Testing for multivariate normality via univariate tests: A case study using lead isotope ratio data

Abstract

Samples from ore bodies, mined for copper in antiquity, can be characterized by measurements on three lead isotope ratios. Given sufficient samples, it is possible to estimate the lead isotope field-a three-dimensional construct-that characterizes the ore body. For the purposes of estimating the extent of a field, or assessing whether bronze artefacts could have been made using copper from a particular field, it is often assumed that fields have a trivariate normal distribution. Using recently published data, for which the sample sizes are larger than usual, this paper casts doubt on this assumption. A variety of tests of univariate normality are applied, both to the original lead isotope ratios and to transformations of them based on principal component analysis; the paper can be read as a case study in the use of tests of univariate normality for assessing multivariate normality. This is not an optimal approach, but is sufficient in the cases considered to suggest that fields are, in fact, 'non-normal'. A direct test of multivariate normality confirms this. Some implications for the use of lead isotope ratio data in archaeology are discussed.