Information Technology Reference
In-Depth Information
Table 11.3.
Two-factor within-subjects ANOVA summary table
Source
SS
df
MS
F
A
(vehicle type)
2.78
1
2.78
1.76
B
(amount of alcohol)
157.39
2
78.70
52.82
∗
A
×
B
17.06
2
8.53
25.85
∗
S
(subject)
30.23
5
6.05
A
×
S
7.88
5
1.58
B
×
S
14.94
10
1.49
A
×
B
×
S
3.28
10
0.33
Total
233.56
35
∗
p
<
.05.
in Table 11.2. These matrices are created by summing the
Y
scores col-
lapsed across various treatment configurations. The reader is encouraged
to examine carefully how these matrices were created before proceeding
with the sum of squares computations.
11.6.1 CALCULATING SUMS OF SQUARES
There are seven sums of squares to be calculated in a two-way within-
subjects ANOVA. These final values can be seen in the ANOVA summary
table in Table 11.3. The preliminary calculations shown in Table 11.2
provide the ingredients for computing the following seven sums of squares:
Sum of squares main effect of Factor
A
(
SS
A
).
Sum of squares main effect of Factor
B
(
SS
B
).
Sum of squares interaction effect of Factors
A
and
B
(
SS
A
×
B
).
Sum of squares main effects of subjects (
SS
S
).
Sum of squares interaction of Factor
A
and subjects (
SS
A
×
S
).
Sum of squares interaction of Factor
B
and subjects (
SS
B
×
S
).
Sum of squares interaction of Factor
A
,Factor
B
,andsubjects
(
SS
A
×
B
×
S
).
Sum of squares total (
SS
T
).
The formulas for these seven sums of squares and the summary of
their calculations based on the data in Table 11.2 are as follows. Each sum
of squares is calculated by focusing on a particular matrix in Table 11.2.
The first three sums of squares (
SS
A
,
SS
B
,
SS
A
×
B
)arederivedfromthe
AB
matrix in Table 11.2.
A
2
(
b
)(
n
)
−
T
2
(
a
)(
b
)(
n
)
SS
A
=
(75)
2
(65)
2
(3)(6)
(140)
2
(2)(3)(6)
=
+
=
−
2.78
(11.1)