Bonferroni Correction

A Bonferroni correction is a simple post-hoc correction designed to correct for the use of multiple comparisons. Two versions exist:

• Original: Divide the $\alpha$ by the number of pairwise comparisons
• Adapted: Assume that the first test (e.g., an ANOVA) controls for N-1 pairwise comparisons. Then divide $\alpha$ by the number of uncontrolled pairwise comparisons.
  • e.g. You have four groups (4*3/2 = 6 pairwise comparisons). The ANOVA tells you that at least one population mean is different, so three of six pairwise comparisons are already controlled for. Divide $\alpha$ by 3.

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Related

baseline correction

References