%0 Journal Article %A John N. Haddad and Serge B. Provost %D 2011 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 52, 2011 %T Approximations to the Distribution of the Sample Correlation Coefficient %U https://publications.waset.org/pdf/13820 %V 52 %X Given a bivariate normal sample of correlated variables, (Xi, Yi), i = 1, . . . , n, an alternative estimator of Pearson’s correlation coefficient is obtained in terms of the ranges, |Xi − Yi|. An approximate confidence interval for ρX,Y is then derived, and a simulation study reveals that the resulting coverage probabilities are in close agreement with the set confidence levels. As well, a new approximant is provided for the density function of R, the sample correlation coefficient. A mixture involving the proposed approximate density of R, denoted by hR(r), and a density function determined from a known approximation due to R. A. Fisher is shown to accurately approximate the distribution of R. Finally, nearly exact density approximants are obtained on adjusting hR(r) by a 7th degree polynomial. %P 658 - 663