Abstract
Li et al. (Comm Statist Theory Methods 49: 924–941, 2020) introduced the concept of inverse Yates-order (IYO) designs, and obtained most of two-level IYO designs have general minimum lower-order confounding (GMC) property. For this reason, the paper extends two-level IYO designs to three-level cases. We first propose the definition of \(3^{n-m}\) IYO design \(D_q(n)\) from the saturated design \(H_q\) with three levels. Then, the formulas of lower-order confounding are obtained according to the factor number of \(3^{n-m}\) IYO design: (i) \(q<n<3^{q-1}\), and (ii) \(3^{q-1}\le n\le (N-1)/2\), where \(N=3^{n-m}\). Under case (ii), we obtain the explicit expressions of lower-order confounding for four structure types of IYO designs. Some examples are given to illustrate the theoretical results. Compared with GMC designs, three-level IYO designs with 27- and 81-run are tabulated to show that some of them have GMC property through lower-order confounding.
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Acknowledgements
We are grateful to the editor and two referees for their insightful comments and constructive suggestions. The work was supported by the National Natural Science Foundation of China (12061070), and the Natural Science Foundation of Xinjiang Uygur Autonomous Region (2021D01E13).
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Huang, Z., Li, Z., Zhang, G. et al. Lower-order confounding information of inverse Yates-order designs with three levels. Metrika 86, 239–259 (2023). https://doi.org/10.1007/s00184-022-00876-z
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DOI: https://doi.org/10.1007/s00184-022-00876-z