Optimal Incomplete Block Designs for Comparing Treatments with a Control

Abstract

The problem of finding optimal incomplete blocks designs for comparing $p$ test treatments with a control is studied. B.I.B. designs are found to be $D$-optimal. $A$- and $E$-optimal designs are also obtained. For a large class of functions $\phi$, conditions for a design to be $\phi$-optimal are found. Most of the optimal designs are certain types of B.T.I.B. designs, introduced by Bechhofer and Tamhane (1981), which are binary in test treatments.