In applications where duplicate values (ties) are known to be absent, a simpler procedure can be used to calculate ρ.[3][4]
Note that this method should not be used in cases where the data set is truncated; that is, when the Spearman correlation coefficient is desired for the top X records (whether by pre-change rank or post-change rank, or both), the user should use the Pearson correlation coefficient formula given above.
The standard error of the coefficient (σ) was determined by Pearson in 1907 and Gosset in 1920. It is