On the design of experiments with ordered treatments

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2019 · Volume 81 · Issue 5

Abstract

There are many situations where one expects an ordering amongK⩾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.

Keywords

Intersection–union tests, Least favourable configuration, Likelihood ratio test, Maxi-min designs, Non-centrality parameter, Order restricted inference, Power

Enable JavaScript for citation tools and additional paper interactions.