OPTIMAL DESIGNS FOR COMPARING SEVERAL TREATMENTS WITH A CONTROL IN THE PRESENCE OF EXPLANATORY VARIABLES

We consider an experiment with blocks of equal size involving some qua litative treatments, one of which is a control treatment, and some con trolled explanatory variables that can vary only from one block to ano ther. The assumed model includes interactions between treatments and e xplanatory variables. The objective of the experiment is to compare th e mean responses of the treatments with the mean response of the contr ol for all possible values of the explanatory variables. First, condit ions for a design to be optimal are established in the set-up of exact design theory. Then, the construction of designs that satisfy these c onditions is studied. Conditions for a design to be optimal under seve ral models are also given. Finally, an example is presented.