Tukey's multiple comparison test is one of several tests that can be used to
determine which means amongst a set of means differ from the rest. Tukey's
multiple comparison test is also called Tukey's honestly signi®cant difference
test or Tukey's HSD. Alternative multiple comparison tests include SheffeÂ's test
and Dunnett's test. With only two groups of observations we could compare the
two group means using a t-test. When we have more than two groups, it is
inappropriate to simply compare each pair using a t-test because of the problem
of multiple testing. The correct way to do the analysis is to use a one-way
analysis of variance (ANOVA) to evaluate whether there is any evidence that the
means of the populations differ. If the ANOVA leads to a conclusion that there is
evidence that the group means differ, we might then be interested in
investigating which of the means are different. This is where the Tukey
multiple comparison test is used. The test compares the difference between each
pair of means with appropriate adjustment for the multiple testing. The results
are presented as a matrix showing the result for each pair, either as a P-value or
as a con®dence interval. The Tukey multiple comparison test, like both the t-test
and ANOVA, assumes that the data from the different groups come from
populations where the observations have a normal distribution and the standard
deviation is the same for each group. Many statistical packages offer Tukey
multiple comparison test as an option when conducting a one-way ANOVA, for
example this test is available in SPSS and Minitab.
Considering the results in the above paper, we see that the conclusions are not
absolutely clear cut. There appear to be two groups of manufacturers with
similar means ± A, B, D, E, F and B, C ± but B appears in both groups. This is
typical for what can happen with a multiple comparison test.