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On the design of experiments with ordered treatments
Author(s) -
Singh Satya Prakash,
Davidov Ori
Publication year - 2019
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12335
Subject(s) - context (archaeology) , sample size determination , computer science , design of experiments , order (exchange) , sample (material) , reduction (mathematics) , work (physics) , power (physics) , mathematics , statistics , engineering , mechanical engineering , paleontology , chemistry , geometry , physics , finance , chromatography , quantum mechanics , economics , biology
Summary 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.