Skip to main content
SpringerLink
Log in
Book cover

Techniques in Archaeological Geology pp 271–296Cite as

Statistics in Archaeological Geology

  • Chapter
  • First Online:

  • 1186 Accesses

Part of the book series: Natural Science in Archaeology ((ARCHAEOLOGY))

Abstract

Waltham (1994) considers statistics the most intensively used branch of mathematics in the earth sciences. His textbook, along with that of Robert Drennan, Statistics for Archaeologists (1996), is an excellent introduction to statistics appropriate for archaeological geology. Following Waltham, the definition of a statistic is simply an estimate of a parameter—mass, velocity, dimension, etc.—based upon a sample from a population. Unless that population is composed of a relatively small number of items or objects, then it is almost certain that estimates must be made of the populations using independently drawn samples. As archaeology is largely a study of population of “things,” reliable estimates of these collections are best made using statistical techniques. These techniques include parametric measures of central tendency and dispersion such as the mean, the standard deviation, and the variance.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Chebyshev’s Rule for Samples and Populations

    The Russian mathematician P.L. Chebyshev formalized the rule that holds for any data set. The first property of this rule states that 75 % of all observations will lie within two standard deviations of the mean; the second property states that ~90 % will lie within three standard deviations on both sides of the mean (Hassett and Weiss 1991:98). Recalling our discussion of the Z-score, its meaning now should be more apparent. Chebyshev’s rule gives us the means to constrain the variability inherent in our samples.

    For example, property three of this rule states that for any number, k, greater than 1, observations in a data set, at least 1 − 1/k 2 of the observations, must lie within k standard deviations of the mean.

References

  • Baxter MJ, Jackson CM (2001) Variable selection in artefact compositional studies. Archaeometry 43:253–268

    Article  Google Scholar 

  • Bayes T (1763) An essay towards solving a problem in the doctrine of chances. Philos Trans R Soc Lond 53:370–418, A postscript and a LaTec source file version of this paper are available at URL: http://www.york.ac.uk/depts/maths/histstat/essay.ps and http://www.york.ac.uk/depts/maths/histstat/essay.htm respectively

  • Bronk RC (1995) Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37(2):425–430

    Google Scholar 

  • Buck CE, Millard AR (eds) (2004) Tools for constructing chronologies: crossing disciplinary boundaries, vol 177, Lecture Notes in Statistics. Springer, London

    Google Scholar 

  • Cannon MD (2001) Archaeological relative abundance, sample size and statistical methods. J Archaeol Sci 28:185–195

    Article  Google Scholar 

  • Cowgill GL (1964) The selection of samples from large sherd collections. Am Antiq 29(4):467–473

    Article  Google Scholar 

  • Craddock PT, Cowell MR, Leese MN, Houghes MJ (1983) The trace element composition of polished flint axes as an indicator of source. Archaeometry 25:135–163

    Article  Google Scholar 

  • Davis JC (1986) Statistics and data analysis in geology. Wiley, New York

    Google Scholar 

  • de Bruin M, Korthoven TJM, van der Steen AJ, Huitman JPW, Duin RPW (1976) The use of trace element concentrations in the identification of objects. Archaeometry 18:75–83

    Article  Google Scholar 

  • Douglas MC (2000) An electron microprobe study of 19th century staffordshire glazes and pigments including those of the spode pottery works. Unpublished Masters thesis. University of Georgia, Athens

    Google Scholar 

  • Drennan RD (1996) Statistics for archaeologists. Plenum, New York

    Book  Google Scholar 

  • Dye TD (2004) Bayesian statistics for archaeologists. T. S. Dye & Colleagues, Archaeologists, Honolulu

    Google Scholar 

  • Flam FD (2014) The odds, continually updated. The New York Times, Science Times, 9-30-2014: D1–D2

    Google Scholar 

  • Fowkles EB, Gnanadesikan R, Kettenring JR (1988) Variable selection in clustering. J Classif 5:205–288

    Article  Google Scholar 

  • Garrison EG (1973) Alpha-recoils tracks for archaeological dating. Unpublished Master’s Thesis. The University of Arkansas. Fayatteville

    Google Scholar 

  • Garrison EG, McGimsey CR, Zinke OH (1978) Alpha‐recoil tracks in archaeological ceramic dating. Archaeometry 20(1):39–46

    Article  Google Scholar 

  • Gorsuch R (1984) Factor analysis. L. Erlbaum Associates, Hillsdale

    Google Scholar 

  • Hampton RE (1994) Introductory biological statistics. Wm. C. Brown Publishers, Dubuque

    Google Scholar 

  • Harbottle G (1976) Activation analysis in archaeology. Radiochemistry 3:33–72, The Chemical Society. London

    Article  Google Scholar 

  • Hawkes J (1995) Discovering statistics. Quant Publishing, Charleston

    Google Scholar 

  • Johnson NL, Leone FC (1964) Statistics and experimental design in engineering and the physical sciences, vol I. Wiley, New York

    Google Scholar 

  • Kempthorne O, Allamaras RR (1986) Errors and variability of observations. Methods of soil analysis. Part I. Agronomy-Soil Science Society of America, Madison, pp 1–31

    Google Scholar 

  • Kish L (1965) Survey sampling. Wiley, New York

    Google Scholar 

  • Klecka WR (1975) Discriminate analysis. In: Nie NH et al (eds) Statistical package for the social sciences (SPSS). McGraw-Hill, Englewood Cliffs, pp 434–467

    Google Scholar 

  • Kovarovic K, Aiello LC, Cardini A, Lockwood CA (2011) Discriminant function analyses in archaeology: are classification rates too good to be true? J Archaeol Sci 38:3006–3018

    Article  Google Scholar 

  • Krings M, Stone A, Schmitz RW, Krainitzi H, Stoneking M, Pääbo S (1997) Neanderthal DNA sequences and the origin of modern humans. Cell 90:19–30

    Article  Google Scholar 

  • Kuhn RD, Sempowski ML (2001) A new approach to dating the league of the Iroquois. Am Antiq 66:301–314

    Article  Google Scholar 

  • Kzanowski WJ (1988) Principles of multivariate analysis. Clarendon Press, Oxford

    Google Scholar 

  • Lazerwitz B (1968) Sampling theory and procedures in methodology in social research. McGraw-Hill, New York

    Google Scholar 

  • Leach F, Manley B (1982) Minimum Mahalanobis distance functions and lithic source characterization by multi-element analysis. N Z J Archaeol 4:77–109

    Google Scholar 

  • Levin SA (1992) The problem of pattern and scale in ecology. Ecology 73:1943–1967

    Article  Google Scholar 

  • Mulaik S (1972) The foundations of factor analysis. McGraw-Hill, New York

    Google Scholar 

  • Papageogiou I, Baxter MJ, Cau MA (2001) Model-based cluster analysis of artefact compositional data. Archaeometry 43:571–588

    Article  Google Scholar 

  • Picon M, Carre C, Cordoliani ML, Vicky M, Hernandez JC, Mignard MG (1975) Composition of the La Granfensengue, Banassac and Moutans Terra Sigillata. Archaeometry 17:191–199

    Article  Google Scholar 

  • Rapp G Jr, Albns J, Henrickson E (1984) Trace element discrimination of discrete sources of copper. In: Lambert JB (ed) Archaeological chemistry III. Am. Chem. Soc., Washington, DC, pp 273–293

    Chapter  Google Scholar 

  • de Sieveking G, Bush P, Ferguson J, Craddock PT, Hughes MJ, Cowell MR (1972) Prehistoric flint mines and their identification as sources as raw materials. Archaeometry 14:151–176

    Article  Google Scholar 

  • Singleton KL, Odell GH, Harris TM (1994) Atomic absorption spectrometry analysis of ceramic artefacts from a protohistoric site in Oklahoma. J Archaeol Sci 21:343–358

    Article  Google Scholar 

  • Sneath PHA, Sokal RR (1973) Numerical taxonomy: the principles and practice of numerical classification. W.F. Freeman, San Francisco

    Google Scholar 

  • Sokal RR, Rohlf FJ (eds) (1981) Biometry, 2nd edn. W.H. Freeman, New York. Spectroscopy of quartz grains as a tool for ceramic provenance. J Archaeol Sci 26(8):943–949

    Google Scholar 

  • Speakman et al (2011a)

    Google Scholar 

  • Speakman RJ, Little NC, Creel D, Miller MR, Iñañez JG (2011b) Sourcing ceramics with portable XRF spectrometers? A comparison with INAA using Mimbres pottery from the American Southwest. J Archaeol Sci 38:3483–3496

    Article  Google Scholar 

  • Starr JL, Parkin TB, Meisinger JJ (1995) Influence of sample-size on chemical and physical soil measurments. Soil Sci Soc Am J 59(3):713–719

    Article  Google Scholar 

  • Stuiver M, Reimer PJ, Braziunas TF (1998) High precision radiocarbon age calibration for terrestrial and marine samples. Radiocarbon 40(3):1041–1083

    Google Scholar 

  • Thomas DH (1976) Figuring anthropology. Holt, Rinehart and Winston, New York

    Google Scholar 

  • Tukey JW (1977) Exploratory data analysis. Addison-Wesley, Reading

    Google Scholar 

  • Vitali W, Franklin UM (1986) New approaches to the characterization and classification of cermics on the basis of their elemental composition. J Archaeol Sci 13:161–170

    Article  Google Scholar 

  • Waltham D (1994) Mathematics: a simple tool for geologists. Chapman and Hall, London

    Book  Google Scholar 

  • Ward G (1974) A systematic approach to the definition of sources of raw material. Archaeometry 16:55–63

    Article  Google Scholar 

  • Williams AN (2012) The use of summed radiocarbon probability distributions in archaeology: a review of methods. J Archaeol Sci 39(3):578–589

    Article  Google Scholar 

  • Hassett MJ, Weiss M (1991) Introductory statistics. Addison-Wesley, New York

    Google Scholar 

  • Hassett MJ, Weiss M (1993) Introductory statistics, 3rd edn. Addison-Wesley, New York

    Google Scholar 

  • Shott MJ (2010) Size dependence in assemblage analysis measure: essentialism, materialism and “SHE” analysis in archaeology. Am Antiq 75(4):886–906

    Article  Google Scholar 

  • Green RE, Krause J, Briggs AW, Maricic T, Stenzel U, Kircher M, Patterson N, Li H, Zhai W, Fritz MHY, Hansen NF (2010) A draft sequence of the Neandertal genome. Science 328(5979):710–722

    Article  Google Scholar 

  • Steier P, Rom W (2000) The use of Bayesian statistics for 14C dates of chronologically ordered samples: a critical analysis. Radiocarbon 42(2):183–198

    Google Scholar 

  • Ramsey CB (1995) Radiocarbon calibration and analysis of stratigraphy; the OxCal program. Radiocarbon 37(2):425–430

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geology, University of Georgia, Athens, Georgia, USA

    Ervan Garrison

Authors
  1. Ervan Garrison
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Garrison, E. (2016). Statistics in Archaeological Geology. In: Techniques in Archaeological Geology. Natural Science in Archaeology. Springer, Cham. https://doi.org/10.1007/978-3-319-30232-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30232-4_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30230-0

  • Online ISBN: 978-3-319-30232-4

  • eBook Packages: Social SciencesSocial Sciences (R0)

Publish with us

Policies and ethics

Search

Navigation