Table 11: Power of the competitors dCov and HHG on ranks as well as on data for N = 100. The tests on data have greater power than on ranks in most, but not all, examples. HHG on data has the best power out of these four competitors, but like the HHG on ranks it has a disadvantage in comparison with our novel minimum p -value test when the relationship is more complex, especially in the Sine, Heavisine, Spiral, Circles, and 5Clouds examples. dCov HHG Setup on data on ranks on data on ranks W 0.467 0.351 0.876 0.813 Diamond 0.136 0.076 0.997 0.968 Parabola 0.418 0.369 0.727 0.795 2Parabolas 0.183 0.120 0.873 0.726 Circle 0.001 0.003 0.791 0.858 Cubic 0.631 0.612 0.660 0.742 Sine 0.412 0.427 0.803 0.788 Wedge 0.471 0.327 0.755 0.661 Cross 0.184 0.138 0.795 0.704 Spiral 0.182 0.130 0.598 0.335 Circles 0.054 0.059 0.479 0.357 Heavisine 0.476 0.470 0.471 0.570 Doppler 0.747 0.736 0.901 0.914 5Clouds 0.000 0.001 0.738 0.903 4Clouds 0.050 0.050 0.050 0.050 D.A. Darling. The kolmogorov-smirnov, cramer-von mises tests. The Annals of Math- ematical Statistics , 28(4):823–838, 1957. D. Donoho and I. Johnstone. Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association , 90(432):1200–1224, 1995. A. Feuerverger. A consistent test for bivariate dependence. International Statistical Review , 61(3):419–433, 1993. M. Gorfine, R. Heller, and Y. Heller. Comment on detecting novel associations in large data sets by reshef et al., science. Available: http: // iew3technionacil/ ~ gorfinm/ files/ science6. pdf , 2011. A. Gretton and L. Gyorfi. Consistent nonparametric tests of independence. Journal of Machine Learning Research , 11:1391–1423, 2010. A. Gretton, K.M. Bogwardt, M.J. Rasch, B. Scholkopf, and A. Smola. A kernel 75