Lower-order confounding information of inverse Yates-order two-level designs

Abstract

Based on the effect hierarchy principle, a good design should minimize the confounding among the lower-order effects. Thus, it is important to obtain the confounding information of effects of a design. This paper analyzes the aliased pattern of two-level designs and obtains the confounding information among lower-order effects for a class of two-level designs, called inverse Yates-order (IYO) designs. The expressions of confounding among lower-order effects are obtained. Some examples are provided to illustrate these results. The important elements in classification patterns of some IYO designs under some optimality criteria are tabulated.

Keywords:

• Aliased effect-number pattern
• lower-order confounding
• inverse Yates-order (IYO) design

Mathematics Subject Classification:

• 62K15
• 62K05

Acknowledgments

We would like to thank the two referees for their insightful comments which lead to a significant improvement of the paper. This work was supported by the Natural Science Foundation of China (Grant Nos. 11661076, 11771250) and the Science and Technology Project Foundation of Xinjiang Uygur Autonomous Region (Grant No. 2016D01C043).

Funding

This work was supported by the Natural Science Foundation of China (Grant Nos. 11661076, 11771250) and the Science and Technology Project Foundation of Xinjiang Uygur Autonomous Region (Grant No. 2016D01C043).