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**Optimal paired comparison designs for factorial experiments.**
*(English)*
Zbl 0614.62096

CWI Tracts, 31. Centrum voor Wiskunde en Informatica. Amsterdam: Mathematisch Centrum. II, 153 p. Dfl. 24.20 (1987).

This monograph is divided into five sections. Section 1 discusses some models and procedures for paired comparison experiments. Making the assumption of no differences in treatment, it is shown that an ordinary linear model can be applied for constructing optimal designs. In section 2 a general approach for the construction of D-optimal designs for paired comparisons is given. This approach assumes an underlying structure. It uses the equivalence of the D-criterion and the G-criterion, when adapted to the situation of paired comparisons. The concept of exact and discrete designs is introduced. The latter designs are useful in constructing optimal designs.

Section 3 deals with a factorial model with main effects and first-order interactions. Exact D-optimal designs are given both for the case of a hypersphere as experimental region and for the case of a hypercube as experimental region. Sections 4 and 5 deal with a quadratic model, in section 4 with a hypersphere as experimental region, in section 5 with a hypercube as experimental region. In both sections D-optimal designs are presented. Using these designs the author constructs exact designs with a high efficiency and with a relatively small number of pairs. The robustness of the discrete designs is also investigated.

Section 3 deals with a factorial model with main effects and first-order interactions. Exact D-optimal designs are given both for the case of a hypersphere as experimental region and for the case of a hypercube as experimental region. Sections 4 and 5 deal with a quadratic model, in section 4 with a hypersphere as experimental region, in section 5 with a hypercube as experimental region. In both sections D-optimal designs are presented. Using these designs the author constructs exact designs with a high efficiency and with a relatively small number of pairs. The robustness of the discrete designs is also investigated.

Reviewer: V.P.Gupta

### MSC:

62K05 | Optimal statistical designs |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62J15 | Paired and multiple comparisons; multiple testing |

62K15 | Factorial statistical designs |