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 see advertisements for active young men, as if activity were the whole of a young man’s capital. Yet I have been surprised when one has with confidence proposed to me, a grown man, to embark in some enterprise of his, as if I had absolutely nothing to do, my life having been a complete failure hitherto. What a doubtful compliment this to pay me!”
—Henry David Thoreau (1817–1862)
“Yet shall he mount, and keep his distant way
Beyond the limits of a vulgar fate:
Beneath the Good how far—but far above the Great.”
—Thomas Gray (1716–1771)