7.4.7.1. Tukey's method

Tukey's method considers all possible pairwise differences of means at the same time	The Tukey method applies simultaneously to the set of all pairwise comparisons {i - j} The confidence coefficient for the set, when all sample sizes are equal, is exactly 1-. For unequal sample sizes, the confidence coefficient is greater than 1-. In other words, the Tukey method is conservative when there are unequal sample sizes.
	Studentized Range Distribution
The studentized range q	The Tukey method uses the studentized range distribution. Suppose we have r independent observations y1, ..., yr from a normal distribution with mean  and variance 2. Let w be the range for this set , i.e., the maximum minus the minimum. Now suppose that we have an estimate s2 of the variance 2 which is based on  degrees of freedom and is independent of the yi. The studentized range is defined as
The distribution of q is tabulated in many textbooks and can be calculated using Dataplot	The distribution of q has been tabulated and appears in many textbooks on statistics. In addition, Dataplot has a CDF function (SRACDF) and a percentile function (SRAPPF) for q.As an example, let r = 5 and  = 10. The 95th percentile isq.05;5,10 = 4.65. This means: So, if we have five observations from a normal distribution, the probability is .95 that their range is not more than 4.65 times as great as an independent sample standard deviation estimate for which the estimator has 10 degrees of freedom. Read More