The Role of Permutation Groups in Randomization Tests

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.