Tukey's multiple comparison method determines a critical number, , such that if any pair of sample means has a difference greater than , we conclude that the pair's two corresponding population means are different.

Tukey's method determines a critical value, also known as the Tukey's HSD (honestly significant difference), which is used to determine whether the pairwise difference between sample means is statistically significant or not. If the difference between any two sample means is greater than the HSD value, we can conclude that the two corresponding population means are different.