ANOVA tests only tell us whether there are differences in the means. It does not tell us
which means differ.
Thus, if we reject H i0 an ANOVA test, we need to perform a multiple comparisons
procedure to find where the differences are.
There are many procedures to do so. One is Tukey-Kronen (T-K) method.
Suppose we rejected an ANOVA test with k = 3 groups. We have 3 differences to
μ 1 μ ,2μ –1μ , 3 –2μ 3
Direction doesn’t matter
We computer T-K confidence intervals for each difference. If the interval contains 0,
there is no significant difference between the two means. If the interval does not contain