Compositional Data Analysis in Population Studies

Many analyses of population data are based on percentages or proportions. Such data are referred to as compositional and complete compositions typically sum to 100 (if expressed as percentages) or one (if expressed as proportions). In geography, the vast majority of analyses of such data make use of standard statistical approaches. There are many warnings, however, both in the geographical literature and elsewhere, that such standard approaches should not be employed directly in the analysis of such data. Aitchison (1986 Aitchison, J. 1986. The statistical analysis of compositional data, London: Chapman and Hall. [Crossref] , [Google Scholar]) proposed a methodology for the analysis of compositional data based on taking log-ratios and then applying adapted standard approaches to the transformed data. This article highlights some problems associated with using standard approaches in the analysis of compositional data in population studies and outlines some key log-ratio-based approaches for transformation and the proper analysis of compositional data. A case study is used to demonstrate the application.