Information Technology Reference
In-Depth Information
Table 14.1.
Summary table of the ANOVA
Source
2
SS
df MS
F
η
Between subjects
122.60
Age (
A
)
48.40
1
48.40
46.65
c
.
395
a
Gender (
B
)
57.60
1
57.60
55.52
c
.
470
b
Age
×
Gender (
A
×
B
)
0.00
1
0.00
0.00
Error
Between
(
S
/
AB
)
16.60
16
1.04
Within subjects
35.00
.
483
b
Attract (
C
)
16.90
1
16.90
54.08
c
Age
×
Attract (
A
×
C
)
0.10
1
0.10
0.32
15.68
c
.
140
b
Gender
×
Attract (
B
×
C
)
4.90
1
4.90
25.92
c
.
231
b
Age
×
Gender
×
Attract (
A
×
B
×
C
)
8.10
1
8.10
Error
Within
(
C
×
S
/
AB
)
5.00
16
0.31
a
2
η
is computed based on the total between-subjects portion of the variance.
b
2
η
is computed based on the total within-subjects portion of the variance.
c
p
<.
05
.
14.3 EFFECTS OF INTEREST
The summary table showing the results of the analysis is presented in
Table 14.1. The effects of interest are the same as in any three-way design:
three main effects, three two-way interactions, and one three-way inter-
action. As can be seen, all three main effects, the Gender
Attract inter-
action, and the three-way interaction are all statistically significant.
Theetasquaredvaluesareshowninthelastcolumnofthesummary
table. As we did in Chapter 13, we based these computations on the
separate (sub)total variances of the between-subjects and within-subjects
partitions. Thus, we have computed the eta squared values as follows:
×
÷
SS
A
+
SS
B
+
SS
A
×
B
+
Main effect of
A
:
SS
A
SS
S
/
AB
÷
SS
A
+
SS
B
+
SS
A
×
B
+
Main effect of
B
:
SS
B
SS
S
/
AB
Main effect of
C
:
SS
C
÷
SS
C
+
SS
A
×
C
+
SS
B
×
C
+
SS
A
×
B
×
C
+
SS
C
×
S
/
AB
Interaction
B
×
C
:
SS
B
×
C
÷
SS
C
+
SS
A
×
C
+
SS
B
×
C
+
SS
A
×
B
×
C
+
SS
C
×
S
/
AB
Interaction
A
×
B
×
C
:
SS
A
×
B
×
C
÷
SS
C
+
SS
A
×
C
+
SS
B
×
C
+
SS
A
×
B
×
C
+
SS
C
×
S
/
AB
.
The plot of the interaction is shown in Figure 14.3. We will narrate
these results once we have performed the simple effects analyses.
14.4 COMPUTING THE OMNIBUS COMPLEXMIXED
DESIGN BY HAND
As we have done with previous three-factor designs in this topic, we will
provide the reader with the necessary computational formulas should they
choose to do these analyses by hand (see Table 14.2).
