LAUSR

The first of these two features, feature (i), is rich with an important set of familiar statistical consequences. For one, consider experiments involving a psycho-physical effect that may be a voluntary response by the experimental subject. Fisher's thought experiment (1935, chapter 2) of the Lady Tasting Tea, where she chooses which four cups out of eight to identify as milk first rather than tea first, provides an instance. The properly randomized allocation of the two treatments among eight cups, with four cups prepared each way, removes a worrisome alternative, an alternative explanation that might otherwise be conflated with her professed claim that she has an ability to discriminate tea-milk infusions prepared milk first versus tea first. If, instead of a randomized allocation, the determination among the eight cups of which four are prepared milk first is a result of the experimenter's personal decision, then the subject's pattern of responses might be the result of her (possibly subconscious) ability to anticipate the experimenter's subjective allocation rule, even if she lacks the ability to identify milk-first infusion from tea-first infusions. See, eg, the work of Ross and Levy2 about studies of systematic predictable failures in human judgment concerning random sequences. However, with a properly randomized allocation, this alternative explanation for the Lady's responses is excluded. As a second example of the importance of feature (i), the statistical independence of treatments from other potential causes of the Lady's responses that is assured by randomization serves, in the language of contemporary causal statistical inference,3 to make the treatments an intervention, thereby justifying conclusions about the causes for the Lady's behavior. That is, feature (i) of an RCT underwrites inference about causal relations among variables, not merely prediction of variables. To their credit, it is the relatively less familiar second feature of randomization, feature (ii), that is the authors' focus in section 2 of their article, Randomization as a Basis for Inference. In addition, this feature of randomization also is the focus of my contribution to this discussion. As the authors make clear, when there is a large well-defined statistical population from which one may sample, then randomization affords the basis for an assumption that the observed sample is (approximately) iid. However, the authors are right to point out that in clinical trials there is no evident well-defined (hypothetically infinite) statistical population from which the subjects have been randomly sampled. They emphasize that, instead, there is only the finite population of subjects in the clinical trial. Moreover, they note, with randomized treatment allocation to this finite population, the randomization underwrites statistical inference based on a randomization model, eg, a permutation test under the null hypothesis of no treatment effects.