The problem of testing skew-symmetry of a distribution is studied in a general model of skew distributions. Toward this end, an order statistic-based test is first introduced to test the null hypotheses of symmetry against the alternative of skew-symmetry of a distribution. Some properties of this test are also studied. Then, using the idea of ranked set sampling, some appropriate sampling schemes are used to test skew-symmetry of a given data set. The power of the proposed tests are compared numerically to determine the best ranked set sampling scheme in different situations. Further, a comparison with some of existing non-parametric tests has been done. A real data set is also used to illustrate the results of the paper. Finally, some conclusions are stated.

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