Notes on the statistical analysis of some loomweights from Pompeii

Recent work, in the field, on the dimensions and weights of loomweights from excavations in Insula VI.I, Pompeii suggested – to our surprise – that there was structure in the form of evidence of bi-modality in the weights. The paper has two purposes. One is to illustrate a variety of statistical methods that were used to confirm the validity of our observations. The other is to discuss what the archaeological implications of this might be. A more general point is that if more attention is given to what are often regarded as “uninteresting” artefacts some interesting results may emerge - specifically, it can be asked whether loomweights have chronological significance for interpreting archaeological sites (at Pompeii at least)

An R library for compositional data analysis in archaeometry

Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussedGeologische 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

Notes on some statistical aspects of pottery quantification

The quantification of finds assemblages from excavations, as an aid to the comparative study of assemblages and sites, is a developing and increasingly important aspect of post-excavation analysis. In the area of pottery studies a major influence has been the work of Clive Orton and Paul Tyers, culminating in the recent release of the 'pie-slice' package for computer analysis. Much of the published literature is either highly technical, or of an expository nature which needs a great deal of the technical material and underlying assumptions to be taken on trust. The present paper is intended to be intermediate between these two levels. We address some of the more complex or less obvious issues involved in application of the pie-slice 'philosophy'. A worked example is given to highlight aspects of some of the assumptions and calculations involved. Some attention is given to what can be done outside the pie-slice package. One concern is the analysis of assemblages that have been quantified using estimated vessel equivalents (eves), but not in a manner that allows conversion to pottery information equivalents (pies) in the pie-slice package

Compositional analysis of archaeological glasses

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

Compositional data analysis in archaeometry

We shall call an n × p data matrix fully-compositional if the rows sum to a constant, and sub-compositional if the variables are a subset of a fully-compositional data set1. Such data occur widely in archaeometry, where it is common to determine the chemical composition of ceramic, glass, metal or other artefacts using techniques such as neutron activation analysis (NAA), inductively coupled plasma spectroscopy (ICPS), X-ray fluorescence analysis (XRF) etc. Interest often centres on whether there are distinct chemical groups within the data and whether, for example, these can be associated with different origins or manufacturing technologiesGeologische Vereinigung; Universitat de Barcelona, Equip de Recerca Arqueomètrica; 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

Compositional data analysis of archaeological glass: problems and possible solutions

Presentation in CODAWORK'03, session 4: Applications to archeometryGeologische Vereinigung; Universitat de Barcelona, Equip de Recerca Arqueomètrica; 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

Consequences of temperature and temperature variability on swimming activity, group structure, and predation of endangered delta smelt

The effects of water temperature on individual and group movement behaviour in prey fish can affect ecological interactions such as competition and predation, but how variability in temperature influence fish behaviour is less understood. Of particular concern is how increased warming in tidally fluctuating estuaries may impact the native and endangered delta smelt (Hypomesus transpacificus, Osmeridae). To help address this issue, we tested the effects of increased water temperature (fluctuating [17–21°C] and warm [21°C] acclimated treatments) on juvenile delta smelt individual and group behaviour, response to chemical alarm and predator cues, as well as capacity to evade predation. In addition, predation of delta smelt was tested in the presence of a dominant invasive competitor, Mississippi silversides (Menidia beryllina, Atherinopsidae), as well as comparative predation mortality on Mississippi silversides when isolated. After 7 days of increased temperature treatments, delta smelt in the warm treatment increased swimming velocity, decreased turning angle, and altered group structure with larger inter-individual distances compared to fish in the control (17°C) and fluctuating temperature treatments. Following conspecific and predator chemical alarm cues, delta smelt showed anti-predator responses. Control and fluctuating treatment fish responded to conspecific cues with increased swimming speeds, decreased inter-individual distances and near-neighbour distances, and, after 15 min, fish recovered back to baseline behaviours. In contrast, fish in the warm treatment had not recovered after 15 min, and swimming speeds were maintained at roughly 25 cm/s, close to maximum capabilities. Fish in control and fluctuating treatments showed minimal responses to predator cues, whereas delta smelt exposed to warm conditions significantly increased swimming speeds and decreased turning angle. Predation of delta smelt by largemouth bass (Micropterus salmoides, Centrarchidae) was greatest under the warm treatment, correlating with altered behaviours of delta smelt; however, predation of Mississippi silversides was greater than delta smelt, independent of temperature. This study provides novel insight into the group behaviour of delta smelt, their response to predation, and how prolonged exposure to elevated temperature may induce negative individual and group behaviours causing alterations in predator–prey dynamics. This work highlights the importance of testing ecologically realistic temperature fluctuations in experiments as delta smelt had significantly altered responses to elevated temperature, dependent on variability of warming