Randomization in the Design of Experiments

D. R. Cox

International Statistical Review, 2009, vol. 77, issue 3, 415-429

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.

Date: 2009
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