DocumentCode :
3260290
Title :
Residual Matrix and Statistical Independence in a Contingency Table
Author :
Tsumoto, Shusaku ; Hirano, Shoji
Author_Institution :
Dept. of Med. Informatics, Shimane Univ., Izumo
fYear :
2006
fDate :
Dec. 2006
Firstpage :
433
Lastpage :
437
Abstract :
Marginal distributions play a central role in statistical analysis of a contingency table. However, when the number of partition becomes large, the contribution from marginal distributions decreases. This paper focuses on a formal analysis of marginal distributions in a contingency table. The main approach is to take the difference between two matrices with the same sample size and the same marginal distributions, which we call difference matrix. The important nature of the difference matrix is that the determinant is equal to 0: when the rank of a matrix is r, the difference between an original matrix and the expected matrix become r - 1 at most. Since the sum of rows or columns become zero, which means that the information of one rank corresponds to information on the frequency of a contingency matrix. Interestingly, if we take an expected matrix whose elements are the expected values based on marginal distributions, the difference between an original matrix and expected matrix can be represented by linear combination of determinants of 2times2 submatrices
Keywords :
data mining; decision making; statistical analysis; statistical distributions; contingency matrix; contingency table; difference matrix; marginal distributions; residual matrix; statistical analysis; statistical independent; Biomedical informatics; Bismuth; Cities and towns; Conferences; Data mining; Frequency; Matrix decomposition; Probability; Statistical analysis; Statistical distributions;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Data Mining Workshops, 2006. ICDM Workshops 2006. Sixth IEEE International Conference on
Conference_Location :
Hong Kong
Print_ISBN :
0-7695-2702-7
Type :
conf
DOI :
10.1109/ICDMW.2006.141
Filename :
4063666
Link To Document :
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