An Asymptotically Distribution-Free Test for Symmetry versus Asymmetry

An asymptotically distribution-free procedure is proposed for testing whether a univariate population is symmetric about some unknown value versus a broad class of asymmetric distribution alternatives. The consistency class of the test is discussed and two competing tests are described, one based on the sample skewness, and the other on Gupta's nonparametric procedure. A Monte Carlo study shows that the proposed test is superior to either competitor since it maintains the designated α levels fairly accurately even for sample sizes as small as 20, while displaying good power for detecting asymmetric distributions.