A new form of Sampling Distribution of Bi-variate Sample Correlation Co-efficient
G. S. David Sam Jayakumar, A. Sulthan · Journal of Statistics and Management Systems · 2014
This paper proposed the Sampling distribution of sample correlation coefficient ‘r’ from the bi-variate correlated population of two random variables. The authors showed that the derived density function of the sample correlation co-efficient is different from the pioneering work of the statisticians. Moreover, the first two moments of the distribution are derived and the variance of sample correlation co-efficient is showed in terms of Beta, Gamma and the confluent hyper-geometric function. The shape of the density function of sample correlation co-efficient is also visualized and the authors computed the critical points of ‘r’ at 5% and 1% significance level for different sample sizes. Finally, based on the extracted critical points, we showed a numerical simulation study for testing the equivalence of sample and population correlation co-efficient for a small sample.