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A new Gini correlation between quantitative and qualitative variables

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  • Xin Dang
  • Dao Nguyen
  • Yixin Chen
  • Junying Zhang

Abstract

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.

Suggested Citation

  • Xin Dang & Dao Nguyen & Yixin Chen & Junying Zhang, 2021. "A new Gini correlation between quantitative and qualitative variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1314-1343, December.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:4:p:1314-1343
    DOI: 10.1111/sjos.12490
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    References listed on IDEAS

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