Tukey's HSD test

A multiple comparision procedure developed by tucky is frequently used for testing the null hypothesis that all possible pairs of treatment means are equal when the samples are all of the same size. When this test is employed we select an overall significance level of alpha. The probability is aalpha, then , that one or more of the null hypotheses is false.
Tukey's test, which is usually referred to as the HSD ( honestly significant difference) test, makes use of a single value against which all differences are compared. This value, called the HSD, is given by;

where alpha is the chosen level of significance, k is the no. of means in the experiment, N is the total number of observations in the experiment, n is the number of observations in a treatment, MSE is the error or within mean square from the ANOVA table, and q is obtained by entering Appendix I table  

H with alpha, k and N-k.

All possible differences between pairs of means are computed, and any difference that yields an absolute value that exceeds HSD is declared to be significant.