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198 Part III: Analyzing Variance with ANOVA

Factor B is significant but not Factor A
Figure 11-1c shows where Factor B (times per day) is significant but Factor
A (dosage level) isn’t. The lines are flat across dosage levels, indicating that
dosage has no effect on blood pressure. However, the two lines for times
per day are spread apart, so their effect on blood pressure is significant.
Parallel lines indicate no interaction effect.

Neither factor is significant
Figure 11-1d shows two flat lines that are very close to each other. By the
previous discussions about Figures 11-1b and 11-1c, you can guess that this
figure represents the case where neither Factor A nor Factor B is significant,
and you don’t have an interaction effect because the lines are parallel.

Interaction term AB is significant
Finally you get to Figure 11-1e, the most interesting interaction plot of all. The
big picture is that because the two lines cross, Factors A and B interact with
each other in the way that they operate on the response. If they didn’t inter-
act, the lines would be parallel.

Start with the line in Figure 11-1e that increases from left to right (the one for 2
times/day). This line shows that when you take the drug two times per day at
the low dose, you get a low change in blood pressure; as you increase dosage,
blood pressure change increases also. But when you take the drug once per
day, the opposite result happens, as shown by the other line that decreases
from left to right in Figure 11-1e.

If you didn’t look for a possible interaction effect before you examined the main
effects, you may have thought no matter how many times you take this drug per
day, the effects will be the same. Not so! Always check out the interaction term
first in any two-way ANOVA. If the interaction term is significant, you have no
way to pull out the effects due to just factor A or just factor B; they’re moot.

Checking the main effects of Factor A or B without checking out the interac-
tion AB term is considered a no-no in the two-way ANOVA world. Another
taboo is examining the factors individually (also known as analyzing main
effects) if the interaction term is significant.

Testing the Terms in Two-Way ANOVA

In a one-way ANOVA, you have only one overall hypothesis test; you use an
F-test to determine whether the means of the y values are the same or dif-
ferent as you go across the levels of the one factor. In two-way ANOVA, you
have more items to test besides the overall model. You have the interaction
term AB to examine first, and possibly the main effects of A and B. Each test

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