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New in Mathematica 9Enhanced Probability & Statistics

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

Unlike SpearmanRho, KendallTau, and Pearsons's Correlation, HoeffdingD can be used to detect a wide variety of dependence structures beyond monotonic association.
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Test whether Hoeffding's D is significantly different from zero.

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Here is a collection of datasets with different dependency structures.

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The Hoeffding D statistics and test conclusions for the data grid follow.

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