Abstract
Abstract Compositional data are multivariate vectors that describe parts of some whole. Compositional data occur as vectors of proportions, percentages, or parts per million (ppm), although the definition also includes other types of vectors. If the compositional nature of data is ignored, misleading results may be obtained. In this case, the finding of spurious correlations, the appearance of the Simpson's paradox, and the prediction of negative values for proportions are common issues. To overcome these problems, a mathematical structure for compositional data has been defined: the Aitchison geometry on the simplex and the characterization of the simplex as a Euclidean vector space. This structure allows a suitable treatment of compositional data, either in their sample space or through their expression in coordinates, which are real vectors. Coordinates may be derived by appropriate transformations. Additive logratio (alr), centered logratio (clr), or isometric logratio (ilr) transformations may be selected. The most suitable transformation is tailored to the problem at hand and the statistical tools needed for the subsequent treatment. Several computer tools are available to perform the compositional data analysis.
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