On the design of experiments with ordered treatments
针对实验组或处理间存在顺序的情况，提出两类最优实验设计，用于检验不同假设，能显著提高统计功效或减少所需样本量。
There are many situations where one expects an ordering among K⩾2 experimental groups or treatments. Although there is a large body of literature dealing with the analysis under order restrictions, surprisingly, very little work has been done in the context of the design of experiments. Here, a principled approach to the design of experiments with ordered treatments is provided. In particular we propose two classes of designs which are optimal for testing different types of hypotheses. The theoretical findings are supplemented with thorough numerical experimentation and a concrete data example. It is shown that there is a substantial gain in power, or alternatively a reduction in the required sample size, when an experiment is both designed and analysed by using methods which account for order restrictions.