To compare two means after a significant F test, the Scheffé test and the Tukey test were shown. Another commonly used test is called the Bonferroni multiple-comparison test. This test uses the t distribution, but unlike the t test shown in Chapters 8 and 9, the critical value is adjusted to compensate for multiple comparisons. This is done by dividing the critical value by the number of pairwise comparisons. The formula for the Bonferroni test is

The degrees of freedom used is N ˆ’ k. Use the Bonferroni test to compare the means XÌ…₂ and XÌ…₃ in Example 12€“1.

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X1 – X2 t= Sw