@article{(Open Science Index):https://publications.waset.org/pdf/13820, title = {Approximations to the Distribution of the Sample Correlation Coefficient}, author = {John N. Haddad and Serge B. Provost}, country = {}, institution = {}, abstract = {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.}, journal = {International Journal of Mathematical and Computational Sciences}, volume = {5}, number = {4}, year = {2011}, pages = {658 - 663}, ee = {https://publications.waset.org/pdf/13820}, url = {https://publications.waset.org/vol/52}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 52, 2011}, }