Abstract
Three forms of a general null hypothesis Ho on the factorial parameters of a general asymmetrical factorial paired comparison experiment are considered. A class of partially balanced designscorresponding to each form of H
0
is constructed and the A,D and ioptimal design, minimizing the trace, determinant and largest eigenvalue of a defined covariance matrix of related maximumlikelihoodestimators, in that class is determined. Moreover, the optimal design in each class maximizes the noncentrality parameter λ
2
of the asymptotic noncentral chi-square distribution of the likelihood ratiostatistic -2 log λ for testing H
o
under defined local alternatives. These results apply directly to symmetrical factorial paired comparison experiments as special casesExamples are given forillustrating applications of the developed results