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Table 10.2.
AS
data matrix and preliminary calculations for a (five-group) one-way within-subjects
ANOVA
Factor
A
: Symptom intensity measured before and after drug therapy
One
One
One
One
One
month
week
week
month
year
before
before
after
after
after
Subjects
a
1
a
2
a
3
a
4
a
5
Sum (
S
)
s
1
12
12
7
5
5
41
s
2
9
10
5
6
5
35
s
3
9
8
7
5
6
35
s
4
8
6
6
4
4
28
s
5
8
9
6
4
5
32
s
6
9
10
8
6
7
40
s
7
12
10
7
5
4
38
s
8
6
7
5
7
5
30
Sum of scores
A
1
=
73
A
2
=
72
A
3
=
51
A
4
=
42
A
5
=
41
Y
=
A
=
T
Y
=
A
j
:
=
279
Sum of squared
scores
Y
a
j
:
Y
a
1
=
695
Y
a
2
=
674
Y
a
3
=
333
Y
a
4
=
228
Y
a
5
=
217
Y
aj
=
2, 147
Number of cases:
N
=
8
T
(
a
)(
n
)
=
Mean (
Y
j
):
Y
1
=
9
.
13
Y
2
=
9
.
00
Y
3
=
6
.
38
Y
4
=
5
.
25
Y
5
=
5
.
13
Y
T
=
6
.
98
Va r i a n c e (
s
j
):
s
1
=
4
.
13
s
2
=
3
.
71
s
3
=
1
.
13
s
4
=
1
.
07
s
5
=
0
.
98
Standard
deviation (
s
j
):
s
1
=
.
s
2
=
.
s
3
=
.
s
4
=
.
s
5
=
.
2
03
1
93
1
06
1
04
0
99
The formulas for these four sums of squares and the summary of their
calculations based on data from Table 10.2 are as follows:
SumofSquaresfortheTreatmentEffect
(Within-Groups Variance):
SS
A
A
2
n
T
2
(
a
)(
n
)
SS
A
=
−
(73)
2
(72)
2
(51)
2
(42)
2
(41)
2
(279)
2
(5)(8)
+
+
+
+
=
−
8
=
2, 069
.
88
−
1, 946
.
03
=
123.85 ,
(10.1)
S
2
a
T
2
(
a
)(
n
)
SS
S
=
−
(41)
2
(35)
2
(35)
2
(28)
2
(32)
2
(40)
2
(38)
2
(30)
2
+
+
+
+
+
+
+
=
5
(279)
2
(5)(8)
−
=
1, 976
.
60
−
1, 946
.
03
=
30.57 ,
(10.2)
