Ricardo a Valls

Why and How Should Geologists Use Compositional Data Analysis. Ricardo a Valls

Compositional data arise naturally in several branches of science, including geology. In geochemistry, for example, these constrained data seem to occur typically, when one normalizes raw data or when one obtains the output from a constrained estimation procedure, such as parts per one, percentages, ppm, ppb, molar concentrations, etc. Compositional data have proved difficult to handle statistically because of the awkward constraint that the components of each vector must sum to unity. The special property of compositional data (the fact that the determinations on each specimen sum to a constant) means that the variables involved in the study occur in constrained space defined by the simplex, a restricted part of real space. Pearson was the first to point out dangers that may befall the analyst who attempts to interpret correlations between Ratios whose numerators and denominators contain common parts. More recently, Aitchison, Pawlowsky-Glahn, S. Thió, and other statisticians have developed the concept of Compositional Data Analysis, pointing out the dangers of misinterpretation of closed data when treated with "normal" statistical methods It is important for geochemists and geologists in general to be aware that the usual multivariate statistical techniques are not applicable to constrained data. It is also important for us to have access to appropriate techniques as they become available. This is the principal aim of this book.