Monte Carlo Exact Methods Used for Analysing Interethnic Unions in Great Britain

Peter W. F. Smith, John W. McDonald, Jonathan J. Forster and Ann M. Berrington

Journal of the Royal Statistical Society Series C, 1996, vol. 45, issue 2, 191-202

Abstract: In the analysis of symmetric intermarriage and social mobility tables, interest is focused on the models of quasi‐independence and quasi‐symmetry for the off‐diagonal cells. Typically, many of the off‐diagonal cell counts are small. This causes concern about the validity of using asymptotic tests, and exact tests should be considered. We develop Markov chain Monte Carlo methods for estimating the exact conditional p‐value and the exact distribution of the residuals, for quasi‐independence and quasi‐symmetry. These methods are used to analyse a sparse 10 × 10 symmetric table of interethnic unions, extracted from the 1% household sample of anonymized records from the 1991 UK census. With the exception of Pakistani/White and Other Asian/White unions, there is no evidence against quasi‐symmetry. We conclude that, with these exceptions, there are no gender differences in the affinities between ethnic groups.

Date: 1996
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