Spearman’s Rank correlation Coefficient

Let $(x_1, y_1), (x_2, y_2), \cdots , (x_n, y_n)$ be the ranks of $n$ individuals in two characteristics $A$ and $B$ respectively.


Spearman’s rank correlation coefficient is denoted by $\varrho$ and is given by

$\varrho = 1- \dfrac{6 \sum_{i=1}^{n}d_i^2}{n(n^2-1)}$


  • $n$ is the number of pairs of observations,
  • $d_i = x_i - y_i$ is the difference between the pairs of ranks of the $i^{th}$ individual in the two characteristics.

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