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Bonferroni Correction Calculator

Adjust your significance level for multiple comparisons — Bonferroni and Šidák thresholds, plus the family-wise error rate you would face without correcting.

Family-wise α

Number of tests (m)

Your smallest p-value (optional)

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How it works

α_per-test = α ÷ m · Šidák: 1 − (1−α)^(1/m) · FWER = 1 − (1−α)^m

Each extra hypothesis test is another chance for a false positive. Bonferroni divides the error budget evenly across tests, which controls the family-wise error rate but is conservative. Šidák is slightly less strict when tests are independent; Holm’s step-down method is uniformly more powerful and still simple.

Worked example

α = 0.05, m = 12: Bonferroni threshold 0.00417; the uncorrected chance of a spurious hit is 46%.

Frequently asked questions

Is Bonferroni too conservative?

Often, for many correlated tests. Consider Holm (sequential Bonferroni) or false-discovery-rate control (Benjamini–Hochberg) in exploratory work.

Do I divide α or multiply p?

Equivalent: compare p to α/m, or compare p × m to α.

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