Detecting induced correlations in hydrochemistry

Plots containing common variables are prone to induced correlations. These plots are commonly used in hydrochemistry and other branches of geochemistry with no discussion of the potential influence of the common variables on the observed trends. Some examples from the literature include: (1) Comparison of a sum to a component of the sum. (2) Comparison of a ratio to its own numerator or denominator. (3) Comparison of two ratios with the same numerator or denominator. These types of common variable plots may increase or decrease the correlation that exists between two independent variables. This paper presents a randomisation method for distinguishing between the “real” and induced relationships that can occur in plots of type 1, 2 or 3 above, thereby enabling a distinction between hydrochemical processes and induced correlation(s). If the slope and correlation coefficient of the actual data are similar to the randomised data, the relationship cannot be attributed to a hydrochemical process alone. If the slope and correlation coefficient are different, it is likely that the data trend is the result of a real process, but we recommend this be confirmed using additional evidence such as relationships between other element/ion concentrations or independent isotopic evidence. Common variable plots are useful tools for identifying and describing hydrochemical processes, but the data trends need to be tested to ensure that correlations are a result of real processes rather than an artefact caused by a common variable.

Research highlights
► Plots containing common variables are prevalent in the geochemistry literature.
► They may contain correlations strongly induced by the common variable(s).
► A method to test for induced correlation is presented in this paper.
► The method reinforces the utility of common variable plots in geochemistry.