Databases Reference
In-Depth Information
7.2 Contingency Table (4
×
4, Rank: 3)
From four-way tables, the situation becomes more complicated. In the similar
way to Sect. 7.1, a four-way contingency table is defined as:
⎛
⎝
⎞
⎠
x
11
x
12
x
13
x
14
x
21
x
22
x
23
x
24
x
31
x
32
x
33
x
34
x
41
x
42
x
43
x
44
M
(4
,
4) =
When its rank is equal to 3, it can be assumed that the fourth row is repre-
sented by the first to third row:
(
x
41
x
42
x
43
x
44
)=
p
(
x
11
x
12
x
13
x
14
)
+
q
(
x
21
x
22
x
23
x
24
)
+
r
(
x
31
x
32
x
33
x
34
)
(19)
Then, the following three types of equations are obtained by simple calcu-
lation.
∆
(1
,j
)=(1+
q
)
x
1
j
4
4
x
2
k
−
x
2
j
x
1
k
k
=1
k
=1
+(1 +
r
)
x
1
j
4
4
x
3
k
−
x
3
j
x
1
k
k
=1
k
=1
∆
(2
,j
)=(1+
p
)
x
2
j
4
4
x
1
k
−
x
1
j
x
2
k
k
=1
k
=1
4
4
+(1 +
r
)
x
2
j
x
3
k
− x
3
j
x
2
k
k
=1
k
=1
∆
(3
,j
)=(1+
p
)
x
2
j
4
4
x
1
k
−
x
1
j
x
2
k
k
=1
k
=1
+(1 +
q
)
x
1
j
4
4
x
2
k
−
x
2
j
x
1
k
k
=1
k
=1
q
)
x
1
j
4
4
∆
(4
,j
)=(
p
−
x
2
k
−
x
2
j
x
1
k
k
=1
k
=1
p
)
x
3
j
4
4
+(
r
−
x
1
k
−
x
1
j
x
3
k
k
=1
k
=1
r
)
x
2
j
4
4
+(
q
−
x
3
k
−
x
3
j
x
2
k
k
=1
k
=1
