In 30 blood samples portions of three kinds of white cells
granulocytes,
lymphocytes,
monocytes,
were determined with two methods, time-consuming microscopic and automatic image analysis. The resulting 30 pairs of 3-part compositions are recorded.
data(WhiteCells)A 30x6 matrix
In an experiment each of 30 blood samples was halved, one half being assigned randomly to one method, the other half to the other method. We have 60 cases of 3-part compositions but these are essentially 30 pairs of related compositions. All 3-part portions sums to one, except for some rounding errors.
Aitchison, J. (1986) The Statistical Analysis of Compositional Data, 1986 (Data 9) pp16.