Bonferroni correction — how does it work?

medium

Answer

${\alpha}_{\mathrm{adjusted}}\; = \;{\alpha}\; / \;k$
$Guarantees P(any false rejection) \leq α under independence, \leq α always (union bound).$
$Very conservative — loses power quickly as k grows.$
$Use for a small number of confirmatory tests (< 20).$
$Holm's step-down variant is uniformly more powerful with the same guarantee.$

Check yourself — multiple choice

${\alpha}_{\mathrm{adj}}\; = \;{\alpha}$
${\alpha}_{\mathrm{adj}}\; = \;{\alpha} / k$ → family-wise error ≤ α; conservative — power decays quickly; Holm improves it
Increases power
Only for one test

Bonferroni: α/k; safe but low-power; Holm dominates uniformly.

#hypothesis-testing#multiple-testing

215 interview questions in this topic.