Optimal designs for asymmetrical factorial paired comparison experiments
- 1 January 1994
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Simulation and Computation
- Vol. 23 (3) , 663-681
- https://doi.org/10.1080/03610919408813192
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 H0 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 λ2 of the asymptotic noncentral chi-square distribution of the likelihood ratiostatistic -2 log λ for testing Ho under defined local alternatives. These results apply directly to symmetrical factorial paired comparison experiments as special casesExamples are given forillustrating applications of the developed resultsKeywords
This publication has 6 references indexed in Scilit:
- Optimal design results for 2nfactorial paired comparison experimentsCommunications in Statistics - Theory and Methods, 1984
- Treatment Contrasts in Paired Comparisons: Large-Sample Results, Applications, and Some Optimal DesignsJournal of the American Statistical Association, 1978
- Treatment contrasts in paired comparisons: convergence of a basic iterative scheme for estimationCommunications in Statistics - Theory and Methods, 1977
- Treatment contrasts in paired comparisons: Basic procedures with application to factorialsBiometrika, 1976
- Rank Analysis of Incomplete Block Designs: A Method of Paired Comparisons Employing Unequal Repetitions on PairsBiometrics, 1960
- A 2 X 2 Factorial with Paired ComparisonsBiometrics, 1954