Determining Spurious Correlation between Two Variables with Common Elements: Event Area-Weighted Suspended Sediment Yield and Event Mean Runoff Depth

Spurious correlation is a classic statistical pitfall pervasive to many disciplines including geography. Although methods of calculating the spurious correlation between two variables possessing a common element in the form of sum, ratio, or product have been developed for a long time, controversial assertions on whether the spurious correlation should be treated or ignored are still prevalent. In this study, we examined this well-known but intriguing issue using the data representing two nonindependent variables, event area-weighted suspended sediment yield ( SSYe) and event mean runoff depth ( h). By transferring the correlation between SSYe and h to that between suspended sediment transport rate ( Qs) and water discharge ( Q), we developed a new method of determining whether Qs is truly correlated to Q. The method involves calculating coefficients of spurious correlation ( rAB) and the associated "pure" spurious correlation ( r0 AB), a hypothesis test, and regression between rAB and r0 AB. Our analysis showed that ( 1) there exists a true correlation between SSYe and h and ( 2) the spurious correlation is strongly related to the variability of the variables. We then proposed a general rule stating that the apparent spurious correlation between two variables could be ignored if the two have a true causal relation. At last, we distinguished the difference between spurious correlation and spurious reference.