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Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD test, is a single-step multiple comparison procedure and statistical test. It can be used to find means that are significantly different from each other.
Named after John Tukey, it compares all possible pairs of means, and is based on a studentized range distribution.
Tukey's test compares the means of every treatment to the means of every other treatment; that is, it applies simultaneously to the set of all pairwise comparisons
and identifies any difference between two means that is greater than the expected standard error. The confidence coefficient for the set, when all sample sizes are equal, is exactly 1 − α {\displaystyle 1-\alpha } for any 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1}. For unequal sample sizes, the confidence coefficient is greater than 1 − α. In other words, the Tukey method is conservative when there are unequal sample sizes.