Statistics of Rothman & Woodroofe (1972) and Srinivasan & Godio (1974) are combined to define a statistic for testing the symmetry of a continuous distribution about a specified median. The proposed statistic is shown to possess a desirable invariance property. Exact and asymptotic null distribution of the statistic and tables of critical values for sample sizes 10 ≤ n ≤ 24 are also given.
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Hill et al. (1977) studied this question.