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Spearman’s rank correlation coefficient

In principle, spearman Spearman is simply a special case of thePearson product-moment coefficient in which two sets of data X(i) X and Y(i) are converted to rankings x(i) and y(i) before calculating the coefficient.i and Yi are converted to rankings xi and yi before calculating the coefficient.

When using rank transformation the data is replaced with their corresponding ranks. Ranks are defined by assigning 1 to the smallest value, 2 to the second smallest and so-on, until the largest value has been assigned the rank N. If there are ties in the data set, then the average rank is assigned to them. The usual regression and correlation procedures are then performed on the ranks instead of the original data values.


  • Francesca Campolongo, Andrea Saltelli, Tine Sørensen, and Stefano Tarantola. Hitchhiker’s guide to sensitivity analysis. In Sensitivity analysis, Wiley Ser. Probab. Stat., pages 15–47. Wiley, Chichester, 2000.