On the behaviour of some transforms of the sample correlation coefficient in samples from the bivariate t and the bivariate X2distribution

The present paper studies the normality of five transformations suggested in the literature to normalize the sample correlation coefficient. The parent populations are the bivariate t and the bivariate X ²The results in the previous work of Subrahmaniam and Gajjar are exploited to assess their performance. The density estimation procedure of Tarter and Kronmal is used to provide empiric support to the asymptotic results     

On the choice of transformations of the correlation coefficient with or without an outlier

Five transformations of the correlation coefficient, namely, Fisher's z, Nair's u, Sankaran's v, Ruben's y and Samiuddin's t are compared numerically using confidence intervals. Samiuddin's t_s transformation is close to the exact nominal confidence level for a small sample size ≤ 25 from a bivariate normal density. For a sample size > 25 both Samiuddin's t_s and Fisher's z can be used. In the presence of an outlier (on a minor axis), both Fisher's z and Samiuddin's t_s are not affected as long as |p| ≤ 0.3 but are seriously affected when |p&| > 0.3.     

On the behaviour of some transforms of the sample correlation coefficient:discretebivariate populations

The present paper investigates for the first time, the robustness of some of the familiar transformations of the sample correlation coefficient when the parent population is discrete. Three specific cases examined are:The bivariate Poisson (BVP):the bivariate negative binomial (BNB):The trinomial (TN). Investigation of the (near) normality of the transformed statistics is done by the techniques considered by Subrahmaniam and Gajjar. In addition, an empirical examination of their behaviour is carried out by the density estimation technique due to Tarter and Kronmal.