Adaptive tests for the median

Various adaptive tests for the median of a distribution are proposed and compared. Each adaptive procedure uses in its first stage some measure or test of symmetry to decide whether the signed rank or the ordinary sign test should be used to test the hypothesis about the median of the distribution. The procedures proposed, A₆ and R, are robust for a wide variety of distributions, whereas other procedures which use highly recommended tests for symmetry in the first stage are very nonrobust. The results show that the robustness of adaptive procedures should be examined carefully before they are accepted for general use. For the problem considered, the author recommends the A₆ and R tests