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

Some investigations of whether disease is related to birth order result in a triangual table of counts of diseased individuals classified by birth and sibshpi size. Here testing for an interaction corresponds to tesing for quasi-independence of the classification factions. 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 conculdue that there is moderate evidence for rejecting quasi-independece 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 assoction model.