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

Author

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  • Qianqian Zhao

    (Qufu Normal University)

  • Shengli Zhao

    (Qufu Normal University)

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.

Suggested Citation

  • Qianqian Zhao & Shengli Zhao, 2019. "Some results on two-level regular designs with multi block variables containing clear effects," Statistical Papers, Springer, vol. 60(5), pages 1569-1582, October.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0886-8
    DOI: 10.1007/s00362-017-0886-8
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    References listed on IDEAS

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    1. Agnieszka Łacka & Maria Kozłowska & Jan Kozłowski, 2009. "Some optimal block designs with nested rows and columns for research on alternative methods of limiting slug damage," Statistical Papers, Springer, vol. 50(4), pages 837-846, August.
    2. Sheng-Li Zhao & Peng-Fei Li, 2016. "Construction of minimum aberration blocked two-level regular factorial designs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 5028-5036, September.
    3. Shengli Zhao & Pengfei Li & Rohana Karunamuni, 2013. "Blocked two-level regular factorial designs with weak minimum aberration," Biometrika, Biometrika Trust, vol. 100(1), pages 249-253.
    4. Sheng-Li Zhao & Qing Sun, 2017. "On constructing general minimum lower order confounding two-level block designs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1261-1274, February.
    Full references (including those not matched with items on IDEAS)

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