Are the Pearson and Spearman rank correlation coefficients related in a specific way for uniform random variables? Specifically, is the relationship $\rho\_{spearman} = 2\*\sin(\frac{\pi}{6}\rho\_{pearson})$? If so, why?



Are the Pearson and Spearman rank correlation coefficients related in a specific way for uniform RVs?
This formula is from Pearson 1907, see e.g. 


Rank Correlation and Product-Moment Correlation
Author(s): P. A. P. Moran
Source: Biometrika, Vol. 35, No. 1/2 (May, 1948), pp. 203-206


Johan


