2013/11/30 by Uwe Saint‐Mont, Uwe Saint-Mont
Mathematics · Medicine · Psychology · #Advanced Causal Inference Techniques #Bayesian inference #Bayesian probability #Biology #Cognitive psychology #Comparability #Computer science #Confounding #Econometrics #Frequentist inference #Mathematics #Medicine #Mendelian randomization #Psychology #Randomization #Randomized controlled trial #Restricted randomization #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics #Wishful thinking #msc:62K99 #stat.ME
paper · pdf · doi:10.1371/journal.pone.0132102
arxiv created 2014/10/27 · openalex publication_date 2015/07/20 · arxiv updated 2017/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
According to R.A. Fisher, randomization "relieves the experimenter from the anxiety of considering innumerable causes by which the data may be disturbed."Since, in particular, it is said to control for known and unknown nuisance factors that may considerably challenge the validity of a result, it has become very popular.This contribution challenges the received view.First, looking for quantitative support, we study a number of straightforward, mathematically simple models.They all demonstrate that the optimism surrounding randomization is questionable: In small to medium-sized samples, random allocation of units to treatments typically yields a considerable imbalance between the groups, i.e., confounding due to randomization is the rule rather than the exception.In the second part of this contribution, the reasoning is extended to a number of traditional arguments in favour of randomization.This discussion is rather non-technical, and sometimes touches on the rather fundamental Frequentist/Bayesian debate.However, the result of this analysis turns out to be quite similar: While the contribution of randomization remains doubtful, comparability contributes much to a compelling conclusion.Summing up, classical experimentation based on sound background theory and the systematic construction of exchangeable groups seems to be advisable. The logic of the experimentRandomization, the allocation of subjects to experimental conditions via a random procedure, was introduced by eminent statistician R.A. Fisher [1].Arguably, it has since become the most important statistical technique.In particular, statistical experiments are defined by the use of randomization [2,3], and many applied fields, such as evidence based medicine, draw a basic distinction between randomized and non-randomized evidence.In order to explain randomization's eminent role, one may refer to the logic of the experiment, largely based on J. S. Mill's method of difference[4]: If one compares two groups of subjects (Treatment T versus Control C, say) and observes a salient contrast in the end (e.g.X À T > X À C ), that difference must be due to the experimental manipulation-IF the groups were equivalent at the very beginning of the experiment.