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Part III: Comparing Many Means with ANOVA
Group 3: Adult males 40-59 years old
Group 4: Adult females 60 years old and over
You collect data on a random sample of 10 people from each group (where no
one knows anyone else to keep independence), and you record the number of
minutes each person used their cell phone in one month. The first ten lines of
a hypothetical data set are shown in Table 10-1.
Table 10-1 One Month’s Cell Phone Minutes for Four Age Groups
19 and Under
(Group 3)
(Group 4)
(Group 1)
(Group 2)
800
250
700
200
120
350
700
850
800 20–39 40–59 60 and Over
150
750
375
650 320 650 90
750 430 550 20
680 380 580 150
800 325 700 200
750 410 700 130
690 450 590 160
710 390 650 30
The means and standard deviations of the sample data are shown in Figure 10-1,
as well as confidence intervals for each of the population means separately (see
Chapter 3 for info on confidence intervals). Looking at Figure 10-1, it appears
that all four means are different, with 19 and under heading the pack, with
40- to 59-year-olds not far behind, and with 20- to 39-year-olds and those over
60 bringing up the rear (in that order).
Knowing that man can’t live by sample results alone, you decide that ANOVA
is needed to see whether any differences that appear in the samples can
be extended to the population (see Chapter 9). By using the ANOVA proce-
dure, you test whether the average cell minutes used is the same across all
groups. The results of the ANOVA, using the data from Table 10-1, are shown
in Figure 10-2.