Randomized trial compares a new test for bivariate symmetry to existing methods, showing improved performance.
A conditionally distribution-free test of bivariate symmetry based on the sample distribution function is introduced. The test is shown to be consistent against a wide class of alternatives. In particular, if the underlying bivariate distribution is absolutely continuous, then the test is consistent against all alternatives to the null hypothesis. Power comparisons of the conditional test, a normal theory test devised by Bell and Haller, and the Wilcoxon signed rank test are given for bivariate normal and bivariate exponential populations.
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Myles Hollander (1971) studied this question.
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