  The categorical Gini covariance is a dependence measure between a numerical
variable and a categorical variable. The Gini covariance measures dependence by
quantifying the difference between the conditional and unconditional
distributional functions. A value of zero for the categorical Gini covariance
implies independence of the numerical variable and the categorical variable. We
propose a non-parametric test for testing the independence between a numerical
and categorical variable using the categorical Gini covariance. We used the
theory of U-statistics to find the test statistics and study the properties.
The test has an asymptotic normal distribution. As the implementation of a
normal-based test is difficult, we develop a jackknife empirical likelihood
(JEL) ratio test for testing independence. Extensive Monte Carlo simulation
studies are carried out to validate the performance of the proposed JEL-based
test. We illustrate the test procedure using real a data set.
