A new Gini correlation between quantitative and qualitative variables

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.