At CoDaWork'03 we presented work on the analysis of archaeological glass composi-
tional data. Such data typically consist of geochemical compositions involving 10-12
variables and approximates completely compositional data if the main component, sil-
ica, is included. We suggested that what has been termed `crude' principal component
analysis (PCA) of standardized data often identi ed interpretable pattern in the data
more readily than analyses based on log-ratio transformed data (LRA). The funda-
mental problem is that, in LRA, minor oxides with high relative variation, that may
not be structure carrying, can dominate an analysis and obscure pattern associated
with variables present at higher absolute levels. We investigate this further using sub-
compositional data relating to archaeological glasses found on Israeli sites. A simple
model for glass-making is that it is based on a `recipe' consisting of two `ingredients',
sand and a source of soda. Our analysis focuses on the sub-composition of components
associated with the sand source. A `crude' PCA of standardized data shows two clear
compositional groups that can be interpreted in terms of di erent recipes being used at
di erent periods, re
ected in absolute di erences in the composition. LRA analysis can
be undertaken either by normalizing the data or de ning a `residual'. In either case,
after some `tuning', these groups are recovered. The results from the normalized LRA
are di erently interpreted as showing that the source of sand used to make the glass
di ered. These results are complementary. One relates to the recipe used. The other
relates to the composition (and presumed sources) of one of the ingredients. It seems
to be axiomatic in some expositions of LRA that statistical analysis of compositional
data should focus on relative variation via the use of ratios. Our analysis suggests that
absolute di erences can also be informativeGeologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Consell Social de la Universitat de Girona; Ministerio de Ciencia i Tecnología
