Page 190 - Statistics II for Dummies

174 Part III: Analyzing Variance with ANOVA

Following Up after ANOVA

The main reason folks use ANOVA to analyze data is to find out whether
there are any differences in a group of population means. Your null hypoth-
esis is that there are no differences, and the alternative hypothesis is that
there’s at least one difference somewhere between two of the means. (Note it
doesn’t say that all the means have to be different.)

If it’s established that at least two of the population means are different, the
next natural question is: “Okay, which ones are different?” Although this is a
very simple-sounding question, it doesn’t have a simple answer. The concept
of means being different can be interpreted in hundreds of ways. Is one larger
than all the others? Are three pairs of them different from each other and the
rest all the same? Statisticians have worked long and hard to come up with
a wide range of choices of procedures to explore and find differences of all
types in two or more population means. This family of procedures is called
multiple comparisons.

This section starts off with an example in which the ANOVA procedure was
used and Ho was rejected, leading you to the next step: multiple compari-
sons. You then get an overview of how and why multiple comparison proce-
dures work.

Comparing cellphone minutes: An example

Suppose you want to compare the average number of cellphone minutes
used per month for various age groups, where the age groups are defined as
the following:

✓ Group 1: 19 years old and under
✓ Group 2: 20–39 years old
✓ 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 ten people from each group (where
no one knows anyone else to keep independence), and you record the
number of minutes each person used their cellphone in one month. The first
ten lines of a hypothetical data set are shown in Table 10-1.

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