  We propose a new Gini correlation to measure dependence between a categorical
and numerical variables. Analogous to Pearson $R^2$ in ANOVA model, the Gini
correlation is interpreted as the ratio of the between-group variation and the
total variation, but it characterizes independence (zero Gini correlation
mutually implies independence). Closely related to the distance correlation,
the Gini correlation is of simple formulation by considering the nature of
categorical variable. As a result, the proposed Gini correlation has a lower
computational cost than the distance correlation and is more straightforward to
perform inference. Simulation and real applications are conducted to
demonstrate the advantages.
