Tukey's Range Test

Tukey's Range Test

Tukey's test, also known as the Tukey range test, Tukey method, Tukey's honest significance test, Tukey's HSD (honestly significant difference) test, or the Tukey–Kramer method, is a single-step multiple comparison procedure and statistical test. It is used in conjunction with an ANOVA 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 (q) (this distribution is similar to the distribution of t from the t-test). The Tukey HSD tests should not be confused with the Tukey Mean Difference tests (also known as the Bland-Altman Test).

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. 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.