Page 206 - Intermediate Statistics for Dummies

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Chapter 11
Getting a Little Interaction
with Two-Way ANOVA
In This Chapter
Building and carrying out ANOVA with two factors
Getting familiar with (and looking for) interaction effects and main effects
Putting the terms to the test
Demystifying the two-way ANOVA table
nalysis of variance (ANOVA) is often used in experiments to see whether
Adifferent levels of an explanatory variable (x) get different results on
some quantitative variable y. (See Chapter 9.) The x variable in this case is
called a factor, and it has certain levels to it, depending on how the experiment
is set up. For example, say you want to compare the average reduction in blood
pressure on certain dosages of a drug. The factor is drug dosage. Suppose it
has three levels: 10mg per day, 20mg per day, or 30mg per day. Suppose some-
one else studies the response to that same drug and examines whether the
times taken per day (one time or two times) has any effect on blood pressure.
In this case, the factor is number of times per day, and it has two levels: once
and twice.

Suppose you want to study the effects of dosage and number of times taken
together, because you believe both may have an affect on the response. So
what you have is called a two-way ANOVA, using two factors together to com-
pare the average response. So it’s an extension of one-way ANOVA (refer to
Chapter 9) with a twist, because the two factors you use may operate on the
response differently together than they would separately.

In this chapter, you examine two-way ANOVA — setting up the model, making
your way through the ANOVA table, taking the F-tests, and drawing the appro-
priate conclusions.