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A Distribution-Free Test for Symmetry Based on a Runs Statistic

Thomas P. McWilliams
Journal of the American Statistical Association
Vol. 85, No. 412 (Dec., 1990), pp. 1130-1133
DOI: 10.2307/2289611
Stable URL: http://www.jstor.org/stable/2289611
Page Count: 4
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A Distribution-Free Test for Symmetry Based on a Runs Statistic
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Abstract

I present a simple test, based on a runs statistic, for symmetry of a continuous distribution about a known median. The statistic has a binomial sampling distribution and desirable invariance properties. Monte Carlo studies demonstrate that, for a wide variety of alternative asymmetric distributions, the test is more powerful than tests proposed by Butler (1969), Rothman and Woodroofe (1972), or Hill and Rao (1977).

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