Question

How are linear correlation and rank correlation alike?

How are linear correlation and rank correlation different?

Answer 1

 

How are linear correlation and rank correlation alike?

Here' are the similarities between linear ( Pearson' correlation ) and ranked ( Spearman' ) correlation :

If the true relationship between the data is nearly linear over the observed range of the variables, then Pearson's r and Spearman's Rs will largely agree, and Pearson's will almost surely be larger in magnitude because Pearson's method has higher sensitivity for linear relationships.

In other words:  If each value in X and Y is a linear function of its rank, the Pearson and Spearman correlation coefficients will be identical. Pearson and Spearman correlation coefficients will be similar when there's an underlying linear relationship between X and Y. But, the reverse isn't necessarily true.

How are linear correlation and rank correlation different?

As the association becomes less linear, but still monotonic, Pearson's rr will shrink toward 0, while Spearman's Rs may remain unchanged (i.e. with values approaching 1 or –1).