Optimal Designs for Comparing Test Treatments with Controls

: The authors introduce the problem with an example. How should we design an experiment to compare 4 test treatments with a control, using 18 experimental units? As a statistical question we will not be able to answer it unless it is asked in a more precise manner. To begin with we need to postulate a model for the response observed upon application of a treatment, test treatment or control, to an experimental unit. This paper shall consider three possible models: 1) O-way elimination of heterogeneity model in which all experimental units are homogeneous before application of treatments; 2) 1-way elimination of heterogeneity model in which experimental units can be divided into several homogeneous blocks; and 3) 2-way elimination of heterogeneity model in which the experimental units can be conceptually arranged according to rows and columns.