Page 207 - Intermediate Statistics for Dummies

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Part III: Comparing Many Means with ANOVA
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 dosages 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 it 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 exam-
ple, Treatment 4 is the combination of 20mg of the drug taken in two doses of
10mg each per day.
Table 11-1 The Six Treatment Combinations for the Drug Study
Amount One Time/Day Two Times/Day
10mg Treatment 1 Treatment 2
20mg Treatment 3 Treatment 4
30mg Treatment 5 Treatment 6
If factor A has i levels and factor B has j levels, you have i * j different combi-
nations of treatments in your two-way ANOVA model.

Stepping through the sums of squares

The two-way ANOVA model contains three terms: