Journal
BIOMETRIKA
Volume -, Issue -, Pages -Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asac046
Keywords
Confounding; Factorial design; Interaction; Row-column design
Funding
- National Natural Science Foundation of China
- Natural Science Foundation of Tianjin
- LPMC
- KLMDASR
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In this study, a theoretical framework is established to evaluate the optimality of row-column designs with prime level, and a method is proposed to construct optimal row-column designs with prime level, providing unconfounded estimation of all main effects and as many interactions as possible. Additionally, optimal full factorial three-level row-column designs are constructed for any parameter combination, and optimal fractional factorial two-level and three-level row-column designs are constructed for cost saving.
Row-column designs have been widely used in experiments involving double confounding. Among them, one that provides unconfounded estimation of all main effects and as many two-factor interactions as possible is preferred, and is called optimal. Most current work focuses on the construction of two-level row-column designs, while the corresponding optimality theory has been largely ignored. Moreover, most constructed designs contain at least one replicate of a full factorial design, which is not flexible as the number of factors increases. In this study, a theoretical framework is built up to evaluate the optimality of row-column designs with prime level. A method for constructing optimal row-column designs with prime level is proposed. Subsequently, optimal full factorial three-level row-column designs are constructed for any parameter combination. Optimal fractional factorial two-level and three-level row-column designs are also constructed for cost saving.
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