  We propose a new definition of the chi-square divergence between
distributions. Based on convexity properties and duality, this version of the
{\chi}^2 is well suited both for the classical applications of the {\chi}^2 for
the analysis of contingency tables and for the statistical tests for parametric
models, for which it has been advocated to be robust against inliers. We
present two applications in testing. In the first one we deal with tests for
finite and infinite numbers of linear constraints, while, in the second one, we
apply {\chi}^2-methodology for parametric testing against contamination.
