Keywords: statistics, geochemistry, discrimination diagrams, Monte Carlo simulation, discordancy tests, regression, uncertainty, ternary diagrams
AbstractAnalogous to chemometrics, geochemometrics can be defined as the science resulting from the combination of statistics, mathematics and computation with geochemistry. This term in Spanish –geoquimiometría– has already been explicitly used in the literature. Here I elaborate on the numerous basic subjects or areas that the geochemometrics should cover. These include, but are not limited to, the following research topics: data quality, regressions, robust methods, outlier-based methods, significance tests, error or uncertainty propagation in diagrams through Monte Carlo simulation, correlation coefficient, petrogenetic modeling, and geothermometers. Equations for uncertainty propagation in analytical work have also been proposed; similarly, new indications are provided on how to calculate and report the sensitivity and limit of detection of analytical experiments. The conventional linear correlation coefficient, though useful for non-compositional data, is not recommended to be used for interpreting geochemical data. Because compositional data represent a closed unit-sum constrained system and ternary diagrams impose a further unit-sum constraint on any experimental data, these diagrams become statistically unsuitable to handle experimental data, whether compositional or of continuous variable type. Error propagation through Monte Carlo is reported for the first time to illustrate the inconvenience in using such ternary diagrams for compositional data, and an alternative log-transformed bivariate diagram is proposed to replace (or at least complement) ternary diagrams. Topics of further research have been identified, in particular, those applicable to all science and engineering fields.