Confidence Limits
The Tukey confidence limits for all pairwise comparisons with confidence coefficient of at least 1 − α are
Notice that the point estimator and the estimated variance are the same as those for a single pairwise comparison. The only difference between the confidence limits for simultaneous comparisons and those for a single comparison is the multiple of the estimated standard deviation.
Also note that the sample sizes must be equal when using the studentized range approach. is the standard deviation of the entire design, not just that of the two groups being compared. The Tukey–Kramer method for unequal sample sizes is as follows:
where n i and n j are the sizes of groups i and j respectively. The degrees of freedom for the whole design is also applied.
Read more about this topic: Tukey's Range Test
Famous quotes containing the words confidence and/or limits:
“I cannot give them my confidence; pardon me, gentlemen, confidence is a plant of slow growth in an aged bosom: youth is the season of credulity.”
—William, Earl Of Pitt (1708–1778)
“Europe has what we do not have yet, a sense of the mysterious and inexorable limits of life, a sense, in a word, of tragedy. And we have what they sorely need: a sense of life’s possibilities.”
—James Baldwin (1924–1987)