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Asymmetrical split-plot designs with clear effects

Author

Listed:
  • Xiaoxue Han

    (Nankai University)

  • Jianbin Chen

    (Nankai University)

  • Min-Qian Liu

    (Nankai University)

  • Shengli Zhao

    (Qufu Normal University)

Abstract

The fractional factorial split-plot (FFSP) design is an important experimental design both in theory and in practice. There is extensive literature on the two-level FFSP design and its various variants. However, there is little work on the s-level FFSP design and its variants in the asymmetrical (i.e., mixed-level) case, where s is any prime or prime power. Such designs are commonly used e.g. in agriculture, medicine and chemistry. This paper provides the necessary and sufficient conditions for the existence of resolution III or IV regular $$s^{(n_1+n_2)-(k_1+k_2)}(s^r)$$ s ( n 1 + n 2 ) - ( k 1 + k 2 ) ( s r ) designs which contain clear main effects or two-factor interaction components. In particular, the sufficient conditions are proved through constructing the corresponding designs, and some examples are provided to illustrate the construction methods.

Suggested Citation

  • Xiaoxue Han & Jianbin Chen & Min-Qian Liu & Shengli Zhao, 2020. "Asymmetrical split-plot designs with clear effects," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 779-798, October.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:7:d:10.1007_s00184-019-00755-0
    DOI: 10.1007/s00184-019-00755-0
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    References listed on IDEAS

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    1. Eric Schoen, 1999. "Designing fractional two-level experiments with nested error structures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 495-508.
    2. S. Zhao & R. Zhang, 2008. "2 m 4 n designs with resolution III or IV containing clear two-factor interaction components," Statistical Papers, Springer, vol. 49(3), pages 441-454, July.
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