Page 212 - Statistics II for Dummies

196 Part III: Analyzing Variance with ANOVA

✓ 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, so you don’t examine A or B
separately.

Figure 11-1 depicts each of these five situations in terms of a diagram using
the drug study example. Plots that show how Factors A and B react sepa-
rately and together on the response variable y are called interaction plots.
In the following sections, I describe each of these five situations in detail in
terms of what the plots tell you and what the results mean in the context of
the drug study example.

Factors A and B are significant
Figure 11-1a shows the situation when both A and B are significant in the
model and no interaction is 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,
which is change in blood pressure, at each combination of treatments.

In order to interpret these interaction plots, you first look at the general
trends each line is making. The top line in Figure 11-1a is moving uphill from
left to right, meaning that when the drug is taken two times per day, the
changes in blood pressure increase as dosage level increases. The bottom
line shows a similar result when the drug is taken once per day; blood pres-
sure changes increase as dosage level increases. Assuming these differences
are large enough, you conclude that dosage level (Factor A) is significant.

Now you look at how the lines compare to each other. Note that the lines,
although parallel, are quite far apart. In particular, the amounts of blood
pressure changes are higher overall when taking the drug twice per day (top
line) than they are when taking the drug once per day (bottom line). Again,
assuming these differences are large enough, you conclude that times per
day (Factor B) is significant.
In this case, the different combinations of Factors A and B don’t affect the
overall trends in blood pressure changes in opposite ways (that is, the lines
don’t cross each other) so there’s no interaction effect between dosage level
and times per day.

Two parallel lines in an interaction plot indicate a lack of an interaction effect.
In other words, the effect of Factor A on the response doesn’t change as you
move across different levels of Factor B. In the drug study example, the levels
of A don’t change blood pressure differently for different levels of B.

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