Information Technology Reference
In-Depth Information
Table 15.1.
Summary ANOVA table
Source
2
SS
df
MS
F
η
Between subjects
135.53
Gender (
A
)
46.23
1
46.23
4.14
S
/
A
89.30
8
11.16
Within subjects
607.28
Color (
B
)
140.63
1
140.63
15.82
c
.
232
b
Gender
×
Color (
A
×
B
)
65.03
1
65.03
7.32
c
B
×
S
/
A
71.10
8
8.89
To y t y p e (
C
)
3.03
1
3.03
0.36
16.52
c
.
232
b
Gender
×
To y Ty p e (
A
×
C
)
140.63
1
140.63
C
×
S
/
A
68.10
8
8.51
Color
×
To y Ty p e (
B
×
C
)
5.63
1
5.63
1.41
20.37
c
.
134
b
Gender
×
Color
×
To y Ty p e (
A
×
B
×
C
)
81.23
1
81.23
B
×
C
×
S
/
A
31.90
8
3.99
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.
of the between-subjects independent variable and an error term (
S
A
).
The within-subjects effects have specialized error terms keyed to the par-
ticular within-subjects “effect.” There are three “pure” within-subjects
effectsinthisdesign:Factor
B
: color, Factor
C
: toy type, and the (
B
/
×
C
)
Color
Toy Type interaction. Each of these effects is associated with its
own error term as shown in the summary table in Table 15.1.
These pure within-subjects effects not only stand by themselves - each
of them also interacts with gender, the between-subjects factor. The error
term for the pure within-subjects effect contained in the interaction is
used in the computation of the
F
ratio. The specifics follow here:
×
Color is one of the pure within-subjects effects and is associated with
its own error term (
B
A
). We can also evaluate its interaction
with gender (
A
). This results in the (
A
×
S
/
Color two-
way interaction; the error term for this interaction is the error term
associated with color (
B
×
B
)Gender
×
×
S
/
A
).
To y t y p e (
C
) is another of the pure within-subjects effects and is
associated with its own error term (
C
A
). We can also evaluate
its interaction with gender. This results in the (
A
×
S
/
To y
Type two-way interaction; the error term for this interaction (
C
×
C
)Gender
×
×
S
/
A
) is the error term associated with toy type (
C
).
The (
B
ToyTypeinteractionisthethirdofthepure
within-subjects effects and is associated with its own error term
(
B
×
C
)Color
×
A
). We can also evaluate its interaction with gender.
This results in the (
A
×
C
×
S
/
Toy Type three-
way interaction; the error term for this three-way interaction (
B
×
B
×
C
)Gender
×
Color
×
×
C
×
S
/
A
) is the error term associated with (
B
×
C
) Color
×
To y
Type two-way interaction.
