Information Technology Reference
In-Depth Information
Sum of squares within groups or error (
SS
S
/
AB
)inwhichthesub-
script
S
AB
indicates subjects within each level of the
AB
treatment
combinations.
Sum of squares total (
SS
T
).
/
The formulas for these five sums of squares and the summary of their
calculations based on the data in Table 8.3 are as follows:
A
2
(
b
)(
n
)
−
T
2
(
a
)(
b
)(
n
)
SS
A
=
(155)
2
(330)
2
(260)
2
(745)
2
(3)(2)(5)
+
+
=
−
(2)(5)
24,225
+
108,900
+
67,600
555,025
30
=
−
10
=
20,052
−
18,500.83
=
1,551.17 ;
(8.1)
B
2
(
a
)(
n
)
−
T
2
(
a
)(
b
)(
n
)
SS
B
=
(475)
2
(270)
2
(3)(5)
(745)
2
(3)(2)(5)
+
=
−
225,625
+
72,900
555,025
30
=
−
15
=
19,901.67
−
18,500.83
=
1,400.84 ;
(8.2)
(
AB
)
2
n
A
2
(
b
)(
n
)
−
B
2
(
a
)(
n
)
+
T
2
(
a
)(
b
)(
n
)
SS
A
×
B
=
−
(75)
2
(190)
2
(210)
2
(80)
2
(140)
2
(50)
2
+
+
+
+
+
=
5
−
20,052
−
19,901.67
+
18,500.83
=
22,865
−
20,052
−
19,901.67
+
18,500.83
=
1,412.16 ;
(8.3)
SS
S
/
AB
=
Y
2
(
AB
)
2
n
−
=
1,247
+
7,398
+
8,990
+
1,402
+
4,090
+
622
−
22,865
=
23,749
−
22,865
=
884.00 ;
(8.4)
T
2
(
a
)(
b
)(
n
)
SS
T
=
Y
2
−
=
23,749
−
18,500.83
=
5,248.17
.
(8.5)
