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Chapter 11: Finding Your Way through Two-Way ANOVA 195

What is interaction, anyway?

Interaction is when two factors meet, or interact with each other, on the
response in a way that’s different from how each factor affects the response
separately.
For example, before you can test to see whether dosage of medicine (Factor
A) or number of times taken (Factor B) are important in explaining changes
in blood pressure, you have to look at how they operate together to affect
blood pressure. That is, you have to examine the interaction term.

Suppose you’re taking one type of medicine for cholesterol and another
medicine for a heart problem. Suppose researchers only looked at the effects
of each drug alone, saying each one was good for managing the problem for
which it was designed with little or no side effects. Now you come along and
mix the two drugs in your system. As far as the individual study results are
concerned, all bets are off. With only those separate studies to go on, no one
knows how the drugs will interact with each other, and you can find yourself
in a great deal of trouble very quickly if you take them together.

Fortunately, drug companies and medical researchers do a great deal of work
studying drug interactions, and your pharmacist knows which drugs interact
as well. You can bet a statistician was involved in this work from day one!

Baking is another good example of how interaction works. Slurp down one
raw egg, drink a cup of milk, and eat a cup of sugar, a cup of flour, and a stick
of margarine. Then eat a cup of chocolate chips. Each one of these items has
a certain taste, texture, and effect on your taste buds that, in most cases, isn’t
all that great. But mix them all together in a bowl and voilà! You have a batch
of chocolate chip cookie dough, thanks to the magical effects of interaction.

In any two-way ANOVA, you must check out the interaction term first. If A and
B interact with each other and the interaction is statistically significant, you
can’t examine the effects of either factor separately. Their effects are inter-
twined and can’t be separated.

Interacting with interaction plots

In the two-way ANOVA model, you’re dealing with two factors and their inter-
action. A number of results could come out of this model in terms of signifi-
cance of the individual terms, as you can see in the following list:

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