Efficient designs for one-sided comparisons of two or three treatments with a control in a one-way layout

The problem of providing lower confidence bounds for the mean improvements of p ≥ 2 test treatments over a control treatment is considered. The expected average and expected maximum allowances are two criteria for comparing different systems of confidence intervals or bounds. In this paper, lower bounds are derived for the expected average allowance and the expected maximum allowance of Dunnett’s simultaneous lower confidence bounds for the p mean improvements. These lower bounds hold for any p ≥ 2 and any allocation of sample sizes. For p = 2 test treatments, sample allocations are given for which the bounds are achievable. For p = 3 test treatments, a tighter set of bounds is derived which enables easy determination of the sample allocation to achieve highly efficient designs. A table of the bounds for the expected average and expected maximum allowances and the sample allocation that achieves these bounds is given for p = 2, 3. The theoretical results can easily be adapted to cover upper confidence bounds. Some key words: Control treatment; Dunnett’s critical values; Expected average allowance; Expected maximum allowance; Multiple comparisons; One-way layout; Optimal design