Abstract
Two-factor experiments in which both factors are ordinal are considered. If it is believedapriori 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 thep-values from a test concerning the rows and a test concerning the columns is studied. Fisher's method of combiningp-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.
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This research was supported by the National Institutes of Health under Grant 1R01GM42584-01. Part of this work is taken from the first author's dissertation submitted in partial fulfillment for the Ph.D. degree at the University of Missouri-Columbia.
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Moonesinghe, R., Wright, F.T. Testing homogeneity with an ordered alternative in a two-factor layout by combiningp-values. Ann Inst Stat Math 47, 505–523 (1995). https://doi.org/10.1007/BF00773399
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DOI: https://doi.org/10.1007/BF00773399