Journal ArticleDOI
Testing for multivariate normality via univariate tests: A case study using lead isotope ratio data
Mike Baxter,N. H. Gale +1 more
TLDR
In this paper, 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; this is not an optimal approach, but is sufficient in the cases considered to suggest that fields are, in fact, "non-normal".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'....read more
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Journal ArticleDOI
Metal provenancing using isotopes and the Oxford archaeological lead isotope database (OXALID)
Zofia A. Stos-Gale,N. H. Gale +1 more
TL;DR: The lead isotope database (OXALID) as mentioned in this paper was created at the University of Oxford between 1975 and 2002, at first in the Geological Age and Isotope Research Laboratory, later in the Isotrace Laboratory based in the Department of Nuclear Physics, and eventually part of the Research Laboratory of Archaeology and the History of Art.
Journal ArticleDOI
Invariant tests for multivariate normality: a critical review
TL;DR: A synopsis of affine invariant tests of the hypothesis that the unknown distribution of a d-dimensional random vector X is some nondegenerate d-variate normal distribution is given in this article.
MonographDOI
Beyond Provenance : New Approaches to Interpreting the Chemistry of Archaeological Copper Alloys
TL;DR: Beyond Provenance as discussed by the authors considers the trace element composition of the metal, the alloying elements, and the lead isotopic composition, showing how a combination of these aspects, along with archaeological context and typology, can reveal much more about the life history of such artefacts, expanding considerably upon the rather limited ambition of knowing where the ore was extracted.
Journal ArticleDOI
Archaeology, Science-Based Archaeology and the Mediterranean Bronze Age Metals Trade
TL;DR: The underpinnings of science-based archaeology may conflict with social or behavioural factors uns... as discussed by the authors, who often seem either sceptical of science based archaeology or baffled by its results.
Journal ArticleDOI
Stable Lead Isotope Studies of Black Sea Anatolian Ore Sources and Related Bronze Age and Phrygian Artefacts from Nearby Archaeological Sites. Appendix: New Central Taurus Ore Data
TL;DR: The accumulated published database of stable lead isotope analyses of ore and slag specimens taken from Anatolian mining sites that parallel the Black Sea coast has been augmented with 22 additional analyses of such specimens carried out at the National Institute of Standards and Technology, Multivariate statistical analysis has been used to divide this composite database into five separate ore source groups as mentioned in this paper.
References
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Journal ArticleDOI
Measures of multivariate skewness and kurtosis with applications
TL;DR: In this article, the authors developed measures of multivariate skewness and kurtosis by extending certain studies on robustness of the t statistic, and the asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test for multivariate normality is proposed.
Journal ArticleDOI
A Suggestion for Using Powerful and Informative Tests of Normality
TL;DR: For testing that an underlying population is normally distributed the skewness and kurtosis statistics, √b 1 and b 2, and the D'Agostino-Pearson K 2 statistic that combines these two statistics have been shown to be powerful and informative tests.
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An Extension of Shapiro and Wilk's W Test for Normality to Large Samples
TL;DR: Shapiro and Wilk's (1965) W statistic as discussed by the authors provides the best omnibus test of normality, but is currently limited to sample sizes between 3 and 50.
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Approximating the Shapiro-Wilk W-test for non-normality
TL;DR: In this paper, a new approximation for the coefficients required to calculate the Shapiro-Wilk W-test is derived, which is easy to calculate and applies for any sample size greater than 3.
Journal ArticleDOI
Some Techniques for Assessing Multivarate Normality Based on the Shapiro-Wilk W
TL;DR: In this paper, the authors extend the W test to plots of squared radii, and extend the treatment to subsets of variates, and show that W test provides a set of univariate test statistics which show low correlation even when the parent variates are quite highly correlated.