Table of Contents
What Is Bonferroni Correction?
The Bonferroni correction is the simplest method to control the family-wise error rate (FWER) when performing multiple statistical comparisons. When you test multiple hypotheses simultaneously, the probability of at least one false positive increases dramatically. The Bonferroni method divides the significance level by the number of comparisons.
For example, with 20 tests at α=0.05, you expect one false positive by chance alone. Bonferroni adjusts to α/20 = 0.0025 per test to maintain the overall 5% error rate.
Formula
Example
| Tests | Original α | Corrected α |
|---|---|---|
| 5 | 0.05 | 0.01 |
| 10 | 0.05 | 0.005 |
| 20 | 0.05 | 0.0025 |
| 100 | 0.05 | 0.0005 |
FAQ
Is Bonferroni too conservative?
Yes, it is known to be overly conservative, especially with many comparisons or correlated tests. It reduces Type I errors but increases Type II errors (missing true effects). Alternatives like Holm-Bonferroni or Benjamini-Hochberg FDR are less conservative.
When should I use it?
Use Bonferroni when you need strict FWER control, such as confirmatory clinical trials. For exploratory analyses with many tests, FDR methods are often preferred.