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Monte Carlo Exact Tests for Square Contingency Tables

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  • Peter W. F. Smith
  • Jonathan J. Forster
  • John W. McDonald

Abstract

Square contingency tables arise frequently in social research. Typically, many of the off‐diagonal cell counts are small because of the social processes involved. This causes concern about the validity of using asymptotic tests and an exact test should be considered. We develop Markov chain Monte Carlo methods for estimating the exact conditional p‐value for various complex log‐linear models that are useful for the analysis of square contingency tables. These methods are used to analyse a sparse 8×8 intermarriage table.

Suggested Citation

  • Peter W. F. Smith & Jonathan J. Forster & John W. McDonald, 1996. "Monte Carlo Exact Tests for Square Contingency Tables," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(2), pages 309-321, March.
    • Handle: RePEc:bla:jorssa:v:159:y:1996:i:2:p:309-321
    DOI: 10.2307/2983177
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    Cited by:

    1. Fabio Rapallo, 2005. "Algebraic exact inference for rater agreement models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(1), pages 45-66, February.
    2. Krzysztof Malik & Anna Jasińska-Biliczak, 2018. "Innovations and Other Processes as Identifiers of Contemporary Trends in the Sustainable Development of SMEs: The Case of Emerging Regional Economies," Sustainability, MDPI, vol. 10(5), pages 1-17, April.
    3. Satoshi Aoki & Akimichi Takemura, 2008. "Minimal invariant Markov basis for sampling contingency tables with fixed marginals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 229-256, June.
    4. Kim, Sung-Ho & Choi, Hyemi & Lee, Sangjin, 2009. "Estimate-based goodness-of-fit test for large sparse multinomial distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1122-1131, February.

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