Page 210 - Intermediate Statistics for Dummies

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Chapter 11: Getting a Little Interaction with Two-Way ANOVA
Interacting with interaction plots
In the two-way ANOVA model, you have two factors and their interaction. A
number of results could come out of this model in terms of significance of the
individual terms, as you can see in the following:
Factors A and B are both significant.
Factor A is significant but not factor B.
Factor B is significant but not factor A.
Neither factors A nor B are significant.
The interaction term AB is significant.
Figure 11-1 depicts each of these five situations, respectively, in terms of a
diagram, using the drug-study example. Plots that show how factors A and B
react separately and together on the response variable y are called interaction
plots. In the following sections, I describe each of these five situations in 189
detail in terms of what the plots are telling you and what the results mean in
the context of an example.
Factors A and B are significant
Figure 11-1a shows the situation when both A and B are significant in the
model (no interaction present). The lines represent the levels of the times-
per-day factor (B); the x-axis represents the levels of the dosage factor (A);
and the y-axis represents the average value of the response variable y, change
in blood pressure, at each combination of treatments.
The top line moving across Figure 11-1a shows that when the drug is taken two
times per day, the change in blood pressure increases with dosage level. The
bottom line shows the same thing happens when the drug is taken once per
day, except that the effects on blood pressure are lower overall than the effects
of taking the drug twice a day. That means factor A is significant because blood
pressure changes across dosage levels, and factor B is significant because
blood pressure is different from one line to another. (Assume the difference is
large enough to be significant.) Here the different combinations of factors A
and B don’t affect the overall trends, so there’s no interaction effect.
Two parallel lines in an interaction plot means a lack of an interaction effect.
In the drug-study example, the levels of A don’t change blood pressure differ-
ently for different levels of B.
Factor A is significant but not factor B
Figure 11-1b shows that blood pressure changes across dosage levels for
taking the drug once or twice a day. However, the two lines are so close