Bonferroni Correction Calculator

Divide your significance level by the number of tests to get the Bonferroni-adjusted per-test threshold that controls the overall false-positive (family-wise error) rate.

Quick Facts

Method
Adjusted threshold = α / m
Holds the family-wise Type I error rate at or below α across all m tests.

Your Results

Calculated
Adjusted per-test threshold (α/m)
-
Reject a null only if its p-value is below this
Confidence level per test
-
1 − α/m
Uncorrected error rate
-
Chance of ≥1 false positive if you did NOT correct

Ready

Enter your significance level and number of tests, then calculate.

What the Bonferroni correction does

When you run more than one hypothesis test on the same data, the chance of getting at least one false positive (a Type I error) grows with every extra test. The Bonferroni correction is the simplest and most widely taught fix: it lowers the significance threshold each individual test must clear so that the family-wise error rate — the probability of making even one false rejection across the whole family of tests — stays at or below your target α.

The formula

Divide your chosen family-wise significance level by the number of tests:

αadjusted = α / m

Here α is the overall error rate you are willing to tolerate (typically 0.05) and m is the number of hypothesis tests, comparisons, or endpoints in the family. You then reject an individual null hypothesis only when its p-value is smaller than α/m. An equivalent form multiplies each raw p-value by m (capping at 1) and compares the adjusted p-value against the original α.

Why it is needed

Suppose each of m independent tests uses α = 0.05. The probability that all of them avoid a false positive is (1 − 0.05)m, so the probability of at least one false positive is 1 − 0.95m. That climbs to about 23% at m = 5, roughly 40% at m = 10, and above 92% at m = 50. Testing 20 outcomes and reporting only the "significant" ones almost guarantees a spurious finding. Bonferroni counters this by shrinking each per-test threshold: with m = 10 and α = 0.05, every test must now beat p < 0.005.

Common reference points

  • α = 0.05, m = 2 → adjusted threshold 0.025.
  • α = 0.05, m = 5 → adjusted threshold 0.01.
  • α = 0.05, m = 10 → adjusted threshold 0.005.
  • α = 0.05, m = 20 → adjusted threshold 0.0025.
  • α = 0.01, m = 4 → adjusted threshold 0.0025.

Frequently Asked Questions

What counts as "the number of tests" (m)?
Count every hypothesis test in the family you want to protect: each pairwise group comparison, each outcome measure, each subgroup, or each candidate predictor. If a study reports one primary endpoint and 9 secondary endpoints all tested at 0.05, m = 10. Deciding the family is a judgement call — pre-register it, because expanding m after seeing the data inflates the correction unfairly.
Is Bonferroni too conservative?
It can be. Bonferroni assumes the worst case and controls the family-wise error rate even when tests are correlated, so with many or strongly correlated tests it sacrifices power and can miss real effects. Less conservative alternatives that control the same family-wise rate include the Holm-Bonferroni step-down procedure (uniformly more powerful, no extra assumptions) and Sidak (slightly tighter when tests are independent). When you care about the false discovery rate rather than any false positive, Benjamini-Hochberg is usually preferred.
Does Bonferroni change my p-values or my threshold?
Either framing gives the same decision. You can lower the threshold to α/m and compare raw p-values against it, or multiply each raw p-value by m (capped at 1) and compare the adjusted p-values against the original α. Confidence intervals are widened analogously by building each interval at the 1 − α/m level.

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