Compositional Data Analysis - General Principles

Any data measured (or reported) in terms of proportions of a whole is called ‘compositional’. Virtually all geochemical data falls under this category. Because such data has a number of special properties, specific procedures are required for its statistical analysis. Generally, it cannot be meaningfully analyzed by methods designed for the analysis of multivariate Gaussian data, such as the standard regression analysis still used by many geologists.

This lecture is intended to give a brief overview of the most important mathematical characteristics of compositional data, and what consequences these have for the statistical analysis of such data. It will provide the theoretical foundations for the next lecture(s) in which the specific problems associated to the analysis of mineral chemistry data (lecture 2) and hierarchical data structures (lecture 3) will be considered in somewhat more detail. These later two lectures are intended as more practical guides to actual data analysis.