A lot of multivariate data sets of interest to scientists are called compositional or "closed" data sets, and consists essentially of relative proportions. A recent search on the web by entering "chemical compositional data", led to more than 2,730,000 results within different fields and disciplines, but specially, agricultural and food sciences (August 2011 using Google searcher). The driving ...

The estimation of a mean of a proportion is a frequent task in statistical survey analysis, and often such ratios are estimated from compositions such as income components, wage components, tax components, etc. In practice, the weighted arithmetic mean is regularly used to estimate the center of the data. However, this estimator is not appropriate if the ratios are estimated from compositions, ...

We report compositional data for several foods that comprise the annual diet among Hadza foragers near Lake Eyasi in northern Tanzania. Samples collected during daily gathering trips over three "eldwork seasons were prepared according to Hadza methods. All three types of honey show moisture and starch levels similar to United States' honeys but higher levels of protein, fat, and ash. Several sa...

High-throughput sequencing based techniques, such as 16S rRNA gene profiling, have the potential to elucidate the complex inner workings of natural microbial communities - be they from the world's oceans or the human gut. A key step in exploring such data is the identification of dependencies between members of these communities, which is commonly achieved by correlation analysis. However, it h...

Abstract: Within the special geometry of the simplex, the sample space of compositional data, compositional orthonormal coordinates allow the application of any multivariate statistical approach. The search for meaningful coordinates has suggested balances (between two groups of parts)—based on a sequential binary partition of a D-part composition—and a representation in form of a CoDa-dendrogr...

The logratio transformation (Aitchison, 1981, 1986) opened the way to statistically rigorous analysis of compositional data. Most statistical problems in compositional data analysis can be formulated in terms of logratios, and solved accordingly. However, some problems are more easily described and solved in terms of raw compositional variables. Raw compositions with k components are restricted...