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 and/or comparisons:
“A doctor, like anyone else who has to deal with human beings, each of them unique, cannot be a scientist; he is either, like the surgeon, a craftsman, or, like the physician and the psychologist, an artist.... This means that in order to be a good doctor a man must also have a good character, that is to say, whatever weaknesses and foibles he may have, he must love his fellow human beings in the concrete and desire their good before his own.”
—W.H. (Wystan Hugh)
“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)