Introduction

Abstract

Data describing amounts of components of specimens are compositional if the size of each specimen is constant or irrelevant. Ideally compositional data is given by relative portions summing up to 1 or 100 %. But more often compositional data appear disguised in several ways: different components might be reported in different physical units, different cases might sum up to different totals, and almost never all relevant components are reported. Nevertheless, the constraints of constant sum and relative meaning of the portions have important implications for their statistical analysis, contradicting the typical assumptions of usual uni- and multivariate statistical methods and thus rendering their direct application spurious. A comprehensive statistical methodology, based on a vector space structure of the mathematical simplex, has only been developed very recently, and several software packages are now available to treat compositional data within it. This book is at the same time a textbook on compositional data analysis from a modern perspective and a sort of manual on the R-package “compositions”: both R and “compositions” are available for download as free software. This chapter discusses the need of an own statistical methodology for compositions, the historic background of compositional data analysis, and the software needs for compositional data analysis.