression of the effect on the standard error is computed independently in the same pass and printed beside it; the suite asserts on 300 generated study sets that the intercept of one equals the slope of the other and vice versa, to within 1e-8 relative. I² is computed on the same studies so that the two statistics can be read together rather than looked up separately, and the suite asserts that rescaling every effect and standard error by a common factor leaves the Egger intercept unchanged — the test is about shape, not units. Fewer than three studies returns no result rather than a fit with no residual degrees of freedom. That engine is verified on every change against 134 assertions. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Meta-AnalysisPool study effects by inverse variance under both fixed-effect and random-effects models, with τ², a prediction interval, per-study weights and leave-one-out influence.
I²Heterogeneity across studies: I² with a confidence interval, Cochran's Q, τ², H and every study's share of Q.
Linear RegressionThe least-squares line with r and r² — and the regression of x on y beside it, because those are two different lines rather than one line rearranged.
p-valueA p-value from a t or z statistic, one- or two-tailed — with a panel that holds an effect fixed and grows the sample, so you can watch significance appear from nothing but n.
Confidence IntervalIntervals for a mean or a proportion using t at every sample size and Wilson rather than the textbook Wald formula — with both methods shown, because Wald returns [0,0] at zero successes.
Hedges' gBias-corrected standardised mean difference using the exact gamma correction, with Cohen's d beside it and a confidence interval.
An educational tool. A significant Egger test is evidence of small-study effects, not proof of publication bias — smaller trials also differ in conduct, population and protocol, and for odds ratios and standardised mean differences the effect appears in its own variance formula, which can tilt a funnel with no bias present. Below ten studies the test is underpowered and should not be run.
Launched Egger test for funnel-plot asymmetry with the regression itself plotted rather than summarised.
Shipped mirror-image presets: one with I-squared 0.00% and p = 0.01558, one with I-squared 58.00% and p = 0.88262, to separate asymmetry from heterogeneity.
Computed the equivalent weighted regression of effect on standard error independently and printed both, so the coefficient-swap identity is visible.
Added a four-study preset showing the same asymmetry going undetected at p = 0.12849, and an explicit power warning below ten studies.
Documented the five causes of funnel asymmetry, only one of which is publication bias.
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