On the design of experiments with ordered treatments

• 成果类型: Article
• 署名作者: Singh, Satya Prakash; Davidov, Ori
• 署名单位: University of Haifa
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12335
• 发表日期: 2019
• 页码: 881-900
• 关键词: likelihood ratio tests; power functions; inference; Maximin; set

摘要

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.