The Role of Permutation Groups in Randomization Tests

Abstract

Randomization tests are usually represented as strategies for determining significance through the comparison of the value of an obtained test statistic with a distribution of such values associated with every possible random assignment of subjects to treatments. Randomization tests can, however, also be conducted on the basis of a subset of all possible assignments and justified through the concept of a permutation group as defined by Chung and Fraser (1958). This idea is useful in acquiring a deeper understanding of randomization tests and in facilitating the development of new classes of tests.