TESTING HOMOGENEITY WITH AN ORDERED ALTERNATIVE IN A TWO-FACTOR LAYOUT BY COMBINING p-VALUES

RAMAL MOONESINGHE^{1} AND F. T. WRIGHT^{2}

1National Research Council, 2101 Constitution Avenue, Washington, DC 20418, U.S.A. 2Department of Statistics, University of Missouri, Columbia, MO 65211, U.S.A.

(Received March 29, 1993; revised September 9, 1994)

Abstract. Two-factor experiments in which both factors are ordinal are considered. If it is believed apriori that the mean response is nondecreasing in each factor with the other held fixed, then one may test for a treatment effect by testing homogeneity with the appropriate ordered alternative. The likelihood ratio test has been developed in the literature, but the level probabilities needed to implement the test have only been determined in a few special cases by Monte Carlo techniques. A test obtained by combining the p-values from a test concerning the rows and a test concerning the columns is studied. Fisher’s method of combining p-values is recommended. It is shown that the likelihood ratio test is more powerful, but if one does not want to obtain Monte Carlo estimates of the level probabilities, then the procedure proposed here should be considered.

Key words and phrases: Bivariate trends, combining p-values, Fisher’s method, likelihood ratio tests, matrix ordering, order restricted tests, two-moment approximations.