Two statistics are considered to test the population correlation for non-normally distributed bivariate data. A simulation study shows that both statistics control type I error rates well for left-tailed tests and have reasonable power performance.
Beversdorf, L. and Sa, Ping
"Tests for Correlation on Bivariate Non-Normal Data,"
Journal of Modern Applied Statistical Methods:
2, Article 29.
Available at: http://digitalcommons.wayne.edu/jmasm/vol10/iss2/29