Databases Reference
In-Depth Information
Tabl e 3 .
Statistics of
M
(2
,
2
,
10)
det
|
det
|
min
−
25
0
25%
−
6
2
50%
0
6
75%
6
11.75
max
25
25
Tabl e 4 .
Statistics of
M
(2
,
2
,
50)
det
|
det
|
min
−
625
0
25%
−
140
60
50%
0
140
75%
140
256
max
625
625
7 Conclusion
In this paper, the nature of the dependence of a contingency matrix and the
statistical nature of the determinant are examined.
Especially, the constraint on the sample size
N
of a contingency table will
determine the number of 2
2 matrices. As
N
grows, the ratio of matrices with
zero determinant rapidly decreases, which shows that the number of matrix
with statistical dependence will increase. However, due to the nature of the
determinant, the average of absolute value of the determinant also increase
with the order of
N
2
, whereas the increase in the size of total number of
matrix is of
N
3
.
This is a preliminary work on the statistical nature of the determinant,
and it will be our future work to investigate the nature of 3
×
×
3 or higher
dimensional contingency matrices.
References
1. Tsumoto, S.: Statistical independence as linear independence. In Skowron, A.,
Szczuka, M., eds.: Electronic Notes in Theoretical Computer Science. Volume 82.,
Elsevier, Amsterdam (2003)
2. Tsumoto, S., Hirano, S.: Determinantal divisors for the degree of independence
of a contingency matrix. In: Proceedings of NAFIPS 2004, IEEE press (2004)
3. Tsumoto, S., Hirano, S.: Degree of dependence as granularity in contingency
table. In Hu, T., Lin, T., eds.: Proceedings of IEEE GrC 2005, IEEE press (2005)
4. Skowron, A., Grzymala-Busse, J.: From rough set theory to evidence theory. In
Yager, R., Fedrizzi, M., Kacprzyk, J., eds.: Advances in the Dempster-Shafer
Theory of Evidence. Wiley, New York (1994) 193-236
