\(S=\sum_{i=1}^{n-1}{\sum_{j=i+1}^{n}{\text{sign}\left(y_{j}-y_{i}\right)}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ sign}\left(y_{j}-y_{i}\right)=\left\{\begin{matrix}1;\mathrm{\text{if\ }}y_{j}>y_{i}\\ 0;\mathrm{\text{if\ }}y_{j}=y_{i}\\ -1;\mathrm{\text{if\ }}y_{j}<y_{i}\\ \end{matrix}\right.\ \) (Equation 1)
\(\tau=\frac{S}{n\left(n-1\right)/2}\) (Equation 2)