  The categorical Gini correlation is an alternative measure of dependence
between a categorical and numerical variables, which characterizes the
independence of the variables. A nonparametric test for the equality of K
distributions has been developed based on the categorical Gini correlation. By
applying the jackknife empirical likelihood approach, the standard limiting
chi-square distribution with degree freedom of $K-1$ is established and is used
to determine critical value and $p$-value of the test. Simulation studies show
that the proposed method is competitive to existing methods in terms of power
of the tests in most cases. The proposed method is illustrated in an
application on a real data set.
