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A new Gini correlation between quantitative and qualitative variables
Author(s) -
Dang Xin,
Nguyen Dao,
Chen Yixin,
Zhang Junying
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12490
Subject(s) - mathematics , categorical variable , distance correlation , correlation , statistics , independence (probability theory) , pearson product moment correlation coefficient , correlation coefficient , inference , measure (data warehouse) , econometrics , random variable , artificial intelligence , data mining , computer science , geometry
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 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.