Experimental Randomization and the Validity of Normal-Theory Inference

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Abstract
This article examines how randomization helps to validate model-based probability statements. The asymptotic validity of normal-theory tests for means in multivariate linear models is established under general conditions. Numerical results are presented showing how randomization provides a limited degree of robustness in small experiments. The conditional relevance of randomization is also discussed. Consider the following additive model for a comparative experiment: Y = θ + GU, where Y is a vector of responses, θ is a vector of treatment effects, U is a vector of unit effects, and G is a permutation representing the assignment of treatments to units. The vector GU is obtained by using G to permute the coordinates of U. It is assumed that θ is fixed and G and U are random and independent. The experimenter observes Y and G, but not θ or U, and chooses the distribution of G, that is, the randomization strategy. In this setup, three probabilities may be considered: conditional given G, conditional g...

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