Spearman's rank correlation coefficient

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.