Comparing Means with a Control (1 of 4)
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.