Information Technology Reference
In-Depth Information
Political Preference
Liberal
Moderate
Conservative
Figure 9.2
Means for the
Voting
Political Preference
interaction.
×
Vote Yes
34.50
24.50
15.00
Vote No
31.50
25.00
25.50
We show the means for this interaction effect in Figure 9.2. For each
cell in this 2
×
3 configuration, we combined the data for the two children
in the home cells. For example, the mean for liberals who voted in the
last election is 34.50. This is the average of liberals who voted in the last
election who have children in the home (mean
36.00) and liberals who
voted in the last election who do not have children in the home (mean
=
=
33.00).
Visual inspection of the means for this Voting
Political Preference
interaction suggests that there might very well be a significant effect.
Looking across the top row of means shows a steady drop in satisfaction
from liberal to moderate to conservative participants, but looking across
the bottom row shows a drop in satisfaction from liberals to moderates that
levels off such that conservatives and moderates are approximately equally
satisfied. Our visual inspection is confirmed by the statistical analysis. As
we can see from the summary table in Table 9.1, this interaction effect is
statistically significant,
F
(2, 48)
×
2
=
6
.
979,
p
<.
05,
η
=
.
070.
9.2.4 THE THREE-WAY INTERACTION
Because we have three independent variables, it is possible for the unique
combinations of all three to be differentially associated with participant
performance; thus, one of the effects evaluated in the design is the three-
way interaction of Children in Home
×
×
Political Preference. This
is the highest order (most complex) effect in the design; that is, this effect
deals with the cell means (twelve cell means in this case) at the most
detailed tier of the design.
The means that are evaluated for this three-way interaction are shown
in Figure 9.1. As you can see, this is the most fundamental tier of the design
in which each combination of the levels of the independent variables is
represented by its own mean.
The summary of the analysis in Table 9.1 indicates that the three-way
interaction is statistically significant,
F
(2, 48)
Vo t i n g
2
=
19
.
562,
p
<.
05,
η
=
.
195. Although it is much more complex than the two-way interaction we
discussed in the previous chapter, to understand the three-way interaction
we approach it in much the same way that we dealt with the two-way inter-
action. That is, we ultimately interpret statistically significant three-way
interactions by breaking them down into a set of two-way interactions.
We do this by splitting one of the independent variables by its levels and
examining each level separately, leaving the other two independent vari-
ables in factorial (two-way) combinations. When we examine each level,
