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Multiple randomizations

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  • C. J. Brien
  • R. A. Bailey

Abstract

Summary. Multitiered experiments are characterized by involving multiple randomizations, in a sense that we make explicit. We compare and contrast six types of multiple randomizations, using a wide range of examples, and discuss their use in designing experiments. We outline a system of describing the randomizations in terms of sets of objects, their associated tiers and the factor nesting, using randomization diagrams, which give a convenient and readily assimilated summary of an experiment's randomization. We also indicate how to formulate a randomization‐based mixed model for the analysis of data from such experiments.

Suggested Citation

  • C. J. Brien & R. A. Bailey, 2006. "Multiple randomizations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 571-609, September.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:4:p:571-609
    DOI: 10.1111/j.1467-9868.2006.00557.x
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    Cited by:

    1. D. R. Cox, 2009. "Randomization in the Design of Experiments," International Statistical Review, International Statistical Institute, vol. 77(3), pages 415-429, December.
    2. Bradley Jones & Peter Goos, 2009. "D-optimal design of split-split-plot experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 67-82.
    3. Clayton R. Forknall & Arūnas P. Verbyla & Yoni Nazarathy & Adel Yousif & Sarah Osama & Shirley H. Jones & Edward Kerr & Benjamin L. Schulz & Glen P. Fox & Alison M. Kelly, 2024. "Covariance Clustering: Modelling Covariance in Designed Experiments When the Number of Variables is Greater than Experimental Units," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(2), pages 232-256, June.
    4. Richard G. Jarrett & Katya Ruggiero, 2008. "Design and Analysis of Two-Phase Experiments for Gene Expression Microarrays—Part I," Biometrics, The International Biometric Society, vol. 64(1), pages 208-216, March.

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