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Homogeneity Tests for 2×2 Contingency Tables

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Interdisciplinary Bayesian Statistics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 118))

Abstract

Using the likelihood ratio statistic, we develop a significance index, called P-value, to test the hypothesis of homogeneity in 2×2 contingency tables. The P-value does not depend on asymptotic distributions, and is based on the elimination of the nuisance parameter. Therefore, we obtain the exact distribution of the likelihood ratio statistic in a way that is, moreover, compatible with the likelihood principle. For a better understanding of significance indices to test homogeneity, we perform a study comparing the P-value with some indices (likelihood ratio test (LRT), chi-square test) and with the full Bayesian significance test (FBST). This comparative study shows an interesting relation between all the analyzed indices, Bayesian and frequentist.

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Author information

Authors and Affiliations

  1. Federal University of Sao Carlos, Rod. Washington Luiz, km 235, Sao Carlos, SP, 13565-905, Brazil

    Natalia Oliveira, Marcio Diniz & Adriano Polpo

Authors
  1. Natalia Oliveira
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  2. Marcio Diniz
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  3. Adriano Polpo
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Corresponding author

Correspondence to Natalia Oliveira .

Editor information

Editors and Affiliations

  1. Federal University of Sao Carlos, Sao Carlos, Brazil

    Adriano Polpo

  2. University of Sao Paulo, Sao Carlos, Brazil

    Francisco Louzada

  3. Campinas State University, Campinas, Brazil

    Laura L. R. Rifo

  4. Dept. of Applied Mathematics, University of Sao Paulo Institute of Mathematics and Statistics, Sao Paulo, São Paulo, Brazil

    Julio M. Stern

  5. School of Arts, Sciences and Humanities, University of Sao Paulo, Sao Paulo, São Paulo, Brazil

    Marcelo Lauretto

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Oliveira, N., Diniz, M., Polpo, A. (2015). Homogeneity Tests for 2×2 Contingency Tables. In: Polpo, A., Louzada, F., Rifo, L., Stern, J., Lauretto, M. (eds) Interdisciplinary Bayesian Statistics. Springer Proceedings in Mathematics & Statistics, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-12454-4_13

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