Why correct for multiple comparisons
When you run many statistical tests at the same significance level, the chance that at least one comes out “significant” purely by chance grows quickly. This inflated risk is called the family-wise error rate. The Bonferroni correction is a simple, widely used way to control that risk by making each individual test stricter.
The formula
The Bonferroni-corrected significance threshold is alpha_corrected = alpha / m, where alpha is your original significance level (commonly 0.05) and m is the number of comparisons being made. Only results with a p-value below this corrected threshold are considered significant. The tool also shows the family-wise error rate you’d have if you used the original, uncorrected alpha across all m tests: 1 – (1 – alpha)^m.
- The Bonferroni correction is conservative: it strongly reduces false positives but can also reduce your power to detect real effects, especially with many comparisons.
- Less conservative alternatives (such as the Holm-Bonferroni or Benjamini-Hochberg procedures) are often preferred for large numbers of tests.
This calculator is for general educational and statistical-planning purposes only.