Biostatistics

360 CHAPTER 8 ANALYSIS OF VARIANCE
TABLE 8.5.2 Data of Table 8.5.1 Altered to Show
the Effect of One Type of Interaction
Factor B—Drug Dosage
Factor A—Age j ¼ 1 j ¼ 2 j ¼ 3
Young ði ¼ 1Þ m 11 ¼ 5 m 12 ¼ 10 m 13 ¼ 20
Old ði ¼ 2Þ m 21 ¼ 15 m 22 ¼ 10 m 23 ¼ 5
Reduction in reaction time
30
Age
25
20
a 1
15
10
5
a 2
0
b 1 b 2 b 3
Drug dosage
FIGURE 8.5.2 Age and drug effects, interaction present.
Reduction in reaction time
30
25
20
15
10
5
0
a 1 a 2
Age
Drug dosage
b 1
b 2
b 3
The presence of interaction between two factors can affect the characteristics of the
data in a variety of ways depending on the nature of the interaction. We illustrate the effect
of one type of interaction by altering the data of Table 8.5.1 as shown in Table 8.5.2.
The important characteristics of the data in Table 8.5.2 are as follows.
1. The difference between means for any two levels of factor B is not the same for both
levels of factor A. We note in Table 8.5.2. for example, that the difference between
levels 1 and 2 of factor B is 5 for the young age group and þ5 for the old age group.
2. The difference between means for both levels of factor A is not the same at all levels
of factor B. The differences between factor A means are 10, 0, and 15 for levels 1, 2,
and 3, respectively, of factor B.
3. The factor level curves are not parallel, as shown in Figure 8.5.2.
When population data exhibit the characteristics illustrated in Table 8.5.2 and
Figure 8.5.2, we say that there is interaction between the two factors. We emphasize
that the kind of interaction illustrated by the present example is only one of many types of
interaction that may occur between two factors.
&
In summary, then, we can say that there is interaction between two factors if a change
in one of the factors produces a change in response at one level of the other factor different
from that produced at other levels of this factor.
Advantages
The advantages of the factorial experiment include the following.
1. The interaction of the factors may be studied.
2. There is a saving of time and effort.