Basu on Randomization Tests

Basu’s paper on randomization tests (Basu, 1980) is a critique of the use of randomization as a basis for inference (i.e. as the source of the variability underlying the application of statistical arguments). The paper focusses on analyzing data obtained from an experiment, making it a direct companion piece to Basu (1978) and Basu (1971) which consider very similar issues in analyzing data obtained from sample surveys. It fits comfortably with Basu’s work on sample surveys and more generally on statistical inference, enriching and being enriched by the whole body of work. However, part of the attractiveness and strength of the present paper is that it can also be read alone, without reference to Basu’s other work, as a relatively accessible, stimulating illustration of Basu’s approach to thinking about statistical inference. It is a classic Basu paper highlighting the hallmarks of his style: it is provocative and challenging, based on simple examples pushed to extremes, and illustrated in an entertaining way by a conversation between three people. Underlying all this of course is deep thinking on serious issues. And, as an additional benefit, the discussion and Basu’s rejoinder are insightful and interesting, adding much to the original paper.