ON OPTIMAL BLOCK-DESIGNS FOR COMPARING A STANDARD TREATMENT TO TEST TREATMENTS

We consider the problem of comparing a standard treatment to test treatments in incomplete blocks. We seek designs that maximize the coverage probability P{tau(0) - tau(i) greater than or equal to tau(0) - tau(i) - d, i - 1,..., upsilon}, where upsilon is the number of test treatments, d is a positive constant, tau(0) - tau(i) is the difference in effect between the standard treatment and the i-th test treatment, and tau(0) - tau(i) is the best linear unbiased estimator of tau(0) - tau i. Computational results, assuming a multivariate normal distribution for the vector of observations, are presented for upsilon = 4, blocks of size 3 and various values of the number of blocks b. Optimal designs are identified within the class of group divisible treatment designs for b less than or equal to 25 and are compared to A-optimal designs over the same class of designs.