Comparison of Source and Artifact Characterization Data Using a Generalized Distance Measure

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Abstract
A major difficulty arises in sourcing studies when more than two or three elements are used in the comparison of artifacts with a number of potential sources. Multivariate statistical analysis can be used to define source groups and to allocate artifacts to their most likely sources. In this study of North Island, New Zealand, obsidian sources used in prehistory, the generalized distance measure of Mahalanobis and Rao is applied in three phases: first, to define source groups in terms of their inter- and intrasource variation using characterization data from X-ray fluorescence spectrography of five trace element constituents; second, the five-dimensional array was reduced to a three-dimensional figure for visual presentation; and finally, the highest probability of the association of an artifact data-set with that of a source group is used to allocate archaeologically derived material to its most likely source of raw material.