Use Hoeffding's D to Quantify and Test Non-monotonic Dependence

Unlike SpearmanRho, KendallTau, and Pearson's Correlation, HoeffdingD can be used to detect a wide variety of dependence structures beyond monotonic association.

    
Test whether Hoeffding's is significantly different from zero:
A collection of datasets with different dependency structures:
The Hoeffding statistics and test conclusions for the data grid: