Databases Reference
In-Depth Information
x
13
N
=
x
11
+
x
12
+
x
13
x
13
+
x
23
N
×
(5)
N
x
21
N
=
x
21
+
x
22
+
x
23
x
11
+
x
21
N
×
(6)
N
x
22
N
=
x
21
+
x
22
+
x
23
x
12
+
x
22
N
×
(7)
N
x
23
N
=
x
21
+
x
22
+
x
23
x
13
+
x
23
N
×
(8)
N
From (3) and (6),
x
11
x
21
=
x
11
+
x
12
+
x
13
x
21
+
x
22
+
x
23
In the same way, the following equation will be obtained:
x
11
x
21
=
x
12
x
22
=
x
13
x
23
=
x
11
+
x
12
+
x
13
x
21
+
x
22
+
x
23
(9)
Thus, we obtain the following theorem:
Theorem 2.
If two attributes in a contingency table shown in Table 3 are
statistical indepedent, the following equations hold:
x
11
x
22
−
x
12
x
21
=
x
12
x
23
−
x
13
x
22
=
x
13
x
21
−
x
11
x
23
= 0
(10)
It is notable that this discussion can be easily extended into a 2
×n
contingency
table where
n>
3. The important (9) will be extended into
x
11
x
21
=
x
12
x
22
=
x
1
n
x
2
n
=
···
=
k
=1
x
1
k
=
x
11
+
x
12
+
···
+
x
1
n
k
=1
x
2
k
(11)
x
21
+
x
22
+
···
+
x
2
n
Thus,
Theorem 3.
If two attributes in a
2
×
k contingency table (k
=2
,
···
,n)are
statistical indepedent, the following equations hold:
x
11
x
22
−
x
12
x
21
=
x
12
x
23
−
x
13
x
22
=
···
=
x
1
n
x
21
−
x
11
x
n
3
= 0
(12)
It is also notable that this equation is the same as the equation on collinearity
of projective geometry [1].
