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Chapter 10: Pairing Things Down with Multiple Comparisons
Separating the turkeys with Tukey’s test
This section dives into Tukey’s test and applies it to the cell-phone example.
Setting up Tukey’s test
The basic idea behind Tukey’s test is to provide a series of simultaneous con-
fidence intervals for the differences in the means. It still examines all possible
pairs of means and keeps the overall error rate (also known as the familywise
error rate) at α (like Fishers LSD), but it also keeps the individual Type I error
rate for each pair of means at α as well. This difference takes care of a lot of
issues raised with Fisher’s LSD procedure (refer to the preceding section).
Although the details of the formulas used for Tukey’s test are beyond the scope
of this book, they’re not based on the t-test, but rather something called a stu-
dentized range statistic, which is based on the highest and lowest means in the
group, and their difference. The individual error rates are held at 0.05 because
Tukey developed a cutoff value for his test statistic, which is based on all pair- 183
wise comparisons (no matter how many means are in each group).
If you calculate the results by hand, you can look at tables to make your con-
clusions. However, all applications I have ever seen both in the classroom
and outside of it use a computer for these calculations. (For sanity’s sake, I
suggest you do the same.)
To conduct Tukey’s test, go to Stat>ANOVA>One-way or One-way unstacked.
(If your data appears in two columns with Column 1 representing the popula-
tion number and Column 2 representing the response, just click One-way
because your data is stacked. If your data is shown in k columns, one for
each of the k populations, click One-way unstacked.) The next step is to
highlight the data for the groups you’re comparing and click Select. Then
click on Comparisons. Click on Tukey’s. The familywise (overall) error rate
is listed at 5 (percent), which is typical. If you want to change it, type in the
desired error rate (between 0.5 and 0.001) and click OK. You may type in your
error rate as a decimal, such as 0.05, or as a number greater than one, such
as 5. Numbers greater than one are interpreted as a percentage.
Doing Tukey’s test on the cell phone data
The Minitab output for comparing the groups regarding cell-phone use by using
Tukey’s test appears in Figure 10-4. Looking at Figure 10-4, you see that its
results can be interpreted in the same was as for Figure 10-3. Some of the num-
bers in the confidence intervals are different, but in this case, the main conclu-
sions are the same: Those 19 and under use their cell phones most, followed
by 40- to 59-year-olds, then 20- to 39-year-olds, and finally those 60 and over.