Comparison of test vs. control treatments using distance optimality criterion

Abstract.

We consider the problem of comparison of one test treatment (τ₀) with a set of v control treatments (τ₁, τ₂, …, τ_v) using distance optimality [DS-optimality] criterion introduced by Sinha (1970) in some treatment-connected design settings. It turns out that the nature of DS-optimal designs is quite similar to that for the usual A−, D− and E− optimality criteria. However, the optimality problem is quite complicated in most situations. First we deal with the CRD model and derive DS-optimal allocations for a given set of treatments. The results are almost identical to the A-optimal allocations for such problems. Then we consider a block design set-up and examine the nature of DS-optimal designs. In the process, we introduce the method of weighted coverage probability and maximize the resulting expression to obtain an optimal design.