Readme file

SERIES C 
Applied Statistics

Biplots of compositional data by J. Aitchison and M. Greenacre, Journal of the Royal Statistics Society, Series C, Applied Statistics, Volume 51 (2002), Part 4, 375 - 392

The data matrix consists of six-part colour compositions in 22 paintings created for teaching purposes. Each painting was divided into a number of rectangles, in the style of a Mondrian abstract painting, and the rectangles were each coloured in one of six colours: black, white, blue, red, yellow, and one further colour, labelled "other", which varies from painting to painting. The data are the proportions of surface area occupied by the six colours. For example, the first painting has 12.5% of the area in black, 24.3% in white, and so on. One of the questions posed to the students was to orientate the pictures in the same way as the artist. The results of this experiment showed that successful orientation followed a binomial distribution with success probability 1/4, a result that was in fact replicated with real Mondrian paintings. Another question was to have the students estimate the proportions of each colour, both to illustrate variability of estimation of proportions and the nature of compositional variability. Our present interest in these data is to
see whether there is any pattern discernible in the construction of these paintings. There is considerable variation from painting to painting in their colour compositions and the challenge is to describe the patterns of variability appropriately in simple terms while maintaining the unit-sum constraint inherent in the data.

The data matrix is 22 x 6. The data file consists of 22 lines, one line for each painting, and each line consists of six values, the proportions of the colours black, white, blue, yellow, red and "other" respectively. The sum of each row of data is 1.

Along with the data file we give the program in R which will produce the compositional biplot.

Michael Greenacre
Department of Economics and Business
Universitat Pompeu Fabra
Ramon Trias Fargas 25 - 27
08005 Barcelona
Spain

E-mail: michael@upf.es

Dataset (colours.dat, size = 2kb)

SERIES A
Statistics in Society

SERIES B
Statistical Methodology

SERIES C
Applied Statistics

SERIES D
The Statistician