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Summary Modifications of the logit and likelihood-ratio methods of analysing two-and three-dimensional contingency tables are developed from a semi-empirical approximation to the multinomial distribution. The modified likelihood-ratio test is shown to have an approximate relationship to the Freeman and Halton (1951) criterion for choosing a critical region for the exact test. A Bayesian argument leading to the same results is discussed.
John J. Gart (Sat,) studied this question.