Some results on two-level regular designs with multi block variables containing clear effects

Qianqian Zhao () and Shengli Zhao ()
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Qianqian Zhao: Qufu Normal University
Shengli Zhao: Qufu Normal University

Statistical Papers, 2019, vol. 60, issue 5, No 7, 1569-1582

Abstract: Abstract In this paper, the idea of clear effects is extended to the case of blocked regular $$2^{n{-}m}$$ 2 n - m designs with multi block variables. Some necessary and sufficient conditions on the existence of clear treatment main effects and clear treatment two-factor interactions (2fi’s) in $$2^{n{-}m}:2^l$$ 2 n - m : 2 l designs with resolution III, IV $$^- $$ - and IV are obtained, where the notation $$2^{n-m}:2^l$$ 2 n - m : 2 l means that there are n treatment factors, m treatment defining words and l block variables. We discuss how to find $$2^{n-m}:2^l$$ 2 n - m : 2 l designs with the maximum number of clear 2fi’s with resolution III, IV $$^-$$ - or IV, and present some 16-, 32-, 64-run designs containing the maximum number of clear 2fi’s in tables.

Keywords: Clear effect; Multi block variables; Resolution; Two-factor interaction; 62K15; 62K05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00362-017-0886-8

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