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:
“Just as a new scientific discovery manifests something that was already latent in the order of nature, and at the same time is logically related to the total structure of the existing science, so the new poem manifests something that was already latent in the order of words.”
—Northrop Frye (b. 1912)
“Feminism, like Boston, is a state of mind. It is the state of mind of women who realize that their whole position in the social order is antiquated, as a woman cooking over an open fire with heavy iron pots would know that her entire housekeeping was out of date.”
—Rheta Childe Dorr (1866–1948)
“The surest route to breeding jealousy is to compare. Since jealousy comes from feeling “less than” another, comparisons only fan the fires.”
—Dorothy Corkville Briggs (20th century)