Decomposition of Contingency Table using Expected Values
نویسنده
چکیده
A contingency table summarizes the conditional frequencies of two attributes and shows how these two attributes are dependent on each other with the information on a partition of universe generated by these attributes. Thus, this table can be viewed as a relation between two attributes with respect to information granularity. This paper focuses on decomposition of a contingency matrix by using a matrix of expected values based on marginal distribution (expected matrix). Especially when the rank of a matrix is full, say, r, the difference between a original matrix and the expected matrix will become r − 1 at most. Moreover, the sum of rows or columns will become zero, which means that the information of one rank correponds to information on the frequency of a contingency matrix.
منابع مشابه
AN OPTIMALITY THEORY FOR MID p–VALUES IN 2 × 2 CONTINGENCY TABLES
The contingency table arises in nearly every application of statistics. However, even the basic problem of testing independence is not totally resolved. More than thirty–five years ago, Lancaster (1961) proposed using the mid p–value for testing independence in a contingency table. The mid p–value is defined as half the conditional probability of the observed statistic plus the conditional prob...
متن کاملSimple Correspondence Analysis of Nominal-Ordinal Contingency Tables
The correspondence analysis of a two-way contingency table is now accepted as a very versatile tool for helping users to understand the structure of the association in their data. In cases where the variables consist of ordered categories, there are a number of approaches that can be employed and these generally involve an adaptation of singular value decomposition. Over the last few years, an ...
متن کاملPlain Answers to Several Questions about Association/Independence Structure in Complete/Incomplete Contingency Tables
In this paper, we develop some results based on Relational model (Klimova, et al. 2012) which permits a decomposition of logarithm of expected cell frequencies under a log-linear type model. These results imply plain answers to several questions in the context of analyzing of contingency tables. Moreover, determination of design matrix and hypothesis-induced matrix of the model will be discusse...
متن کاملConfidence circles for correspondence analysis using orthogonal polynomials
An alternative approach to classical correspondence analysis was developed in [3] and involves decomposing the matrix of Pearson contingencies of a contingency table using orthogonal polynomials rather than via singular value decomposition. It is especially useful in analysing contingency tables which are of an ordinal nature. This short paper demonstrates that the confidence circles of Lebart,...
متن کاملSingular value decomposition of large random matrices (for two-way classification of microarrays)
Asymptotic behavior of the singular value decomposition (SVD) of blown up matrices and normalized blown up contingency tables exposed to Wigner-noise is investigated. It is proved that such an m×n matrix almost surely has a constant number of large singular values (of order √ mn), while the rest of the singular values are of order √ m + n as m,n → ∞. Concentration results of Alon at al. for the...
متن کامل