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B 2
( a )( n ) −
T 2
( a )( b )( n )
SS B =
(14) 2
(51) 2
(75) 2
(140) 2
(2)(3)(6) =
+
+
=
−
157.39
(11.2)
(2)(6)
AB 2
n
A 2
( b )( n ) −
B 2
( a )( n ) +
T 2
( a )( b )( n )
SS A × B =
−
(6) 2
(24) 2
(45) 2
(8) 2
(27) 2
(30) 2
+
+
+
+
+
=
6
(75) 2
(65) 2
(3)(6)
(14) 2
(51) 2
(75) 2
(140) 2
(2)(3)(6)
+
+
+
−
−
+
(2)(6)
=
17.06
.
(11.3)
Thenexttwosumsofsquaresarederivedfromthe AS matrix of Table 11.2.
S 2
( a )( b ) −
T 2
( a )( b )( n )
SS S =
(22) 2
(27) 2
(21) 2
(13) 2
(140) 2
(2)(3)(6)
+
+···+
+
=
−
(2)(3)
=
30.23
(11.4)
AS 2
b
A 2
( b )( n ) −
S 2
( a )( b ) +
T 2
( a )( b )( n )
SS A × S =
−
(11) 2
+
(13) 2
+···+
(11) 2
+
(6) 2
(75) 2
(65) 2
(3)(6)
+
=
−
3
(22) 2
(27) 2
(21) 2
(13) 2
(140) 2
(2)(3)(6)
+
+···+
+
−
+
(2)(3)
=
7.88
.
(11.5)
The next sum of squares is derived from the BS matrix of Table 11.2.
BS 2
a
B 2
( a )( n ) −
S 2
( a )( b ) +
T 2
( a )( b )( n )
SS B × S =
−
(3) 2
(2) 2
(12) 2
(9) 2
(14) 2
(51) 2
(75) 2
+
+···+
+
+
+
=
−
2
(2)(6)
(22) 2
(27) 2
(21) 2
(13) 2
(140) 2
(2)(3)(6)
+
+···+
+
−
+
(2)(3)
=
14.94
.
(11.6)
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