Testing pairs of continuous random variables for independence: A simple heuristic

Abstract

Detection and examination of pairwise dependence patterns between continuous variables is among the central tasks in the fields of business and economic statistics. To perform this analysis, practitioners frequently resort to Pearson’s (1895) product–moment correlation coefficient and the related significance tests. However, the use of such tests in isolation involves the risk of missing the nonlinear and particularly non-monotonic associations between the variables. This problem is also relevant in the cases where the dependence prevails between higher-order moments, e.g., variances, rather than means. We present a simple, computationally inexpensive heuristic by which this problem can be addressed and demonstrate its usefulness in a small number of example cases.