MULTIVARIATE ANALYSIS OF COMPOSITIONAL DATA: APPLIED COMPARISONS FAVOUR STANDARD PRINCIPAL COMPONENTS ANALYSIS OVER AITCHISON'S LOGLINEAR CONTRAST METHOD

There has been debate about whether standard principal components analysis is appropriate for the multivariate analysis of compositional data (e.g. oxide composition of glass), Loglinear transformation has been recommended by Aitchison as a prerequisite. This paper argues that previous comparisons of methodological merits have tended to circularity of argument by making assumptions about the form of a good multivariate result. To break the circularity of argument the authors have introduced randomized variables into five data sets. A good result must recognize these randomized variables as noise and place them near the centroid of the principal components scattergram of variable loadings. Standard principal components analysis is found to perform better than loglinear transformation in its ability to recognize the randomized variables. It is concluded that loglinear transformation tends to introduce spurious structure into a table of compositional data. This paper is followed by a comment by M. J. Baxter.     

MODIFIED MAHALANOBIS FILTERS FOR GROUPING POTTERY BY CHEMICAL COMPOSITION*

A statistical procedure for grouping pottery in provenance studies by chemical data is presented, which now is routinely in use in our laboratory. It is based on the Mahalanobis filter method and X² -statistics, and can be used for both establishing groups and assigning single sherds to already known groups, thus replacing principal components analysis or cluster analysis and avoiding their problems in grouping pottery. The new method is able to consider correlations, uncertainties of measurement and constant shifts of the data in case of dilution. In particular, considering dilution effects results in both a better assignment to and separation of reference groups and is also equivalent to the compositional data approach, if log-transformed data are used. Other distortions of data (e.g., mixing of clays) can also be considered.     

THE EFFICIENT COMPUTATION OF UNBIASED MAHALANOBIS DISTANCES AND THEIR INTERPRETATION IN ARCHAEOMETRY*

This paper argues for cross-validation to reduce bias in estimating Mahalanobis distances of individuals to groups, a particular problem with small sample sizes. Formulae for the efficient computation of cross-validated distances, which avoid excessive matrix inversion, are given. The use of Mahalanobis distances as measures of consistency, or as indications of outlying values, is described. The little-known technique of gamma plotting is outlined and discussed as an aid to interpreting distances in these terms. Both cross-validation and gamma plotting are illustrated in an example on marble composition.     

NEUTRON ACTIVATION ANALYSIS OF SIXTEENTH- AND SEVENTEENTH-CENTURY EUROPEAN BLUE GLASS TRADE BEADS FROM THE EASTERN GREAT LAKES AREA OF NORTH AMERICA*

Sixteenth- and seventeenth-century European blue glass trade beads from aboriginal sites in the eastern Great Lakes area of North America have been analysed non-destructively using low neutron dose instrumental neutron activation analysis, so that the beads could be returned to their keepers. Dark blue (cobalt-coloured) beads are readily separable from turquoise (copper-coloured) beads. Differences in the chemistries of the turquoise blue beads appear to be useful in separating glass beads from the two centuries. Low calcium, sixteenth-century turquoise beads tend to distintegrate by a leaching of the alkali metals.     

LEAD ISOTOPIC EVIDENCE FOR A MIXED PROVENANCE FOR ROMAN WATER PIPES FROM POMPEII*

Lead isotope analysis has been applied to the investigation of some Roman objects found in the town of Pompeii, consisting mostly of fistulae from the Augustan water supply system. The results of the analyses have produced ratios between 18.10 and 18.66 for ²⁰⁶Pb/²⁰⁴Pb, between 15.63 and 15.72 for ²⁰⁷Pb/²⁰⁴Pb and between 38.21 and 38.98 for ²⁰⁸Pb/²⁰⁴Pb. These data point to a fairly complex origin for the lead artefacts, probably involving several successive meltings and recyclings of a rather heterogeneous lead supply. The spread of lead isotope ratios can only be reconciled with a multiplicity of end‐members, at least three, but very probably more. There is one certain Sardinian ore, other indistinguishable Hercynian ores of Sardinia and/or Spain, and several different Alpine Mesozoic‐Tertiary mineralizations of the Mediterranean basin (Spain, Greece, Tuscany).     

MULTI‐METHOD MARBLE PROVENANCE DETERMINATIONS: THE CARRARA MARBLES AS A CASE STUDY FOR THE COMBINED USE OF ISOTOPIC,ELECTRON SPIN RESONANCE AND PETROGRAPHIC DATA*

A multi‐method approach, based on petrography, stable isotope data and electron spin resonance spectroscopy for assigning the provenance of white marbles, is presented. A total of 11 experimental variables has been used, including the quantitative measurement of the sample colour and its homogeneity. On this basis we attempt to distinguish the three main quarrying basins of the Carrara district, that is, Torano, Miseglia and Colonnata. Such discrimination, extremely uncertain on the basis of the single techniques, may be performed with acceptable confidence’ using a properly selected subset of six petrographic, isotopic and spectroscopic variables. The final resubstitution and jackknifed re‐assignment rates are, respectively, 85% and 81%. Inclusion of the remaining five variables into the classification rule does not improve the results, but simply increases data overinterpretation. The practical possibility of using such an approach for more general provenancing problems is considered.     

RAW MATERIALS OF GLASS FROM AMARNA AND IMPLICATIONS FOR THE ORIGINS OF EGYPTIAN GLASS*

Analysis has been conducted on 19 blue glasses from Amarna in Middle Egypt dated to around 1350 BC. The results suggest that these glasses fall into two distinct types: cobalt coloured glasses with a natron based alkali made from local Egyptian materials, and copper coloured glasses with a plant ash alkali, which follow a Mesopotamian tradition of glass making. It is suggested that at least some of this copper/plant ash glass is imported into Egypt during the Amarna period despite extensive local production of cobalt/natron glass. Existing analyses (Lilyquist and Brill 1995) of the earliest glass from the reign of Tuthmosis III (c. 1450 BC) suggest that during this period the same two types of glass are present. Local Egyptian cobalt and natron in these early glasses implies that, despite the lack of archaeological evidence for production sites, glass was produced from its raw materials in Egypt as early as the reign of Tuthmosis III.     

DIRECT EVIDENCE OF PRIMARY GLASS PRODUCTION IN LATE BRONZE AGE AMARNA,EGYPT

This paper presents direct archaeological evidence for the primary production of glass at the LBA site of Tell el‐Amarna, in the form of numerous finds of semi‐finished glass. The diagnostic microstructural and chemical composition of these finds is presented alongside macroscopically similar finds, of shapeless lumps of finished white glass. The semi‐finished glass was found to contain numerous inclusions of residual quartz and newly formed lime‐rich crystal phases, but no added colorant. However, several samples of semi‐finished glass have antimony oxide levels comparable to those of finished white glass, suggesting that the opacifier was added to the initial glass‐making batch. The results are discussed in comparison with the evidence for glass‐making from Qantir – Pi‐Ramesse, identifying some close technical similarities, which indicate that the same technological processes were used at both sites for the production of glass.     

CLAY RESOURCES AND TECHNICAL CHOICES FOR NEOLITHIC POTTERY (CHALAIN,JURA, FRANCE): CHEMICAL,MINERALOGICAL AND GRAIN‐SIZE ANALYSES*

Many authors have considered pottery manufacturing constraints and sociocultural elements as factors in change in past civilizations over time. The main issue of this research is to better understand the reasons for changes, or choices, in pottery raw materials. The very precise and detailed stratigraphy and cultural succession of occupations is based on dendrochronological data from the lake‐dwelling sites of Chalain (Jura, France). Petrographic, palaeontological and chemical analyses were used to determine the nature and origins of the raw materials used by the Neolithic potters. Stratigraphy and dendrochronological data were used to reconstruct in detail the evolution dynamics of fabric changes. Several raw material sources were identified for many of the pottery groups. Each of them was sampled for qualitative experimental tests of pottery forming. The experimental results show a high variability between the sediments tested. This variability was quantitatively estimated by XRF, XRD, the Rietveld method, calcium carbonate quantification and laser grain‐size analyses of matrices, indirect measures of plasticity. These analytical results allow a better understanding of the differences observed in the experimental tests. On the basis of these experimental and analytical results, changing parameters such as pottery manufacturing constraints, mineralogical characteristics of raw materials and sociocultural factors are considered. In conclusion, all the social and technical parameters, in each archaeological context, must be taken into account for a better understanding of the changes occurring throughout the chronological sequence.