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We study optimal block designs for comparing a set of test treatments with acontrol treatment. We provide the class of all E-optimal approximate blockdesigns characterized by simple linear constraints. Employing thischaracterization, we obtain a class of E-optimal exact designs fortreatment-control comparisons for unequal block sizes. In the studied model, wejustify the use of E-optimality by providing a statistical interpretation forall E-optimal approximate designs and for the known classes of E-optimal exactdesigns. Moreover, we consider the R-optimality criterion, which minimizes thevolume of the rectangular confidence region based on the Bonferroni confidenceintervals. We show that all approximate A-optimal designs and a large class ofA-optimal exact designs for treatment-control comparisons are also R-optimal.This further reinforces the observation that A-optimal designs perform welleven for rectangular confidence regions.

E- and R-optimality of block designs for treatment-control comparisons