Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 2, 198-214

ON TESTING DIAGONAL HOMOGENEITY WITH A ONE-SIDED ALTERNATIVE IN THE ANALYSIS OF VARIANCE

By

BHASKAR BHATTACHARYA, Southern Illinois University, Carbondale

SUMMARY. We consider a two-factor experiment where the factors have the same levels with a natural ordering among the levels. We test the hypothesis that the effects of the treatment combinations at a distance of t over the main diagonal are the same as the effects of the treatment combinations at a distance of t below the main diagonal against a one-sided alternative using the likelihood criteria. Test of the one-sided alternative as a null hypothesis against no restrictions has also been studied. Exact distribution theory under the null hypothesis is derived and is shown to be a weighted mixture of chi-square distributions. An example is used to illustrate the procedure.

 

AMS (1991) subject classification. 62F03, 62E15, 62J10.

Key words and phrases. Antitonic regression, chi-bar square distribution, convex duality, likelihood ratio test, two factor experiment.

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