An efficient asymptotic approach for testing monotone proportions assuming an underlying logit based order dose-response model

When an underlying logit based order dose-response model is considered with small or moderate sample sizes, the Cochran-Armitage (CA) test represents the most efficient test in the framework of the test-statistics applied with asymptotic distributions for testing monotone proportions. The Wald and likelihood ratio (LR) test have much worse behaviour in type error I in comparison with the CA test. It suffers, however, from the weakness of not maintaining the nominal size. In this paper a family of test-statistics based on ϕ-divergence measures is proposed and their asymptotic distribution under the null hypothesis is obtained either for one-sided or two-sided hypothesis testing. A numerical example based on real data illustrates that the proposed test-statistics are simple for computation and moreover, the necessary goodness-of-fit test-statistic are easily calculated from them. The simulation study shows that the test based on the Cressie and Read (Journal of the Royal Statistical Society, Series B, 46, 440-464, 1989) divergence measure usually provides a better nominal size than the CA test for small and moderate sample sizes.

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