Statistics for Business: Decision Making and Analysis, 3rd Edition

... intervals are designed specifically for comparing pairs of averages.

Bonferroni confidence intervals

Confidence intervals that adjust for multiple comparison by changing the α-level used in the standard interval to α/M for M intervals.

The underlying justification for Bonferroni intervals is simple. We found that the chance for a Type I error among M 95% confidence intervals could be as large as M (0.05). If we reduce the Type I error rate of each interval to α = 0.05/M, then the chance for a Type I error among all of the intervals is no more than M(0.05/M) = 0.05. By reducing the chance for a Type I error for each interval to 0.05/M, Bonferroni intervals guarantee that the chance for a Type I error among all of the intervals is less than or equal to ...