The correlation coefficient between X and Y that we usually use is obtained by dividing the covariance of X, Y by the product of the variances of X and Y. It is therefore restricted to lie between -1 and 1. When the correlation is -1, it means that there is a strong negative relationship between the variables. When it is 1, it means that there is a strong positive relationship; and when it is 0, it means that there is no relationship between the variables. But there is an implicit assumption that we usually overlook: the correlation coefficient assumes that there is a linear relationship. So, it is easy to imagine lots of cases where there might be a relationship, but not a linear one.
The Spearman rank statistic does not test correlation in the traditional sense ((whether a greater than average value of X is associated linearly with a...
