All Pairwise Comparisons among Means: Tukey's HSD Procedure (1 of 2)

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The "Honestly Significantly Different" (HSD) test proposed by the statistician John Tukey is based on what is called the "studentized range distribution." To test all pairwise comparisons among means using the Tukey HSD, compute t for each pair of means using the formula:



where M_i - M_j is the difference between the ith and jth means, MSE is the Mean Square Error, and n_h is the harmonic mean of the sample sizes of groups i and j.