Edgeworth Expansions for the Power of Permutation Tests

Abstract

A randomization model for a two-sample situation with additive treatment effects is considered. Edgeworth expansions for the power of the usual permutation test are derived, under some conditions on the unit errors, from previously obtained expansions under the null hypothesis of no treatment effect. A general error structure is considered and conditions for the validity of the expansions for both conditional and unconditional power are examined. The results are shown to generalise expansions obtained earlier by different methods for the special case of independent and identically distributed random variables.