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-dendrogram. Projected samples are represented in a
dendrogram-like graph showing: (a) the way of grouping parts; (b) the explanatory
role of subcompositions generated in the partition process; (c) the
decomposition of the variance; (d) the center and quantiles of each balance.
The representation is useful for the interpretation of balances and to describe
the sample in a single diagram independently of the number of parts. Also,
samples of two or more populations, as well as several samples from the
same population, can be represented in the same graph, as long as they have
the same parts registered. The approach is illustrated with an example of food
consumption in Europe.