# Statistics/Testing Data/Spearmans

Spearman Rank- Correlation coefficient

Spearman developed a method of measuring rank correlation known as spearman rank correlation coefficient. It is generally denoted by rs. There are three cases while calculating Spearman rank correlation coefficient:

Case i When ranks are given

Case ii When ranks are not given

Case iii Repeated ranks

The formula for calculating Spearman rank correlation coefficient is same for case i and ii. The formula is,

                     ${\displaystyle r_{s}=1-{\frac {6\sum \!\,d^{2}}{n(n^{2}-1)}}}$


Where,

n = The number of items or individuals being ranked

d = ${\displaystyle R_{1}-R_{2}}$

${\displaystyle R_{1}}$ = The rank of items with respect to first variable

${\displaystyle R_{2}}$ = The rank of items with respect to second variable