Bonferroni Method

The Bonferroni method controls family-wise error by replacing $\alpha$ with $\alpha / c$ when there are $c$ comparisons.

For simultaneous confidence intervals on pairwise mean differences, a Bonferroni interval has the form

$$ \bar{y}_{i\cdot} - \bar{y}_{j\cdot} \pm t_{N-k,\,\alpha/(2c)} \sqrt{MSE\left(\frac{1}{n_i} + \frac{1}{n_j}\right)}. $$

It is simple and general, but often more conservative than Tukey’s method.

R

pairwise.t.test(dat$y, dat$treatment, p.adjust.method = "bonferroni")