Optimal design results for 2ⁿ factorial paired comparison experiments

Abstract

Four general classes of partially balanced designs for 2ⁿ factorials, corresponding to four different forms of a general null hypothesis H on factorial effects, are presented. For the typical design in each class, the simplified form of the non-centrality parameter λ² of the asymptotic chi-square distribution of the likelihood ratio statistic for testing the corresponding form of H₀ is derived under defined local alternatives. Optimal designs d₁ maximizing λ² in the i-th class and minimizing the trace, determinant and largest eigenvalue of a defined covariance matrix, i =1,…,4, are determined.

Keywords:

• paired comparisons
• factorial treatments
• hypothes on factorial effects
• treatment contracts
• non-centrality parameter
• optimal designs