A novel measure of dependence between a continuous random variable and a multinomial random variable is introduced. The proposed measure is based on the Hellinger distance between conditional distributions. It satisfies the desiderata for a dependence measure without making specific distributional assumptions about the continuous random variable or assuming that the discrete random variable arises from a latent continuous random variable. An estimator of the dependence measure based on data splitting and kernel density estimation is developed. The asymptotic distribution of the estimator has a simple form with a convergence rate of \sqrt{n}, making confidence intervals for the dependence measure and a test for independence straightforward and computationally convenient.

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