Tukey Method of Multiple Comparison

The Tukey method of multiple comparison we will consider applies when the interest is only the pairwise simple contrasts.

Studentised range Distribution

The Tukey method utilises the studentised range distribution. Let \(Y_1, Y_2,\ldots , Y_k\) be independent observations from \(N(\mu ,\sigma ^2)\) and \(W\) be the range of this set of observations i.e \[W=\max \big \{Y_1,Y_2,\ldots ,Y_k\big \}-\min \big \{Y_1,Y_2,\ldots ,Y_k\big \}\] Let \(S^2\) be the estimate of \(\sigma ^2\) based on \(v\) degrees of freedom and is independent of the \(Y_{j'}\)s, then the ratio \(W/S\) is called studentised range as is denoted by \[l(k,v)=\frac {W}{S}\]