TITLE:
A Note on the Relationship between the Pearson Product-Moment and the Spearman Rank-Based Coefficients of Correlation
AUTHORS:
Todd Christopher Headrick
KEYWORDS:
Bivariate Normal Distribution, Product-Moment Correlation, Rank-Based Correlation, Gibbs Phenomenon
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.6,
November
17,
2016
ABSTRACT: This note derives the relationship between
the Pearson product-moment coefficient of correlation and the Spearman
rank-based coefficient of correlation for the bivariate normal distribution.
This new derivation shows the relationship between the two correlation
coefficients through an infinite cosine series. A computationally efficient
algorithm is also provided to estimate the relationship between the Pearson
product-moment coefficient of correlation and the Spearman rank-based
coefficient of correlation. The algorithm can be implemented with relative ease
using current modern mathematical or statistical software programming languages
e.g. R, SAS, Mathematica, Fortran, et al. The algorithm is also available from
the author of this article.