Bonferroni and Scheffé Methods¶
Overview¶
Bonferroni Method¶
Perform each pairwise comparison at \(\alpha/C\) where \(C = \binom{k}{2}\) is the number of pairs. Simple and applicable to any set of comparisons.
Scheffé's Method¶
Controls the FWER for ALL possible contrasts (not just pairwise). Uses the critical value \(\sqrt{(k-1)F_{\alpha,k-1,N-k}}\).
Comparison¶
- Bonferroni: tighter for a small number of planned comparisons
- Scheffé: better when exploring all possible contrasts