A Level Maths Notes: S4 – The Difference Between the Correlation Coefficient and Spearman's Rank Correlation Coefficient
The correlation coefficient, also called Pearson's correlation
coefficient and labelled
tests
the goodness of fit of a set of points to a straight line.
is
between -1 and 1. If
the
points are a perfect fit to a straight line with a positive
correlation and if
they
are a perfect fit to a line with a negative correlation.
Spearman's rank correlation coefficient
only
tests if two quantities increase or decrease together, without
necessarily being a good fit to a straight line. A value of 1
for
means
that if one quantity increases then so does the other with absolute
certainty.

Spearman's rank correlation coefficient is preferable if two quantities are related but the relationship is not linear. It is usual to draw a graph before assessing the nature of any relationship.