Sample Size Allocation for Simultaneous Inference in Comparison with Control Experiments
研究了在比较多个处理与对照的实验中，如何最优分配样本量以最小化同时置信区间的平均允许宽度，提供了最优设计表格。
Abstract A common experiment is to compare p ≥ 2 test treatments with a control in a one-way layout. The object of the experiment can be to establish which test treatments are statistically significantly different from or better than the control or to give simultaneous confidence bounds on the amount of improvement that each of the test treatments offers over the control. Frequently, further experimentation is done with the promising treatments. We consider the problem of optimal allocation of a small to moderate number of observations to treatments in this setting under the assumption of normality with equal variances. The criterion of minimizing the average expected allowance of the simultaneous 95% confidence bounds for the p contrasts between the individual test treatment means and the control mean is used. Dunnett (1955) gave an asymptotic result for the optimal allocation under the assumption of equal test treatment sample sizes. We give tables of optimal designs under the restriction of equal test treatment sample sizes and under the restriction that the test treatment sample sizes differ by at most 1. Considerable tightening of the average allowance can be achieved in some cases by allowing the test treatment sample sizes to differ by 1.