Tendency toward negative correlations for positivelyskewed independent random variables

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 productmoment 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.