The purpose of some experiments is to compare the mean of each of several experimental groups with the mean of a control group. For example, a researcher may wish to find out whether any of four new methods of teaching arithmetic is better than the traditional method. Subjects are taught with one of the four new methods or with the traditional method (the control group). The experimenter then wishes to see which experimental group means (if any) are significantly different from the control group mean. Naturally, one could use a procedure such as Tukey's HSD to compare each mean with each other mean. The problem with using the Tukey's HSD or any other method designed to compare each mean with each other mean is that these methods overcorrect for the number of comparisons made. If each mean is compared to each other mean, then a total of (a)(a-1)/2 comparisons among "a" means would be tested. If there are "a" means (including the control) then there are only (a-1) comparisons between experimental means and the control mean to be tested.