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Exact Conditional Tests of Quasi‐Independence for Triangular Contingency Tables: Estimating Attained Significance Levels

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  • J. W. McDonald
  • P. W. F. Smith

Abstract

Some investigations of whether disease is related to birth order result in a triangular table of counts of diseased individuals classified by birth order and sibship size. Here testing for an interaction corresponds to testing for quasi‐independence of the classification factors. We propose a Monte Carlo algorithm for estimating the significance level of this test, which should be used when the asymptotic results are suspect. We describe the procedure by using a classic triangular table classifying stroke patients. Unlike other researchers, we conclude that there is moderate evidence for rejecting quasi‐independence here. Our main application concerns the relationship between neurosis and birth order. Here there is strong evidence for rejecting quasi‐independence in favour of the uniform association model.

Suggested Citation

  • J. W. McDonald & P. W. F. Smith, 1995. "Exact Conditional Tests of Quasi‐Independence for Triangular Contingency Tables: Estimating Attained Significance Levels," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(2), pages 143-151, June.
    • Handle: RePEc:bla:jorssc:v:44:y:1995:i:2:p:143-151
    DOI: 10.2307/2986340
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