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Randomization in the Design of Experiments

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  • D. R. Cox

Abstract

A general review is given of the role of randomization in experimental design. Three objectives are distinguished, the avoidance of bias, the establishment of a secure base for the estimation of error in traditional designs, and the provision of formally exact tests of significance and confidence limits. The approximate randomization theory associated with analysis of covariance is outlined and conditionality considerations are used to explain the limited role of randomization in experiments with very small numbers of experimental units. The relation between the so‐called design‐based and model‐based analyses is discussed. Corresponding results in sampling theory are mentioned briefly. On passe en revue le rôle du traitement aléatoire dans la conception d'expériences. On distingue trois objectifs, la prévention de biais, la constitution d'une base solide pour l'estimation d'erreur dans les conceptions traditionnelles et la fourniture de tests formellement exacts de signification et de limites de confiance. La théorie du traitement aléatoire approximatif associéà l'analyse de covariance est présentée et des considérations de conditionnalité sont utilisées pour expliquer le rôle limité du traitement aléatoire dans les expériences avec de tròs petits nombres d'unités expérimentales. La relation entre les analyses dites à base de conception et à base de modòle est discutée. Les résultats correspondants dans la théorie des sondages sont briòvement mentionnés.

Suggested Citation

  • D. R. Cox, 2009. "Randomization in the Design of Experiments," International Statistical Review, International Statistical Institute, vol. 77(3), pages 415-429, December.
    • Handle: RePEc:bla:istatr:v:77:y:2009:i:3:p:415-429
    DOI: 10.1111/j.1751-5823.2009.00084.x
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    References listed on IDEAS

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    1. Jean-François Beaumont, 2008. "A new approach to weighting and inference in sample surveys," Biometrika, Biometrika Trust, vol. 95(3), pages 539-553.
    2. Anthony C. Atkinson, 2002. "The comparison of designs for sequential clinical trials with covariate information," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(2), pages 349-373, June.
    3. 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.
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    Cited by:

    1. Kari Lock Morgan & Donald B. Rubin, 2015. "Rerandomization to Balance Tiers of Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1412-1421, December.
    2. Jesse Hemerik & Jelle J. Goeman, 2021. "Another Look at the Lady Tasting Tea and Differences Between Permutation Tests and Randomisation Tests," International Statistical Review, International Statistical Institute, vol. 89(2), pages 367-381, August.
    3. Pashley Nicole E. & Basse Guillaume W. & Miratrix Luke W., 2021. "Conditional as-if analyses in randomized experiments," Journal of Causal Inference, De Gruyter, vol. 9(1), pages 264-284, January.
    4. Elena Pesce & Fabio Rapallo & Eva Riccomagno & Henry P. Wynn, 2023. "Generation of all randomizations using circuits," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 683-704, August.
    5. 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.
    6. Zhenzhen Xu & John D. Kalbfleisch, 2013. "Repeated Randomization and Matching in Multi-Arm Trials," Biometrics, The International Biometric Society, vol. 69(4), pages 949-959, December.

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