  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 {\phi}-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.
