Distribution-free test for symmetry based on Wilcoxon two-sample test

McWilliams introduced a test of symmetry based on a runs statistic for a continuous distribution about a known median. His test statistic R* performs better than other competitors considered in his study. In this paper, we present a conditional test for symmetry based on a Wilcoxon two-sample test. The proposed test turns out to be competitive with the test of McWilliams.