What type of analysis does Tukey HSD perform?

Tukey's Honestly Significant Difference (HSD) is a statistical test used primarily in the context of Analysis of Variance (ANOVA). It specifically addresses the need to identify which means are significantly different after an ANOVA test has indicated that at least one group mean is different from the others.

The application of Tukey HSD is particularly valuable when researchers have three or more groups to compare. After establishing that there are significant differences overall using ANOVA, the Tukey HSD test allows for pairwise comparisons between each group to determine exactly which groups differ from each other and by how much. This control for Type I error helps ensure that the comparisons made are valid and reliable.

Tukey HSD does not focus on assessing the homogeneity of variance, measuring correlation, or evaluating regression coefficients; rather, its primary role is to facilitate the comparison of means across multiple groups, making it a fundamental technique for post-hoc analysis in experimental designs involving multiple group means.