Page 198 - Statistics II for Dummies

182 Part III: Analyzing Variance with ANOVA

Separating the turkeys with Tukey’s test

The basic idea behind Tukey’s test is to provide a series of simultaneous
tests for differences in the means. It still examines all possible pairs of means
and keeps the overall error rate at α and also keeps the individual Type I
error rate for each pair of means at α. Its distinguishing feature is that it per-
forms the tests all at the same time.

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 studentized 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 that’s based
on all pairwise comparisons (no matter how many means are in each group).

To conduct Tukey’s test, go to Stat>ANOVA>One-way or One-way unstacked.
(If your data appear in two columns with Column 1 representing the popula-
tion number and Column 2 representing the response, just click One-way
because your data are stacked. If your data are shown in k columns, one for
each of the k populations, click One-way unstacked.) Highlight the data for the
groups you’re comparing, and click Select. Then click on Comparisons, and
then 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 1, such as 5. Numbers greater than 1 are
interpreted as a percentage.

The Minitab output for comparing the groups regarding cellphone use by
using Tukey’s test appears in Figure 10-4. You can interpret its results in the
same ways as those in Figure 10-3. Some of the numbers in the confidence
intervals are different, but in this case, the main conclusions are the same:
Those age 19 and under use their cellphones most, followed by 40- to 59-year-
olds, then 20- to 39-year-olds, and finally those age 60 and over.

The results of Fisher and Tukey don’t always agree, usually because the over-
all error rate of Fisher’s procedure is larger than Tukey’s (except when only
two means are involved). Most statisticians I know prefer Tukey’s procedure
over Fisher’s. That doesn’t mean they don’t have other procedures they like
even better than Tukey’s, but Tukey’s is a commonly used procedure, and
many people like to use it.

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