Vidal, I. Instituto de Matemática y Física, Universidad de Talca, Casilla 721, Chile.In this work we approach the problem of model comparison between skew families. For the univariate skew model, we measure the sensitivity of the skewness parameter using the L1 distance between symmetric and asymmetric models and we obtain explicit expressions for some of these models. The main result is that the L1 distance between a representable elliptical distribution and a representable skew elliptical distribution remains invariant and it equals to the L1 distance between the normal and skew-normal densities. We also use the Bayes factor to test asymmetry and present some simulation results for the skew-normal and skew-t distributions obtaining expected results for adequate prior distribution. An application in stock markets is also considered.