Spearman's rank correlation coefficient or
<math>\rho</math> (
rho) is a
non-parametric measure of
correlation – that is, it assesses how well a
linear equation describes the relationship between two
variables without making any assumptions about the
frequency distribution of the variables. To calculate <math>\rho</math>,
raw scores are converted to ranks. <math>\rho</math> is a special case of the
Pearson product-moment correlation coefficient in which the data are ranks, although a simpler formula is often used in calculation by hand:
- <math> \rho = 1- {\frac {6 \sum D^2}{N(N^2 - 1)}}</math>
where:
- D = the difference between the ranks of corresponding values of X and Y, and
- N = the number of pairs of values.