Quantifying and testing differences among means of compositional data suites

Abstract

Commonly, geological studies compare mean values of two or more compositional data suites in order to determine if, how, and by how much they differ. Simple approaches for evaluating and statistically testing differences in mean values for open data fail for compositional (closed) data. A new parameter, an “f-value,” therefore has been developed, which correctly quantifies the differences among compositional mean values and allows testing those differences for statistical significance. In general, this parameter quantifies only therelative factor by which compositional variables differ across data suites; however for situations where, arguably, at least one component has neither increased nor decreased, anabsolute f-value can be computed. In situations where the compositional variables have undergone many perturbations, arguments based upon thef-values and the central limit theorem indicate that logratios of compositional variables should be normally distributed.