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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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##### References:
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