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Treatment Contrasts in Paired Comparisons: Large-Sample Results, Applications, and Some Optimal Designs

Abdalla T. El-Helbawy and Ralph A. Bradley
Journal of the American Statistical Association
Vol. 73, No. 364 (Dec., 1978), pp. 831-839
DOI: 10.2307/2286289
Stable URL: http://www.jstor.org/stable/2286289
Page Count: 9
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Treatment Contrasts in Paired Comparisons: Large-Sample Results, Applications, and Some Optimal Designs
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Abstract

Treatment contrasts in paired comparison experiments are considered. Given that specified orthonormal treatment contrasts are null, remaining treatment parameters, orthonormal contrasts among them, and their logarithms are estimated. The estimators are shown to be consistent and, when suitably scaled and centered, to have distribution functions that are normal in the limit for large sample sizes. Hypothesis tests on treatment contrasts are obtained. The limiting distribution functions of related likelihood ratio tests are derived for defined local alternatives and their noncentrality parameters are shown. The theoretical results are applied to experiments with factorial treatment combinations and some optimal design results are obtained.

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