Tukey's HSD test works by first conducting an ANOVA to determine if there are any significant differences among the group means. If the ANOVA is significant, the Tukey's HSD test is then applied. The formula for Tukey's HSD is:
where: - \( q \) is the studentized range statistic (depending on the number of groups and the degrees of freedom). - \( MS_{within} \) is the mean square within groups from the ANOVA. - \( n \) is the number of samples per group.
The test calculates the minimum difference between group means necessary for significance, considering the number of comparisons being made.
