Edgeworth Expansions for the Power of Permutation Tests

Abstract

A randomization model for a two-sample situation withadditive treatment effects is considered. Edgeworthexpansions for the power of the usual permutation test arederived, under some conditions on the unit errors, frompreviously obtained expansions under the null hypothesis ofno treatment effect. A general error structure isconsidered and conditions for the validity of theexpansions for both conditional and unconditional power areexamined. The results are shown to generalise expansionsobtained earlier by different methods for the special caseof independent and identically distributed randomvariables.