Page 212 - Intermediate Statistics for Dummies

17_045206 ch11.qxd 2/1/07 10:15 AM Page 191
Chapter 11: Getting a Little Interaction with Two-Way ANOVA
Factor B is significant but not factor A
Figure 11-1c shows where factor B is significant but A 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 mean 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 are significant,
and you don’t have an interaction effect because the lines are parallel.
Interaction term 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, then factors A and B interact
with each other in the way that they operate on the response. If they didn’t
interact, then the lines would be parallel. 191
Start with the top line of Figure 11-1e. 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 increases also. But when you take the drug once per
day, the opposite result happens.
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 interaction
AB term is considered a no-no in the two-way ANOVA world. Another taboo is
examining the factors individually (also known as the main effect) if the inter-
action term is significant.
Testing the Terms in Two-Way ANOVA
In a one-way ANOVA, you have only one hypothesis test. You use an F-test
to determine whether the means of the y values are the same or different 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
and possibly the main effects of A and B. Each test in a two-way ANOVA is an
F-test based on the ideas of one-way ANOVA (see Chapter 9 for more on this).
First, you test whether the interaction term AB is significant. To do this, you
use the test statistic F = MS AB , which has an F-distribution with (i – 1) ( j – 1)
*
MSE
degrees of freedom from MS AB (mean sum of squares for the interaction term