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Nonresolvable Row–Column Designs with an Even Distribution of Treatment Replications

Author

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  • Hans-Peter Piepho

    (University of Hohenheim)

  • Emlyn R. Williams

    (Australian National University)

  • Volker Michel

    (Landesforschungsanstalt für Landwirtschaft und Fischerei Mecklenburg-Vorpommern)

Abstract

When generating experimental designs for field trials laid out on a rectangular grid of plots, it is useful to allow for blocking in both rows and columns. When the design is nonresolvable, randomized classical row–column designs may occasionally involve clustered placement of several replications of a treatment. In our experience, this feature prevents the more frequent use of these useful designs in practice. Practitioners often prefer a more even distribution of treatment replications. In this paper we illustrate how spatial variance–covariance structures can be used to achieve a more even distribution of treatment replications across the field and how such designs compare with classical row–column designs in terms of efficiency factors. We consider both equally and unequally replicated designs, including partially replicated designs. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Hans-Peter Piepho & Emlyn R. Williams & Volker Michel, 2016. "Nonresolvable Row–Column Designs with an Even Distribution of Treatment Replications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(2), pages 227-242, June.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:2:d:10.1007_s13253-015-0241-2
    DOI: 10.1007/s13253-015-0241-2
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    References listed on IDEAS

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    1. Júlio S. de S. Bueno Filho & Steven G. Gilmour, 2003. "Planning Incomplete Block Experiments When Treatments Are Genetically Related," Biometrics, The International Biometric Society, vol. 59(2), pages 375-381, June.
    2. E. R. Williams & J. A. John & D. Whitaker, 2006. "Construction of Resolvable Spatial Row–Column Designs," Biometrics, The International Biometric Society, vol. 62(1), pages 103-108, March.
    3. Agnes Herzberg & Richard Jarrett, 2007. "A-Optimal Block Designs with Additional Singly Replicated Treatments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 61-70.
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    Cited by:

    1. Emlyn R. Williams & Hans-Peter Piepho, 2018. "An Evaluation of Error Variance Bias in Spatial Designs," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 83-91, March.

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