Publication Bias Test Calculator

Test small-study effects with robust bias diagnostics. Compare intercepts, ranks, z scores, patterns, and symmetry. Turn study inputs into clearer meta-analysis evidence checks today.

Calculator input

Enter one study per line using either Study, Effect, SE or Effect, SE. Tabs, commas, semicolons, and pipes are accepted.

Example data table

Study Effect SE Interpretation note
Study A0.420.10Moderate positive estimate with strong precision.
Study B0.310.12Smaller effect with acceptable precision.
Study C0.270.11Smaller-study result close to pooled center.
Study D0.550.14Larger observed effect and lower precision.
Study E0.180.09Low effect but relatively stable error.
Study F0.610.15Potential outlier with wider uncertainty.
Study G0.350.10Balanced result near the central trend.
Study H0.490.13Useful for checking funnel symmetry.

Formula used

Precision
Precisioni = 1 / SEi
Standard normal deviate
SNDi = Effecti / SEi
Fixed-effect pooled estimate
Weighti = 1 / Variancei
Pooled effect = Σ(Weighti × Effecti) / ΣWeighti
Egger regression test
SNDi = a + b × Precisioni + εi
The intercept a is tested against zero. A statistically nonzero intercept can suggest asymmetry.
Begg rank correlation
Kendall tau measures monotonic association between observed effects and study variances. Stronger association can indicate small-study effects.
Rosenthal fail-safe N
Nfs = (ΣZ)2 / Zcritical2 − k
Orwin fail-safe N
Norwin = k × (Observed mean − Trivial threshold) / (Trivial threshold − Missing-study effect)

These calculations are practical screening formulas. They help identify patterns that may warrant deeper meta-analytic review.

How to use this calculator

  1. Paste one study per line using a label, effect, and SE.
  2. If you only have variances, switch the error type first.
  3. Set the alpha level used for significance screening.
  4. Optionally enter Orwin assumptions for trivial and missing effects.
  5. Choose how many decimals you want to display.
  6. Run the calculator and review the pooled estimate, Egger result, Begg result, and fail-safe values.
  7. Inspect the funnel plot for visible asymmetry or sparse regions.
  8. Download the result summary as CSV or PDF for reporting.

Frequently asked questions

1) What does this calculator test?

It screens for possible publication bias or small-study effects in meta-analysis data. It combines Egger regression, Begg rank correlation, fail-safe estimates, heterogeneity output, and a funnel plot.

2) Does a significant Egger result prove publication bias?

No. A significant intercept suggests asymmetry, but asymmetry can also come from heterogeneity, selective outcome reporting, poor study quality, chance, or effect modification.

3) Why include Begg's test too?

Begg's test uses rank correlation, so it gives a second perspective. Agreement between tests can strengthen concern, while disagreement suggests caution and closer inspection.

4) How many studies should I have?

At least three valid studies are required here, but asymmetry tests are usually more stable with larger sets. With fewer than 10 studies, statistical power can be weak.

5) Should I enter standard error or variance?

Use whichever you have, but match the selector first. If you choose variance, the calculator converts it to standard error internally using the square root.

6) What does Rosenthal fail-safe N mean?

It estimates how many missing null studies would be needed to move the combined result toward non-significance under the selected critical threshold. Larger values suggest more robustness.

7) What is Orwin fail-safe N useful for?

It answers a practical question: how many missing studies would shift the pooled effect to a chosen trivial value, given an assumed mean effect for those missing studies.

8) Can I use this for any effect metric?

Yes, as long as each study has a comparable effect estimate and its sampling error. The tool labels the metric using your chosen effect name.

Related Calculators

prevalence calculatorhistogram generatorhedges g calculatorglass deltalinear regression tooldiagnostic accuracy calculatorroc curve toolsample mean estimator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.