Glossary

What is the Bonferroni correction? Formula, example and alternatives

Q: Why do you need a Bonferroni correction?

Each test at α = 0.05 has a 5% chance of a false positive. Run 20 tests and the chance that at least one is a false positive rises to about 64%.

Q: How do you calculate the Bonferroni correction?

Divide your significance level by the number of tests. With α = 0.05 and 10 tests, each test must reach p < 0.005.

Q: Is the Bonferroni correction too strict?

Often, yes, especially with many tests. It lowers false positives but misses more real effects. Holm’s method is always at least as powerful, and FDR methods are less strict.

Q: When should I not use Bonferroni?

When you test many things in an exploratory way and can accept some false discoveries, use a false discovery rate method such as Benjamini–Hochberg instead.

The Bonferroni correction lowers the significance threshold when you run several tests at once, so the chance of at least one false positive stays near your chosen level. Formula, worked example, and when to use Holm or FDR instead.

Emma Collins Reviewed by Su He Also called Bonferroni adjustment Last updated Nov 4, 2026 Glossary

Quick answer

The Bonferroni correction is a method for multiple comparisons: when you run m tests, you call a result significant only if its p-value is below α divided by m, which keeps the chance of any false positive across all tests at or below α.

Formula: Adjusted threshold = α / m, or adjusted p = min(1, p × m)

What is the Bonferroni correction?

The Bonferroni correction adjusts for running many statistical tests at once. If you test m things, a result is significant only when:

p < α / m

With the usual α = 0.05 and 10 tests, each test needs p < 0.005. Equivalently, multiply each p-value by m (capped at 1) and compare it with 0.05.

Why multiple comparisons are a problem

Every test at α = 0.05 has a 5% chance of a false positive when nothing is really going on. Those chances add up:

Number of tests	Chance of at least one false positive
1	5.0%
5	22.6%
10	40.1%
20	64.2%

(computed as 1 − 0.95^m, assuming independent tests)

This is exactly what happens when you slice a dashboard 20 ways ("conversion by country, device, browser, source…") and report the slice that looks different. The Bonferroni correction keeps the family-wise error rate, the chance of any false positive across the whole set, at or below α.

Worked example

Five segments are tested for a change in conversion. α = 0.05, so the Bonferroni threshold is 0.05 / 5 = 0.01.

Segment	p-value	Bonferroni (p < 0.01)	Holm threshold	Holm
A	0.004	Significant	0.05/5 = 0.010	Significant
B	0.012	Not	0.05/4 = 0.0125	Significant
C	0.020	Not	0.05/3 = 0.0167	Not (stop)
D	0.030	Not	—	Not
E	0.300	Not	—	Not

Without any correction, four of the five would be called significant.

Holm's method: same guarantee, more power

Holm–Bonferroni sorts p-values from smallest to largest and compares the k-th smallest with α / (m − k + 1). It stops at the first one that fails. It controls the same family-wise error rate and never finds fewer results than plain Bonferroni; in the example it keeps segment B too.

Bonferroni vs false discovery rate

Method	Controls	Strictness	Use when
Bonferroni	Chance of any false positive	Very strict	Few tests, false positives are costly
Holm	Same as Bonferroni	Strict, a bit more power	Same situations; a safe default
Benjamini–Hochberg (FDR)	Expected share of false positives among findings	Less strict	Many exploratory tests

In TapCub

TapCub does not run significance tests, but every report invites multiple comparisons: filters, breakdowns and segments let you look at dozens of slices in minutes. Decide in advance which comparison answers your question; if you then scan many slices, treat surprising ones as hypotheses and apply a correction (or retest on a fresh date range) before acting. For the test itself, see t-test and statistical significance.

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Emma Collins

Product Analyst

Focuses on event analysis, conversion funnels, and retention, using clear metric definitions and structured analysis to explain product performance.

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Why do you need a Bonferroni correction?

Each test at α = 0.05 has a 5% chance of a false positive. Run 20 tests and the chance that at least one is a false positive rises to about 64%.

How do you calculate the Bonferroni correction?

Divide your significance level by the number of tests. With α = 0.05 and 10 tests, each test must reach p < 0.005.

Is the Bonferroni correction too strict?

Often, yes, especially with many tests. It lowers false positives but misses more real effects. Holm’s method is always at least as powerful, and FDR methods are less strict.

When should I not use Bonferroni?

When you test many things in an exploratory way and can accept some false discoveries, use a false discovery rate method such as Benjamini–Hochberg instead.

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