Let (Z1,..., ZN ) = (X1,..., Xm, Y1,..., Yn) be distributed according to the joint density (5.55),

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Let (Z1,..., ZN ) = (X1,..., Xm, Y1,..., Yn) be distributed according to the joint density (5.55), and consider the problem of testing H : η = ξ

against the alternatives that the X’s and Y ’s are independently normally distributed with common variance σ2 and means η = ξ . Then the permutation test with rejection region |Y¯ − X¯ | > C[T (Z)], the two-sided version of the test (5.54), is most stringent.

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