Order of Comparisons
If there are a set of means (A, B, C, D), which can be ranked in the order A > B > C > D, not all possible comparisons need be tested using Tukey's test. To avoid redundancy, one starts by comparing the largest mean (A) with the smallest mean (D). If the qs value for the comparison of means A and D is less than the q value from the distribution, the null hypothesis is not rejected, and the means are said have no statistically significant difference between them. Since there is no difference between the two means that have the largest difference, comparing any two means that have a smaller difference is assured to yield the same conclusion (if sample sizes are identical). As a result, no other comparisons need to be made.
Overall, it is important when employing Tukey's test to always start by comparing the largest mean to the smallest mean, and then the largest mean with the next smallest, etc., until the largest mean has been compared to all other means (or until no difference is found). After this, compare the second largest mean with the smallest mean, and then the next smallest, and so on. Once again, if two means are found to have no statistically significant difference, do not compare any of the means between them.
Read more about this topic: Tukey's Range Test
Famous quotes containing the words order of, order and/or comparisons:
“This is one of the worst speeches I’ve ever seen. No one will listen except the Mobil P.R. man. List what we want to say M arrange items in order of priority M then say them plainly and bluntly.... Hit hard and early. Don’t apologize or evade tough issues.”
—Jimmy Carter (James Earl Carter, Jr.)
“You cannot have one well-bred man without a whole society of such. They keep each other up to any high point. Especially women;Mit requires a great many cultivated women,—saloons of bright, elegant, reading women, accustomed to ease and refinement, to spectacles, pictures, sculpture, poetry, and to elegant society, in order that you have one Madame de Staël.”
—Ralph Waldo Emerson (1803–1882)
“I don’t like comparisons with football. Baseball is an entirely different game. You can watch a tight, well-played football game, but it isn’t exciting if half the stadium is empty. The violence on the field must bounce off a lot of people. But you can go to a ball park on a quiet Tuesday afternoon with only a few thousand people in the place and thoroughly enjoy a one-sided game. Baseball has an aesthetic, intellectual appeal found in no other team sport.”
—Bowie Kuhn (b. 1926)