What is the Bonferroni correction?

It is a method for adjusting the significance threshold when performing multiple statistical tests simultaneously. The corrected alpha equals the original alpha divided by the number of tests, ensuring the overall probability of any false positive stays at or below the chosen level.

When should I use Bonferroni vs. other corrections?

Use Bonferroni when tests are independent or you need a simple, conservative correction that is easy to defend. For correlated tests or when power loss is a concern, consider Holm-Bonferroni or Benjamini-Hochberg (FDR) instead.

Why is Bonferroni considered conservative?

It assumes each test is independent. When tests are positively correlated, the true family-wise error rate is actually lower than alpha, meaning the correction over-adjusts and reduces statistical power unnecessarily.

Does Bonferroni correction affect my sample size?

Yes. A smaller alpha threshold requires a larger sample to achieve the same power. After obtaining the corrected alpha, plug it into a power analysis calculator to see the required sample size.

What if my corrected alpha is extremely small?

A very small corrected alpha (e.g. in GWAS with millions of tests) is expected. It reflects the stringency needed to avoid spurious findings at scale. Report both the corrected threshold and any p-values that meet it.

Bonferroni Correction Calculator

Divide your alpha by the number of comparisons to get the Bonferroni-corrected significance threshold.

Input Parameters

Original significance level (α)

Common values: 0.05 (5%), 0.01 (1%), 0.001 (0.1%)

Number of comparisons (n)

The total number of simultaneous tests or hypotheses

Quick presets

Results

Corrected α (per test)

—

Original α —

Number of tests (n) —

Formula α / n

Family-wise error rate controlled at —

Probability of ≥1 false positive (exact) —

Interpretation

Enter values above and click Calculate to see the corrected significance threshold and interpretation.

Corrected α for common test counts (α = 0.05)

Tests (n)	Corrected α	As percentage	Actual FWER

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Summary

The Bonferroni correction is the simplest method for controlling the family-wise error rate (FWER) when performing multiple statistical tests. It divides the desired alpha level by the number of comparisons, reducing the per-test threshold so that the overall probability of at least one false positive stays at or below alpha. While conservative, it is widely accepted and easy to report.

How it works

Enter the original significance level (alpha), typically 0.05.
Enter the number of simultaneous comparisons or hypotheses being tested.
The calculator divides alpha by the number of tests to produce the corrected threshold.
Each individual test must achieve a p-value below the corrected threshold to be considered significant.
Review the critical p-value and the equivalent adjusted alpha percentage for easy reporting.

Use cases

Correcting alpha after running multiple t-tests on the same dataset.
Adjusting significance levels in genome-wide association studies (GWAS).
Controlling error rate in post-hoc pairwise comparisons after ANOVA.
Setting per-feature significance thresholds in A/B tests with multiple metrics.
Academic papers requiring explicit FWER control for peer review.
Clinical trials with multiple primary endpoints requiring a single family-wise alpha.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu