10.6 : Bonferroni Test

The Bonferroni test is a type of multiple comparison test that reduces Type 1 error by dividing the significance alpha value by the number of pairwise comparisons in a dataset.

Consider comparing the students' test scores from three samples with unequal means.

Begin by stating the null hypotheses for each sample pair as follows.

Calculate the modified t-statistic and P-values for all pairs. Compare the P-values with an adjusted alpha, calculated as alpha value divided by the number of pairs, which is three, here.

The P-values of pairs 1 and 2, and 1 and 3 are less than the adjusted alpha value. We infer that these pairs have significantly different means and reject the null hypotheses for both. 

The P-value of the pair 2 and 3 is greater than the adjusted alpha. We infer that the means of this pair aren't significantly different and fail to reject the null hypothesis. 

We can conclude that sample 1 has a significantly different mean among the three samples in the dataset.