ABSTRACT
The terms “randomization test” and “permutation test” are sometimes used interchangeably. However, there are both historical and conceptual reasons for making a clear distinction between the two terms. Using a historical perspective, this chapter emphasizes the contributions made by Edwin Pitman and Bernard Welch to arrive at a coherent theory for randomization and permutation tests. From a conceptual perspective, randomization tests are based on random assignment and permutation tests are based on random sampling. The justification of the randomization test derives from the fact that under the null hypothesis of no treatment effect, the random assignment procedure produces a random shuffle of the responses. The justification of the permutation test derives from the fact that under the null hypothesis of identical distributions, all permutations of the responses are equally likely. It is argued that this terminological distinction is crucial for recognizing the assumptions behind each of the tests and for appreciating the validity of the corresponding inferences.
