The size and power of the exact bivariate symmetry test
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Abstract:

AbstractHollander's bivariate symmetry test for paired data is a two-sided conditional test of the null hypothesis H0: F(y,x)=F(y,x) for all (x, y) versus the alternative hypothesis that H0 fails to hold. Hollander (1971) proved the consistency of this test against a wide range of alternatives. Because of the potential usefulness of this test and because asymptotic distributions of the test statistic defined to date have not performed well, we created an algorithm for conducting exact bivariate symmetry tests. The algorithm computes exact P values in a tiny fraction of the time required for complete enumeration of the sample space. We use the algorithm to demonstrate the exact test's high sensitivity to location and moderate sensitivity to scale alternatives.

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