Marie A. Coffin

James P. Jarvis

Douglas R. Shier

Abstract: In many experimental situations, subjects are randomly allocated to treatment and control groups. Measurements are then made on the two groups to ascertain if there is in fact a statistically significant treatment effect. Exact calculation of the associated randomization distribution theoretically involves looking at all possible partitions of the original measurements into two appropriately-sized groups. Computing every possible partition is computationally wasteful, so our objective is to systematically enumerate partitions starting from the tail of the randomization distribution. A new enumeration scheme that only examines potentially worthwhile partitions is described, based on an underlying partial order. Numerical results show that the proposed method runs quickly compared to complete enumeration, and its effectiveness can be enhanced by use of certain pruning rules.

Key Words: majorization, partition, permutation test, p-value, randomization test, two-sample test