# Are the Pearson and Spearman rank correlation coefficients related in a specific way for uniform RVs?

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?

-
This is a very specific formula that you are asking about, so I don't quite understand the purpose of the question. Is this a formula that you have derived and would like checked, or a formula that you have seen and whose derivation you find unclear? A little more detail on what you know and don't know thus far would be helpful. –  Yemon Choi Feb 7 '10 at 19:50
I came across an unsupported statement of the claim by an unreputable source as part of a method to obtain a specified correlation coefficient between two U(0,1) RVs. –  user3875 Feb 7 '10 at 21:17
wilmott.com/… –  user3875 Feb 8 '10 at 1:43

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

-
Thank you. ------- –  user3875 Feb 22 '10 at 1:19