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On the testing of marginal homogeneity with a one-sided alternative in the analysis of variance |
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| Authors: | Chu-In Charles Lee Tim Robertson F T Wright |
| Institution: | (1) Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7 St. John's, Newfoundland, Canada;(2) Department of Statistics and Actuarial Science, University of Iowa, 52242 Iowa City, IA, U.S.A.;(3) Department of Mathematics and Statistics, University of Missouri-Rolla, 65401 Rolla, MO, U.S.A. |
| Abstract: | We consider a two-factor experiment in which the factors have the same levels with a natural ordering among the levels. Likelihood ratio tests for testing equality of the main effects with a one-sided alternative and for testing the one-sided hypothesis as a null hypothesis are studied. Closed form expressions for the maximum likelihood estimates under the various hypotheses are obtained. The null hypothesis distributions for these test statistics are derived.The efforts of the first author were supported by the NSERC of Canada. The efforts of the second author were supported by the Office of Naval Research under Contract ONR N00014-80-C-0321. The efforts of the third author were supported by the Office of Naval Research under Contract ONR N00014-80-C-0322. |
| Keywords: | Chi-bar-squared distributions convex duality isotonic regression likelihood ratio tests one-sided hypotheses order restricted inference two-factor designs |
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