Simula@bi: Reformulation and decomposition of Pearson and Spearman correlation coefficients into practical measures

We decompose the Pearson and Spearman correlation coefficients into two components. We recommend the first component for detecting linear or monotonic relationships and the second for recognizing patterns of two parallel lines, providing robust versions to outliers.

Finally, we apply members of the proposed family of coefficients with permutation tests to simulated and real data in economics. New coefficients identify two-parallel line correlation, hidden, mixed, influenced, or weaker but significant relationships not recognized by standard coefficients.    

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