Optimal Experimentation in Two Blocks

Faced with cost, time, or other pressures to keep an experiment small, blocking can be an effective tool for increasing precision of treatment comparisons. The simplest implementation of blocking is a division of experimental units into two equi-sized subsets, allocating one degree of freedom to explain unit heterogeneity. Small experiments will have block size k smaller than the number of treatments v being compared. This paper solves the problem of optimal allocation of treatments to two small, equi-sized blocks. The solution depends on the optimality criterion employed as well as the ratio kv . Some key words and phrases: Binary Design, incomplete block design, A-optimality, D-optimality, E-optimality.