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When an underlying logit based order dose-response model is considered withsmall or moderate sample sizes, the Cochran-Armitage (CA) test represents themost efficient test in the framework of the test-statistics applied withasymptotic distributions for testing monotone proportions. The Wald andlikelihood ratio (LR) test have much worse behaviour in type error I incomparison with the CA test. It suffers, however, from the weakness of notmaintaining the nominal size. In this paper a family of test-statistics basedon {\phi}-divergence measures is proposed and their asymptotic distributionunder the null hypothesis is obtained either for one-sided or two-sidedhypothesis testing. A numerical example based on real data illustrates that theproposed test-statistics are simple for computation and moreover, the necessarygoodness-of-fit test-statistic are easily calculated from them. The simulationstudy shows that the test based on the Cressie and Read (Journal of the RoyalStatistical Society, Series B, 46, 440-464, 1989) divergence measure usuallyprovides a better nominal size than the CA test for small and moderate samplesizes.

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