Page 208 - Statistics II for Dummies

192 Part III: Analyzing Variance with ANOVA

In this chapter, first I give you an example of when you’d need to use a two-way
ANOVA. Then I show you how to set up the model, make your way through the
ANOVA table, take the F-tests, and draw the appropriate conclusions.

Setting Up the Two-Way ANOVA Model

The two-way ANOVA model extends the ideas of the one-way ANOVA model
and adds an interaction term to examine how various combinations of the
two factors affect the response. In this section, you see the building blocks of
a two-way ANOVA: the treatments, main effects, the interaction term, and the
sums of squares equation that puts everything together.

Determining the treatments

The two-way ANOVA model contains two factors, A and B, and each factor has
a certain number of levels — say i levels of Factor A and j levels of Factor B.
In the drug study example from the chapter intro, you have A = drug dosage
with i = 1, 2, or 3, and B = number of times taken per day with j = 1 or 2. Each
person involved in the study is subject to one of the three different drug dos-
ages and will take the drug in one of the two methods given. That means you
have 3 * 2 = 6 different combinations of Factors A and B that you can apply
to the subjects, and you can study these combinations and their effects on
blood pressure changes in the two-way ANOVA model.

Each different combination of levels of Factors A and B is called a treatment in
the model. Table 11-1 shows the six treatments in the drug study. For example,
Treatment 4 is the combination of 20mg of the drug taken in two doses of
10mg each per day.

Table 11-1 Six Treatment Combinations
for the Drug Study Example
Dosage Amount One Dose Per Day Two Doses Per Day
10mg Treatment 1 Treatment 2
20mg Treatment 3 Treatment 4
30mg Treatment 5 Treatment 6

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