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Order Restricted Randomized Block Designs

Author

Listed:
  • Omer Ozturk

    (The Ohio State University)

  • Richard Jarrett

    (University of Adelaide, School of Agriculture, Food and Wine)

  • Olena Kravchuk

    (University of Adelaide, School of Agriculture, Food and Wine)

Abstract

Field experiments are run under two competing objectives, high precision and minimal cost. The precision can be increased either by using sound experimentation techniques that account for the sources of variation with reasonable statistical models or by increasing the sample size. Large sample sizes usually increase the cost of the experiment and may not be feasible. This paper uses order restricted randomized designs (ORRD) to increase the precision while keeping the sample size and cost of the experiment minimal. The ORRD described here starts with a randomized block design but adds a second layer of blocking by ranking plots within each block. This creates a two-way lay-out, blocks and ranking groups, and uses a restricted randomization to improve the precision of estimation of the treatment parameters. Ranking groups create a correlation structure for within-block units. The restricted randomization uses this correlation structure to reduce the error variance of the experiment. The paper computes the expected mean square for each source of variation in the ORRD design under a suitable linear model. It also provides approximate F-tests for treatment and ranking group effects. The efficiency of the ORRD is investigated through empirical power studies. Finally, an example based on a uniformity field trial illustrates the use of the method in a split-plot experiment. Supplementary material to this paper is provided online.

Suggested Citation

  • Omer Ozturk & Richard Jarrett & Olena Kravchuk, 2024. "Order Restricted Randomized Block Designs," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(4), pages 831-852, December.
    • Handle: RePEc:spr:jagbes:v:29:y:2024:i:4:d:10.1007_s13253-023-00590-x
    DOI: 10.1007/s13253-023-00590-x
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    References listed on IDEAS

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    1. Juan Du & Steven N. MacEachern, 2008. "Judgement Post-Stratification for Designed Experiments," Biometrics, The International Biometric Society, vol. 64(2), pages 345-354, June.
    2. Gwowen Shieh & Show‐Li Jan, 2004. "The effectiveness of randomized complete block design," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 111-124, February.
    3. Jinguo Gao & Omer Ozturk, 2017. "Rank regression in order restricted randomised designs," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 231-257, April.
    4. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
    5. Omer Ozturk & Steven MacEachern, 2004. "Order restricted randomized designs for control versus treatment comparison," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 701-720, December.
    Full references (including those not matched with items on IDEAS)

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