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Factor A Sum of Squares (SS
A
)
DF = a
−
1
+
Factor B Sum of Squares (SS
B
)
DF = b
−
1
+
Total Sum of Squares SS
T
DF = abn
−
1
=
Interaction AB Sum of Squares (SS
AB
)
DF = (a
−
1)(b
−
1)
+
Error Sum of Squares (SS
E
)
DF = ab(n
−
1)
FIGURE 18.A.1
ANOVA variation decomposition.
Test for Main Effect of Factor A
H
0
: No difference among the a mean levels of factor A (
µ
A
1
=
µ
A
2
=
...
=
µ
Aa
)
H
a
: At least two factor A mean levels differ
Test for Main Effect of Factor B
H
0
: No difference among the a mean levels of factor B (
µ
B
1
=
µ
B
2
=
...
=
µ
Ba
)
H
a
: At least two factor B mean levels differ
Test for Main Effect of Factor A
Factor B Interaction
H
0
: Factor A and factor B do not interact in the response mean
H
a
: Factor A and factor B interact in the response mean
×
TABLE 18.A.1
Degree of Freedom for Two Factor Factorial Design
Effect
Degree of Freedom
A
a-1
B
b-1
AB interaction
(a-1)(b-1)
Error
ab(n - 1)
Total
abn - 1
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