Weighted A-optimal block designs for comparing test treatments with controls with unequal precision

Abstract

The problem of comparing w test treatments with u controls in b blocks of size k(⩽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.