What the Bonferroni method does
The Bonferroni method is one of the most common tools for handling multiple comparisons. When you run many hypothesis tests, the chance of getting at least one false positive increases. Bonferroni controls this by making your significance threshold more strict.
Instead of testing each hypothesis at α (like 0.05), you test each one at α / m, where m is the number of tests. This helps control the family-wise error rate (FWER).
Bonferroni formula
Corrected significance threshold
For a family-wise alpha level and m tests:
αBonferroni = α / m
Adjusted p-value form
You can also adjust each p-value directly:
padjusted = min(p × m, 1)
Reject the null hypothesis when padjusted ≤ α.
How to use this calculator
- Enter your desired family-wise alpha (commonly 0.05).
- Enter the total number of tests you are performing.
- Optionally paste p-values to get adjusted p-values and significance decisions.
- Click Calculate to see the corrected threshold and full result table.
Example
Suppose you run 20 independent tests and want to keep the overall error rate at 0.05.
- α = 0.05
- m = 20
- Bonferroni threshold = 0.05 / 20 = 0.0025
Any individual p-value must be at or below 0.0025 to be considered significant after correction.
When Bonferroni is a good choice
- You have a small-to-moderate number of planned tests.
- False positives are costly and you need strict control.
- You want a simple, transparent correction method.
Limitations to keep in mind
Bonferroni is conservative, especially when the number of tests is large or when tests are correlated. That means reduced statistical power and potentially more false negatives.
In some research settings, alternatives like Holm-Bonferroni or Benjamini-Hochberg (FDR control) may provide a better balance between error control and power.
Quick FAQ
Is Bonferroni only for independent tests?
No. It still controls FWER under general conditions, but it can become extra conservative when tests are dependent.
Can I use this for post hoc analysis?
Yes, Bonferroni correction is frequently used in post hoc pairwise testing after ANOVA and similar workflows.
What alpha should I use?
Most commonly 0.05, but this depends on your field, study design, and risk tolerance for Type I errors.