Are our data symmetric?

Skewness indicates a lack of symmetry in a distribution. Knowing the symmetry of the underlying data is essential for parametric analysis, fitting distributions or doing transformations to the data. The coefficient of skewness is the commonly used measure to identify a lack of symmetry in the underlying data, although graphical procedures can also be effective. We discuss three different methods to assess skewness: traditional coefficient of skewness index, skewness index based on the L-moments discussed by Hosking and the asymptotic test of symmetry developed by Randles et al. With this work, we provide easy-to-implement S-PLUS® functions as well as discuss the advantages and shortcomings of each technique.