Open Access
February, 1969 Bivariate Symmetry Tests: Parametric and Nonparametric
C. B. Bell, H. Smith Haller
Ann. Math. Statist. 40(1): 259-269 (February, 1969). DOI: 10.1214/aoms/1177697821


In testing whether a treatment has an effect or not, the experimenter is often obliged to use the same subjects for control and treated groups. In such a case it is generally unrealistic to assume independence and one is led to tests of bivariate symmetry. The object of this paper is to show that bivariate symmetry is not equivalent to univariate symmetry; that there exists a feasible procedure different from the likelihood ratio test in the normal case; that there is no unique "natural" concept of rank; that all distribution-free (DF) procedures are based on permutations; and that optimal DF procedures for a simple alternative are based on permutations of the likelihood function.


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C. B. Bell. H. Smith Haller. "Bivariate Symmetry Tests: Parametric and Nonparametric." Ann. Math. Statist. 40 (1) 259 - 269, February, 1969.


Published: February, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0177.22505
MathSciNet: MR235658
Digital Object Identifier: 10.1214/aoms/1177697821

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 1 • February, 1969
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