Block Designs for Comparison of Two Test Treatments with a Control
In an experiment to compare p = 2 test treatments with a control, simultaneous confidence bounds (or intervals) for the amount by which each test treatment is better than (or differs from) the control are required. When an experiment is arranged in b blocks of size k, the optimal allocation of a fixed number of experimental units to the individual test treatments and the control within each block need to be determined. The optimality criteria of interest are the minimization of the expected average allowance (EAA) or the minimization of the expected maximum allowance (EMA) of the simultaneous confidence bounds for the p = 2 treatment-control mean contrasts. This paper provides bounds on the EAA and EMA which are then used in search algorithms for obtaining optimal or highly efficient experimental design solutions.
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