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

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.

Key Words:

• Paired comparisons
• Treatment contrasts
• Factorial treatments
• Asymptotic power
• Optimal design
• Taste testing