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Goodness of fit of an assigned set of scores for the analysis of association in a contingency table

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Abstract

The problem of association between two attributes in ap×q contingency table can be looked upon as the problem of relationship between two vector variablesx andy. If there is only one true non-zero canonical correlation betweenx andy, the association between the two attributes is of rank 1 and in this case, one set of scores is adequate to describe the association completely; these scores are nothing but the coefficients in the canonical variates corresponding to the true non-zero canonical correlation. Given a set of hypothetical scoresα 1,α1,⋯,αp for the rows, one is interested in testing their goodness of fit. Tests for this are suggested in this paper. For obtaining these tests, a preliminary result about direction and collinearity factors in discriminant analysis, whenS irrelevant variables are eliminated, is needed. This is derived in part one of this paper.

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Authors and Affiliations

  1. Southern Methodist University, Dallas, USA

    A. M. Kshirsagar

Authors
  1. A. M. Kshirsagar
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Additional information

This research was sponsored by the Office of Naval Research, Contract No. N00014-68-A-0515, Project No. NR042-260. Reproduction in whole or in part is permitted for any purpose of the United States Government.

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Kshirsagar, A.M. Goodness of fit of an assigned set of scores for the analysis of association in a contingency table. Ann Inst Stat Math 22, 295–306 (1970). https://doi.org/10.1007/BF02506345

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  • DOI: https://doi.org/10.1007/BF02506345

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