We describe a novel non parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables one to answer whether one source variable is significantly more dependent on the first target variable or the second. Dependence is measured via the Hilbert-Schmidt Independence Criterion (HSIC), resulting in a pair of empirical dependence measures (source-target 1, source-target 2). Modeling the covariance between these HSIC statistics leads to a provably more powerful test than the construction of independent HSIC statistics by sub sampling. The resulting test is consistent and unbiased, and (being based on U-statistics) has favorable convergence properties. The test can be computed in quadratic time, matching the computational complexity of standard empirical HSIC estimators. We demonstrate the effectiveness of the test on a real-world linguistics problem of identifying language groups from a multilingual corpus.