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Families of A-optimal block designs for comparing test treatments with a control. (English) Zbl 0586.62113

Authors’ abstract: A-optimal designs for comparing each of \(\nu\) test treatments simultaneously with a control, in b blocks of size k each are considered. It is shown that several families of BIB designs in the test treatments augmented by t replications of a control in each block are A- optimal.
In particular these designs with \(t=1\) are optimal whenever \((k-2)^ 2+1\leq \nu \leq (k-1)^ 2\) irrespective of the number of blocks. This includes BIB designs associated with finite projective and Euclidean geometries.
Reviewer: A.C.Tamhane

MSC:

62K05 Optimal statistical designs
62K10 Statistical block designs
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