A New Test for correlation on Bivariate Non-Normal Distribution

The sampling distribution of the sample correlation coefficient is unstable, even when the population is bivariate normally distributed. It is the main reason why a reasonably good test for the correlation is difficult to obtain, not to mention that most of the populations in the real world are not normally distributed. This thesis proposes a new method to conduct a right-tailed test for the correlation on bivariate non-normal distributions. The test unitizes the inverse Edgeworth expansion on the standardized form of the sample correlation. A comparative simulation study shows that the new test controls the type I error rates very well for all the distributions considered. An investigation of the power performance of the new test is also provided