Efficiency of block designs for simultaneous comparison of two test treatments with a control

In an experiment for comparing two test treatments with a control treatment, simultaneous confidence bounds for the amount by which each test treatment differs from the control is generally required. When the experiment is arranged as a block design, the optimal allocation of experimental units within the blocks to the individual test treatments and to the control needs to be determined. The optimality criterion of interest is the minimization of the expected average allowance (EAA) or the expected maximum allowance (EMA), where an allowance represents the “plus and/or minus” attached to point estimates and is the product of a standard error and the critical value. Lower bounds for the EAA and EMA values are provided for both one-sided and two-sided confidence intervals. A search algorithm for obtaining efficient designs is described.