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Optimal designs for \(2^k\) paired comparison experiments. (English) Zbl 0993.62061
Summary: We establish the form of the optimal paired comparison design when there are \(k\) attributes, each with two levels, for testing for main effects, for main effects and two factor interactions and for main effects and two and three factor interactions. In all cases we assume that all pairs with the same number of attributes different appear equally often. In this setting the \(D\)- and \(A\)- optimal designs for main effects are the foldover pairs and those for main effects and two factor interactions have pairs in which about half the attributes are different.

MSC:
62K05 Optimal statistical designs
62J15 Paired and multiple comparisons; multiple testing
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