2 II
III II
III II
f f
x f
f −
= ω
2.5
3. The Analysis of Variance
From the attribute accumulation, The fraction defective analysis needs some quantities to conduct the analysis of Variance. And the following quantity should be calculated.
3.1 The Total Sum of Squares Due To Class I
S
1
= total sum of squares of class I
I III
f f
f ω
⎟ ⎟
⎠ ⎞
⎜ ⎜
⎝ ⎛
− =
2 1
1
I III
III III
III I
f f
x f
f x
f f
f f
− −
=
1 2
2 1
2 I
III I
III III
I III
I
f f
x f
f x
f f
f x
f −
− =
III
f =
3.1 Similarly, the total sum of squares of class II is also
III
f
a. The Overall Total Sum of Squares Due To Class I and Class II
ST = total sum of squares of class I and class II
III III
f f
+ =
3.2 In general :
ST = total sum of squares of class I and class II = total number of measurements x number of classes - 1
3.3 The Degrees of Freedom Due To Class I
The degrees of freedom of class I is v
I
.
1 −
=
III I
f v
3.3 Similarly, the degrees of freedom of class II is also
1 −
III
f
3.4 The Total Degrees of Freedom
The total degrees of freedom due to class I and class II.
= vT
total degrees of freedom of class I dan class II 3.4 =
1 1
− +
−
III III
f f
In general:
= vT
total degrees of freedom of class I dan class II = total number of measurements -1 x number of classes -1
3.5 The Sum of Squares Due to The Mean of Each Class
Sm
1
= sum of squares due to mean of class I
I III
f f
ω
2 1
=
3.5 3.6
The Total Sum of Squares Due to The Mean
Sm = sum of squares due to mean of class I and class II
II III
II I
III
f f
f f
ω ω
2 2
1
+ =
II
Sm Sm
+ =
1
3.6
3.7 The Overall Total Sum of Squares Due to Class I and Class II
ST = total sum of squares of class I and class II 3.7
III III
f f
+ =
In general : ST = total sum of squares of class I and class II
= total number of measurements x number of classes - 1
3.8 The Degrees of Freedom Due to Class I
The degrees of freedom of class I is v
I
.
1 −
=
III I
f v
3.8 Similarly, the degrees of freedom of class II is also
1 −
III
f
3.9 The Total Degrees of Freedom
The total degrees of freedom due to class I and class II.
= vT
total degrees of freedom of class I dan class II =
1 1
− +
−
III III
f f
3.9 In general:
= vT
total degrees of freedom of class I dan class II = total number of measurements -1 x number of classes -1
3.10
The Sum of Squares Due to The Mean of Each Class
Sm
1
= sum of squares due to mean of class I
I III
f f
ω
2 1
=
3.10 3.11
The Total Sum of Squares Due to The Mean
Sm = sum of squares due to mean of class I and class II
II III
II I
III
f f
f f
ω ω
2 2
1
+ =
II
Sm Sm
+ =
1
3.11
3.12 The Sum of Squares Due to A Factor
