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Visualisation and permutation methods for archaeological data analysis

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Abstract

Archaeologists routinely analyse bivariate data, whether in raw form or as output from principal components or discriminant function analyses. Often, the aim is to test hypotheses regarding the relationships between two or more groups of data. This paper demonstrates two techniques that are rarely used in archaeology yet, together, refine the presentation and testing of such relationships. Confidence ellipses provide statistically meaningful summaries of location and dispersion, and allow the analyst to judge the feasibility of hypotheses. Permutation tests provide analogues of parametric statistics but do not require the sampling or distributional assumptions that such tests demand; further to this, they have greater statistical power than non-parametric statistics. The value of these two methods in combination is illustrated via a case study of stable isotope ratio data.

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Acknowledgments

We would like to thank Ken Kahn of Oxford University Computing Services for bringing to our attention the article by Cobb (2007), and for valuable discussions of the pedagogical value of simulation methodologies. The comments of two AAS reviewers improved and clarified several aspects of the paper.

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Authors and Affiliations

  1. Archaeology, Classics and Egyptology, University of Liverpool, Hartley Building, Brownlow Street, Liverpool, L69 3GS, UK

    Matt Grove & Jessica Pearson

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  1. Matt Grove
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  2. Jessica Pearson
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Corresponding author

Correspondence to Matt Grove.

Electronic supplementary material

Below is the link to the electronic supplementary material.

ESM 1

(M 2.74 kb)

ESM 2

(M 4.98 kb)

ESM 3

(M 5.72 kb)

Note on Supplementary Materials

The data used in the above analyses is provided as a supplementary spreadsheet, Data.xlsx. In addition, three appendices are provided that contain MATLAB code for drawing the ellipses (ellipses.m, Appendix 1), performing the one-tailed permutation tests on the standard deviations (SDs.m, Appendix 2), and performing the two-tailed permutation tests on means (means.m, Appendix 3). Once the data in Sheet 2 of Data.xlsx have been loaded into MATLAB as a matrix labelled ‘data’, the .m files can be added to the MATLAB search path and called by typing, for example:

>> run ellipses

In the command window (note that MATLAB is case sensitive). This will initiate the full procedure in each case, including plotting of the results.

ESM 4

(DOC 20 kb)

XLSX 5

(XLSX 9.22 kb)

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Grove, M., Pearson, J. Visualisation and permutation methods for archaeological data analysis. Archaeol Anthropol Sci 6, 319–328 (2014). https://doi.org/10.1007/s12520-013-0158-z

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  • DOI: https://doi.org/10.1007/s12520-013-0158-z

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