Bonferroni Correction Calculator
Enter the number of tests, overall alpha, and optionally an observed p-value to compute Bonferroni-adjusted thresholds.
Enter 0 ≤ p ≤ 1 to see the adjusted p-value and significance decision.
Corrected α (α / m): 0.005000
Adjusted p-value (p × m): 0.100000
Significant? No, fail to reject H₀.
How to Use This Calculator
- Enter the total number of hypothesis tests (m).
- Provide the desired family-wise error rate α (e.g., 0.05).
- Optionally input an observed p-value to adjust.
- Review the Bonferroni-corrected significance threshold and adjusted p-value.
Formula
Corrected α = α / m
Adjusted p = min(p × m, 1)
Bonferroni controls family-wise error rate by making individual tests more stringent or inflating p-values to account for multiple comparisons.
Full Description
The Bonferroni correction guards against Type I errors when running multiple hypothesis tests. By dividing α by the number of tests, or equivalently multiplying p-values by the number of tests, the family-wise error rate remains bounded by α.
While conservative, Bonferroni is simple and widely accepted. For large numbers of tests, consider Holm-Bonferroni or false discovery rate procedures for more power.
Frequently Asked Questions
Is Bonferroni too conservative?
It can be stringent, especially with many tests. Use more powerful corrections if Type II errors are a concern.
What if tests are not independent?
Bonferroni is valid regardless of dependence but becomes more conservative when tests are highly correlated.
Can corrected α exceed α?
No. Corrected α is always α / m, which is less than or equal to α.
Should adjusted p-values be capped?
Yes, adjusted p-values are typically capped at 1 to remain interpretable as probabilities.