Tendency toward negative correlations for positively-skewed independent random variables
Bardsley, W. E. (2014). Tendency toward negative correlations for positively-skewed independent random variables. Journal of Hydrology, 53(2), 175–177.
Permanent Research Commons link: https://hdl.handle.net/10289/11350
Hydrological variables often display positive skewness, with means exceeding medians. Even when two such variables are independent, there is a more than 50% chance that a bivariate random sample will yield a negative value of the Pearson product-moment linear correlation coefficient r. Simulations from inverse Gaussian distributions suggest that this effect is small and unlikely to have any effect on significance tests of r if two skewed variables are in fact independent. However, a high frequency of negative sample correlations in a multi-site hydrological study could result in an incorrect deduction that some weak but widespread physical process is in operation.
New Zealand Hydrological Society
© 2014 New Zealand Hydrological Society. Used with permission.