What is the Bonferroni correction?
The Bonferroni correction is a multiple-comparisons adjustment used when you run several hypothesis tests at once. If you test many hypotheses with the same alpha level (like 0.05), your chance of at least one false positive increases. Bonferroni controls this by making each individual test more strict.
In practice, it protects your overall family-wise error rate (FWER). Instead of accepting a 5% false-positive risk for each test, you cap the risk across the whole set of tests.
How this bonferroni correction calculator works
This page computes two common outputs:
- Corrected alpha threshold: the per-test significance cutoff.
- Adjusted p-values (optional): each p-value multiplied by the number of tests.
If you enter a list of p-values, the calculator also marks each result as significant or not significant using the Bonferroni-adjusted threshold.
Formula
adjusted p-value = min(p × m, 1)
Where α is your desired family-wise error rate (for example, 0.05), and m is the number of tests performed.
Step-by-step usage
- Enter your family-wise alpha (α).
- Enter the number of tests (m).
- Optionally paste your p-values.
- Click Calculate to get corrected alpha, adjusted p-values, and significance decisions.
Worked example
Suppose you run 8 comparisons and want a family-wise alpha of 0.05. The Bonferroni threshold is:
So each individual test must have p ≤ 0.00625 to be considered significant under Bonferroni. A p-value like 0.01 might look significant under 0.05, but it is not significant after correction.
When to use Bonferroni
Good use cases
- Small-to-moderate numbers of planned comparisons.
- Studies where false positives are costly (clinical, safety, regulatory work).
- Confirmatory analyses where conservative inference is preferred.
Potential downsides
- It can be overly conservative, especially with many tests.
- May increase false negatives (missed true effects).
- Not always optimal for exploratory high-dimensional data.
Bonferroni vs other corrections
Bonferroni is simple and strict. Alternatives may offer more power:
- Holm-Bonferroni: controls FWER but is usually less conservative than plain Bonferroni.
- Benjamini-Hochberg (FDR): controls false discovery rate, often better for large-scale exploratory studies.
If your primary goal is strict control of any false positive, Bonferroni remains a dependable default.
Interpretation tips
- Always define your testing family clearly before correction.
- Report both raw and adjusted p-values for transparency.
- Include effect sizes and confidence intervals; p-values alone are not enough.
- State the correction method in your methods section.
Frequently asked questions
Do tests need to be independent?
Bonferroni is valid regardless of independence, which is one reason it is widely used. However, with correlated tests, it may become especially conservative.
Can I use this for A/B tests?
Yes. If you are running multiple simultaneous variants or outcomes and want to control family-wise false positives, Bonferroni is appropriate.
What if adjusted p-values are above 1?
They are capped at 1.00 by definition. This calculator automatically applies that cap.
Final note
This bonferroni correction calculator is designed for quick, practical analysis. It is useful for statistics homework, research planning, and reporting corrected thresholds in papers. For complex designs, pair these results with subject-matter judgment and, when needed, a full statistical workflow in R, Python, SPSS, or Stata.