From Fisher to CARA: the evolution of randomization and randomization-based inference

R. A. Fisher was a devoted Darwinian, and, like Darwin, created science out of nothing. The list is long, but one thinks of likelihood-based estimation, analysis of variance, principles of experimental design, and randomization as standing the tests of time. Such accomplishments 'from scratch' (or nearly so) can amaze the fine statisticians who made meaningful incremental contributions to work begun by others, the few 'greats' among us who invented something important, and the unusually perceptive introductory statistics student, alike. Fisher thought of randomization in the context of agricultural experiments, but it has impacted most profoundly the science of medicine. Bradford Hill brought randomization to clinical trials. The concept of randomization-based inference, now resurrected in causal inference, was largely forgotten as design and analysis became segregated, perhaps due to analysis software packages. This talk will attempt to give the historical context of randomization and randomization-based inference from Fisher to the present day, including newer concepts such as response-adaptive, covariate-adaptive, and covariate-adjusted response-adaptive randomization. It will be challenging to condense a year of material into one hour, but a devoted Fisherian should be able to be efficient and sufficient.