We propose a new Gini correlation to measure dependence between a categorical and numerical variables. Analogous to Pearson R² 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 simpler computation implementation than the distance correlation and is more straightforward to perform inference. Simulation and real data applications are conducted to demonstrate the advantages.

中文翻译：

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定量和定性变量之间的新基尼相关性

我们提出了一个新的基尼相关性来衡量分类变量和数值变量之间的依赖关系。类似于 ANOVA 模型中的 Pearson R ²，基尼相关被解释为组间变异与总变异的比值，但它表征了独立性（零基尼相关相互意味着独立）。与距离相关性密切相关的是，基尼相关性通过考虑分类变量的性质而具有简单的表述。因此，所提出的基尼相关性比距离相关性具有更简单的计算实现，并且更易于执行推理。进行模拟和真实数据应用以展示优势。