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Weighted A-optimal block designs for comparing test treatments with controls with unequal precision. (English) Zbl 1127.62387
Summary: The problem of comparing \(w\) test treatments with \(u\) controls in \(b\) blocks of size \(k\) \((\leq w)\) each is considered. Conditions under which a design is weighted A-optimal for estimating test treatments vs. controls contrasts with unequal precision are derived, the weights being given according to the relative importance of the controls. A new class of designs, called generalised balanced treatment incomplete block (GBTIB) designs, has been introduced. A general method of construction of GBTIB designs for two controls is given. Catalogues of weighted A-optimal designs for two controls and weighted A-efficient GBTIB designs are given. A method of construction of GBTIB designs using resolvable balanced incomplete block designs has also been given and illustrated through an example.

MSC:
62K05 Optimal statistical designs
62K10 Statistical block designs
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