The defenders of randomisation point to the long run properties that randomisation underwrites. The critics argue that a long-run average is not relevant to the case in hand. Here I argue that both are right in a sense. Randomisation permits one to use the distribution in probability of the effects of covariates one has not seen but this distribution is not relevant for those one has. However, conditional inferences are embedded within marginal ones. Thus, although the latter should not be substituted for the former, the former are unlikely to be right if the latter are wrong. Randomisation is valuable for what we don’t see and don’t know. It should not be used as an excuse for ignoring what we do. I shall claim that randomisation does not solve all problems but doing better is harder than many suppose.
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Stephen Senn, Consultant Statistician University of Sheffield, Medical University of Vienna and University of St. Andrews
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