Table 10: The power of competitors (rows 3–7), along with the minimum p -value statistic based on DDP (row 1) and on ADP (row 2) and the different maximum variants (rows 8–11), for N = 100. The standard error is at most 0 . 011. see that although dCov on data may have more power than dCov on ranks, it has far less power than HHG on data, and that HHG on data has less power than our test when the relationship is more complex, especially in the Sine, Heavisine, Spiral and Circles examples. References T.W. Anderson and D.A. Darling. Asymptotic theory of certain ”goodness of fit” criteria based on stochastic processes. The Annals of Mathematical Statistics , 23 (2):193–212, 1952. L. Baringhaus and C. Franz. On a new multivariate two-sample test. Journal of Multivariate Analysis , 88:190–206, 2004. Y. Benjamini and Y. Hochberg. Controlling the false discovery rate - a practical and powerful approach to multiple testing. J. Roy. Stat. Soc. B Met. , 57 (1):289–300, 1995. J. Blum, J. Kiefer, and M. Rosenblatt. Distribution free tests of independence based on the sample distribution function. The Annals of Mathematical Statistics , pages 485–498, 1961. 74 Test Line Exp2x Exp10x Sigmoid min$_{m}$$_{∈{}$$_{2}$$_{,...,}$$_{10}$$_{}}$ p$_{m}$ using DDP 0.358 0.763 0.580 0.543 min$_{m}$$_{∈{}$$_{2}$$_{,...,}$$_{10}$$_{}}$ p$_{m}$ using ADP 0.365 0.760 0.555 0.550 Spearman 0.459 0.758 0.396 0.630 Hoeffding 0.446 0.750 0.409 0.637 MIC 0.282 0.198 0.312 0.130 dCov 0.433 0.746 0.395 0.637 HHG 0.337 0.706 0.509 0.545 M DDP 2 × 2 0.287 0.688 0.678 0.438 M DDP 3 × 3 0.203 0.579 0.569 0.355 M DDP 4 × 4 0.177 0.511 0.479 0.301 M ADP 2 × 2 0.294 0.715 0.746 0.440