Information Technology Reference
In-Depth Information
Ta b l e 9 . 1 .
Summary table for three-way between-subjects design
Source
2
SS
df
MS
F
η
Kids home (
A
)
326.667
1
326.667
9.289
0.046
Vo t e r (
B
)
106.667
1
106.667
3.033
0.015
Politics (
C
)
1,672.500
2
836.250
23.780
0.237
A
×
B
326.667
1
326.667
9.289
0.046
A
×
C
1,060.833
2
530.417
15.083
0.151
B
×
C
490.833
2
245.417
6.979
0.070
A
×
B
×
C
1,375.833
2
687.917
19.562
0.195
S
/
ABC
1,688.000
48
35.167
Total
7,048.000
59
We have computed the ANOVA for the data shown in our numerical
example.ThesummarytableforthecorrectedmodelisshowninTable9.1.
As can be seen from Table 9.1, the total variance is partitioned into many
morepartsthanwehavethusfarencounteredinthepreviouschapters.
We look at these below.
9.2.2 THERE ARE THREE MAIN EFFECTS
With three independent variables in the design, each is associated with its
own main effect on the dependent variable. Thus, we evaluate the main
effects for children in the home, having voted in the last election, and
political preference. Take the main effect of having children in the home
as an example. We ask: Are participants who have school-aged children
at home more or less satisfied than those who do not have children at
home? Using Figure 9.1 as a frame of reference, we would compute the
mean of all those in the upper panel (children at home) and compare it
to the mean of all those in the lower panel (no children at home). Such
computations yield a mean satisfaction score for those with children in the
home of 23.67 and a mean satisfaction score for those without children
in the home of 28.33. This difference is evaluated by the
F
ratio and,
as shown in the summary table, those means are statistically significant,
F
(1, 48)
2
=
9
.
289,
p
<.
05,
η
=
.
046.
9.2.3 THERE ARE THREE TWO-WAY INTERACTIONS
Three-way designs also allow us to evaluate two-way interactions. Uni-
quely combining three independent variables two at a time can be done in
three different ways, which represent the three interactions: Children in
Home
×
Political Preference, Children in Home
×
Voting, and Voting
×
Political Preference. Each of these is separately evaluated.
For example, consider the Voting
Political Preference interaction.
To evaluate this interaction, we collapse across the third independent
variable, children in home. The Voting
×
×
Political Preference interaction
thus represents a 2
3 design (two levels of voting and three levels of
political preference) in which each cell contains data pooled together
from participants with and without children in the home.
×
