Bonferroni Correction Calculator
Use this calculator to control the family-wise error rate when running multiple hypothesis tests. Enter your overall alpha, the total number of comparisons, and (optionally) your p-values for instant interpretation.
What is a Bonferroni test?
A Bonferroni test (or Bonferroni correction) is a method used in statistics to reduce false positives when you run many hypothesis tests at once. Every time you test a hypothesis, there is a chance of a Type I error (rejecting a true null hypothesis). If you run many tests, that chance accumulates.
The Bonferroni approach is simple: divide your desired overall alpha (like 0.05) by the number of tests you run. That gives a stricter threshold for each individual test.
How this bonferroni test calculator works
Core formulas
- Adjusted threshold: αBonferroni = α / m
- Adjusted p-value: padj = min(p × m, 1)
Where:
- α = your family-wise significance level (often 0.05)
- m = number of comparisons/hypothesis tests
- p = raw p-value from an individual test
A result is considered statistically significant under Bonferroni if the raw p-value is less than or equal to α/m.
When should you use Bonferroni correction?
Use it when you perform multiple comparisons and want strong control over false positives, such as:
- Post hoc pairwise comparisons after ANOVA
- Testing many outcome variables in one study
- Multiple subgroup analyses
- Screening many biomarkers or survey items
Bonferroni is conservative. That means fewer false positives, but also lower power (you may miss real effects). For exploratory work, some researchers prefer alternatives like Holm, Benjamini-Hochberg, or Tukey methods depending on context.
Example calculation
Scenario
You run 8 hypothesis tests and want to keep your family-wise error rate at 0.05.
- Adjusted alpha = 0.05 / 8 = 0.00625
- Only p-values ≤ 0.00625 are significant after Bonferroni correction
If one of your p-values is 0.004, it remains significant. A p-value of 0.01 would not pass Bonferroni, even though it is below 0.05.
Practical interpretation tips
- Predefine the number of comparisons before analysis when possible.
- Report both raw p-values and corrected thresholds for transparency.
- Discuss effect size and confidence intervals, not only statistical significance.
- If your test count is very high, consider whether Bonferroni is too strict for your research goal.
Frequently asked questions
Is Bonferroni always the best choice?
Not always. It is excellent for strict control of false positives, but can be overly conservative. Choice depends on study design and whether confirmatory or exploratory inference is your priority.
What if my p-values are already adjusted?
Do not re-adjust them. Use either raw p-values with one correction method, or use already corrected values as reported by your software.
Can I use this for pairwise t-tests?
Yes. Set m equal to the number of pairwise tests you run and compare each p-value against α/m.
Bottom line
This bonferroni test calculator gives you a fast, clean way to correct for multiple testing and avoid inflated false positive rates. Enter your alpha and test count to get the corrected threshold, then optionally check a full list of p-values in one click.