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GAMMA PLOTTING : ITS APPLICATION TO ARCHAEOLOGICAL PROBLEMS

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1. The Multivariate Outlier Problem

Outliers are individual values that are inconsistent with the rest of the group to which they are supposed to belong} the inconsistency «ay result from an error in measurement or from a failure to sample a single population. Outliers usually occur in archaeological data because of the difficulty of obtaining truly representative samples of ancient populations. As an example, consider the following typical case :

It is assumed that artefacts found in a particular area originate in local ore, clay or other source Material. However the presence of imported items is suspected, though there is nothing in the appearance of the artefacts to identify then. They have to be removed because their presence invalidates statistics based on the nean composition all items found in the area.

The outlier probleM in this context would be to find a way of identifying these stray items on the basis of the compositional data alone .

Sometimes several distinct populations are intermingled and we wish to separate them and estimate statistics for each group. This case has to be distinguished from the outlier problem where we assume a single population which has been 'contaminated' by a few individuals which are to be removed in order to concentrate on the main group.

If only one variable is involved the outlier problem can be approached using standard univariate techniques. Most compositional data, however, are multivariate in character, since they consist of several jointly distributed variables. This makes the identification of outliers more difficult because a multivarate observation can differ from the average by large amounts in a few variables or by small amounts in all variables and still be equally 'distant' from the mean.

Because of the intrinsic difficulty involved in identifying multivariate outliers, and because of their relative frequency in archaeological data, a plotting method which brings them to light is