Another look at the constant sum problem in geochemistry

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Abstract
Compositional data—that is data where concentrations are expressed as proportions of a whole, such as percentages or parts per million—have a number of peculiar mathematical properties which make standard statistical tests unworkable. In particular correlation analysis can produce geologically meaningless results. Aitchison (1986) proposed a log-ratio transformation of compositional data which allows inter-element relationships to be investigated. This method was applied to two sets of geochemical data—basalts from Kilauea Iki lava lake and grantic gneisses from the Limpopo Belt—and geologically 'sensible' results were obtained. Geochemists are encouraged to adopt the Aitchison method of data analysis in preference to the traditional but invalid approach which uses compositional data.