Pardo Llorente, LeandroMenéndez Calleja, María LuisaBalakrishnan, N.Castillo, EnriqueSarabia, José Maria2023-06-202023-06-202006Armitage, P. (1955). Tests for linear trends in proportions and frequencies, Biometrics 11, 375–386. Ayer, M., Brunk, H. O., Ewing, G. M., Reid, W. I., and Silverman, E. (1955). An empirical distribution function for sampling with incomplete information, Annals of Mathematical Statistics, 26, 641–647. Barlow, R. E., Bartholomew, D. J., Bremmer, J. M., and Brunk, H. D. (1972). Statistical Inference Under Order Restrictions, John Wiley_& Sons, New York. Cressie, N., and Read, T. R. C. (1984). Multinomial goodness-of-fit tests, Journal of the Royal Statistical Society, Series B, 46, 440–464. Grove, D. M. (1980). A test of independence against a class of ordered alternatives in a 2×C contingency table, Journal of the American Statistical Association, 75, 454–459. Lee, M. T. (1989). Some cross-product difference statistics and a test for trends in ordered contingency tables, Statistics_& Probability Letters, 7, 41–46. Menéndez, M. L., Pardo, L., and K. Zografos (2002). Tests of hypotheses for and against order restrictions on multinomial parameters based on φ-divergences, Utilitas Mathematica, 61, 209–223. Menéndez, M. L., Pardo, J. A., and Pardo, L. (2003a). Tests for bivariate symmetry against ordered alternatives in square contingency tables. Australian and New Zealand Journal of Statistics, 45, 1, 115–124. Menéndez, M. L., Morales, D., and Pardo, L. (2003b). Tests based on divergences for against ordered alternatives in cubic contingency tables, Applied Mathematics and Computation, 134, 207–216. Park, C. G. (1998). Testing for unimodal dependence in an ordered contingency table with restricted marginal probabilities, Statistics_& Probability Letters, 37, 121–129. Park, C. G. (2002). Testing for ordered trends of binary responses between contingency tables, Journal of Multivariate Analysis, 81, 229–241. Patefield, W. M. (1982). Exact tests for trends in ordered contingency tables, Applied Statistics, 31, 32–43. Robertson, T., and Wright, F. T. (1983). On approximation of the level probabilities and associated distributions in order restricted inference, Biometrika, 70, 597–606. Robertson, T., Wright, F. T., and Dykstra, R. L. (1988). Order-Restricted Statistical Inference, John Wiley_& Sons, New York.978-0-8176-4361-410.1007/0-8176-4487-3_27https://hdl.handle.net/20.500.14352/53187International Conference on Distribution Theory, Order Statistics, and Inference Location: Univ Cantabria, Santander, SPAIN, JUN 16-18, 2004In this chapter, we consider 2 x k contingency tables and derive a new family of test statistics for detecting positive dependence in them. The family of test statistics introduced here is based on the phi-divergence measures of which the likelihood ratio test is a special case.book parthttp://link.springer.com/chapter/10.1007%2F0-8176-4487-3_27http://link.springer.com/metadata only access519.21asymptotic distributionslikelihood ratio testphi-divergence test statistics2 x k contingency tablesordered-alternativesprobabilitiestrendsEstadística aplicada