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Generalized Proportional Reduction in Variation Measure for Two-Way Contingency Tables

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Abstract

For a two-way contingency table with nominal explanatory and response variables, Goodman and Kruskal (1954), and Theil (1970) proposed the measures which describe the proportional reduction in variation from the marginal distribution to the conditional distributions of the response. This paper proposes a generalization of those measures. The measure is expressed by using the Patil and Taillie’s (1982) diversity index. Special cases of the proposed measure include the Goodman and Kruskal’s and the Theil’s measures.

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References

  • Agresti, A. (1984). Analysis of Ordinal Categorical Data. John Wiley, New York.

    MATH  Google Scholar 

  • Agresti, A. (1990). Categorical Data Analysis. John Wiley, New York.

    MATH  Google Scholar 

  • Andersen, E.B. (1980). Discrete Statistical Models With Social Science Applications. North-Holland, Amsterdam.

    MATH  Google Scholar 

  • Bishop, Y.M.M., Ftenberg, S.E., & Holland, P.W. (1975). Discrete Multivariate Analysis: Theory and Practice. The MIT Press, Cambridge.

    Google Scholar 

  • Cressie, N. & Read, T.R.C. (1984). Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society, Series B 46, 440–464.

    MathSciNet  MATH  Google Scholar 

  • Goodman, L.A. & Kruskal, W.H. (1954). Measures of association for cross classifications. Journal of the American Statistical Association 49, 732–764.

    MATH  Google Scholar 

  • Patil, G.P. & Taillie, C. (1982). Diversity as a concept and its measurement. Journal of the American Statistical Association 77, 548–561.

    Article  MathSciNet  Google Scholar 

  • Read, T.R.C. & Cressie, N. (1988). Goodness-of-Fit Statistics for Discrete Multivariate Data. Springer-Verlag, New York.

    Book  Google Scholar 

  • Theil, H. (1970). On the estimation of relationships involving qualitative variables. American Journal of Sociology 76, 103–154.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Information Sciences, Faculty of Science and Technology, Science University of Tokyo, Noda City, Chiba, 278, Japan

    Sadao Tomizawa, Takashi Seo & Masaki Ebi

Authors
  1. Sadao Tomizawa
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  2. Takashi Seo
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  3. Masaki Ebi
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Tomizawa, S., Seo, T. & Ebi, M. Generalized Proportional Reduction in Variation Measure for Two-Way Contingency Tables. Behaviormetrika 24, 193–201 (1997). https://doi.org/10.2333/bhmk.24.193

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  • DOI: https://doi.org/10.2333/bhmk.24.193

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