Bonferroni correction
The Bonferroni correction divides the target significance level α by the number of simultaneous tests m, setting each individual threshold at α/m to control the chance of any false rejection. It becomes conservative as m grows.
FrameworkMultiple comparisons
See it move
Running twenty hypothesis tests at the usual 5 per cent level risks roughly a 64 per cent chance of at least one false positive. The Bonferroni correction fixes this by dividing α by the number of tests: α* = α ÷ m. For twenty tests at α = 0.05, each individual test must clear 0.0025, not 0.05.
The formula
Variables
- per-test significance threshold after Bonferroni correction (dimensionless)
- desired family-wise error rate (dimensionless)
- number of simultaneous hypothesis tests (dimensionless)
Reject individual test i if pᵢ < α/m. Controls the probability of any false rejection at α but becomes increasingly conservative as m grows.
Check yourself
A researcher conducts 10 independent regression tests — one per nutrient — to identify predictors of a health outcome. Concerned about family-wise Type I error, she applies the Bonferroni correction at an overall significance level of α = 0.05. What individual p-value threshold should she use for each test?