PerspectiveMathematics

A Correlation for the 21st Century

Science  16 Dec 2011:
Vol. 334, Issue 6062, pp. 1502-1503
DOI: 10.1126/science.1215894

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Summary

Most scientists will be familiar with the use of Pearson's correlation coefficient r to measure the strength of association between a pair of variables: for example, between the height of a child and the average height of their parents (r ≈ 0.5; see the figure, panel A), or between wheat yield and annual rainfall (r ≈ 0.75, panel B). However, Pearson's r captures only linear association, and its usefulness is greatly reduced when associations are nonlinear. What has long been needed is a measure that quantifies associations between variables generally, one that reduces to Pearson's in the linear case, but that behaves as we'd like in the nonlinear case. On page 1518 of this issue, Reshef et al. (1) introduce the maximal information coefficient, or MIC, that can be used to determine nonlinear correlations in data sets equitably.