We reformulate and 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. Thus, we...

We decompose the Pearson correlation coefficient into two components. We recommend the first component for detecting linear relationships and the second for recognizing patterns of two parallel lines, providing robust versions to outliers. The significance of the Pearson coefficient without...