Blocked factor aliased effect-number pattern and column rank of blocked regular designs |
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Authors: | Dongying Wang Shili Ye Qi Zhou Runchu Zhang |
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Institution: | 1.KLAS and School of Mathematics and Statistics,Northeast Normal University,Changchun,China;2.LPMC and School of Mathematical Sciences,Nankai University,Tianjin,China;3.Department of Statistics,Tianjin University of Finance and Economics,Tianjin,China;4.Department of Statistics,University of British Columbia,Vancouver,Canada |
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Abstract: | In factorial experiments, estimation precision of specific factor effects depends not only on design selection but also on factor assignments to columns of selected designs. Usually, different columns in a design play different roles when estimating factor effects. Zhou et al. (Can J Stat 41:540-555, 2013) introduced a factor aliased effect-number pattern (F-AENP) and proposed a column ranking scheme for all the GMC \(2^{n-m}\) designs with \(5N/16+1\le n\le N-1\), where \(N=2^{n-m}\). In this paper, we first introduce a blocked factor aliased effect-number pattern (B-F-AENP) for blocked regular designs as an extension of the F-AENP. Then, by using the B-F-AENP, we propose a column ranking scheme for all the B\(^1\)-GMC \(2^{n-m}:2^s\) designs with \(5N/16+1\le n\le N-1\), as well as an assignment strategy for important factors. |
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