EXACT CONDITIONAL TESTS OF QUASI-INDEPENDENCE FOR TRIANGULAR CONTINGENCY-TABLES - ESTIMATING ATTAINED SIGNIFICANCE LEVELS

Some investigations of whether disease is related to birth order resul t in a triangular table of counts of diseased individuals classified b y birth order and sibship size. Here testing for an interaction corres ponds to testing for quasi-independence of the classification factors. We propose a Monte Carlo algorithm for estimating the significance le vel of this test, which should be used when the asymptotic results are suspect. We describe the procedure by using a classic triangular tabl e classifying stroke patients. Unlike other researchers, we conclude t hat there is moderate evidence for rejecting quasi-independence here. Our main application concerns the relationship between neurosis and bi rth order. Here there is strong evidence for rejecting quasi-independe nce in favour of the uniform association model.