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This paper contains two finite-sample results about the sign test. First, weshow that the sign test is unbiased against two-sided alternatives even whenobservations are not identically distributed. Second, we provide simpletheoretical counterexamples to show that correlation that is unaccounted forleads to size distortion and over-rejection. Our results have implication forpractitioners, who are increasingly employing randomization tests forinference.

Some Finite Sample Properties of the Sign Test