Skip to main content
SpringerLink
Log in
Book cover

Dictionary of Mathematical Geosciences pp 637–642Cite as

U

  • Chapter
  • First Online:

  • 1063 Accesses

Abstract

Analysis of variance (ANOVA) is a method of decomposing the total variation displayed by a set of observations (as measured by the sums of squares of differences from the mean) into components associated with defined sources of variation. The relative magnitude of the contribution of each source to the overall observed total variation may thereby be determined. The technique was introduced by the English statistician, (Sir) Ronald Alymer Fisher (1890–1962) in the early 1920s and was widely taken up following later publication of Fisher (1925a). The technique was first introduced into geology by the American statistician, Churchill Eisenhart (1913–1994) (Eisenhart 1935). Classical applications include the investigation of whether a statistically significant difference exists between samples of nominally similar composition (Eisenhart 1935), and the magnitude of variation introduced by different human operators in determination of physical sample composition by modal analysis, determination of grain size, shape, orientation, density, porosity, etc. (Griffiths and Rosenfeld 1954). More recently, it has been widely used in the estimation of relative magnitudes of sources of sampling and analytical (chemical) variance in regional- or local-scale environmental geochemical surveys (Miesch 1967a, b, 1976a, b; Garrett and Goss 1979; Thompson and Ramsay 1995; Ramsay et al. 1995). Garrett and Goss (1980a, b) provided a program for analysis of variance of unbalanced nested sampling designs (UANOVA); see also Goss and Garrett (1978).

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   229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   299.99
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

Bibliography

  • AGTERBERG, F.P. (1990). Automated stratigraphic correlation. Developments in palaeontology and stratigraphy 13. Amsterdam, Elsevier.

    Google Scholar 

  • ANALYTICAL METHODS COMMITTEE (2003). Terminology – the key to understanding analytical science. Part 1: Accuracy, precision and uncertainty. Royal Society of Chemistry AMC Technical Brief 13, London [online: www.rsc.org/Membership/Networking/InterestGroups/ Analytical/ AMC/TechnicalBriefs.asp].

  • BAUMGARTNER, P.O. (1984). Comparison of unitary associations and probabilistic ranking and scaling as applied to Mesozoic radiolarians. Computers & Geosciences, 10, 167–183.

    Article  Google Scholar 

  • BLACKMAN, R.B. and TUKEY, J.W. (1958). The measurement of power spectra from the point of view of communications engineering. Bell System Technical Journal, 37, 185–282, 485–569.

    Article  Google Scholar 

  • BOWLEY, A.L. (1897). Relations between accuracy of an average and that of its constituent parts. Journal of the Royal Statistical Society, 60, 855–866.

    Google Scholar 

  • BULAND, R. (1976). The mechanics of locating earthquakes. Bulletin of the Seismological Society of America, 66, 173–187.

    Google Scholar 

  • BULAND, R. (1986). Uniform reduction error analysis. Bulletin of the Seismological Society of America, 76, 217–230.

    Google Scholar 

  • BUTTKUS, B. (1991). Spektralanalyse und Filtertheorie in der angewandten Geophysik. Berlin, Springer-Verlag.

    Book  Google Scholar 

  • CAMINA, A.R. and JANACEK, G.J. (1984). Mathematics for seismic data processing and interpretation. London, Graham and Trotman.

    Book  Google Scholar 

  • CHAYES, F. (1949). On correlation in petrography. Journal of Geology, 57, 239–254.

    Article  Google Scholar 

  • DAVENPORT, C.B. (1899). Statistical methods: with special reference to biological variation. London, Chapman and Hall.

    Book  Google Scholar 

  • DORIAN, J.P. (1983). Application of a mineral resource assessment technique to developing countries: A revision of the unit regional value concept. [Masters dissertation], Department of Mineral and Energy Economics, West Virginia University, Morgantown, WV.

    Google Scholar 

  • DORIAN, J.P. and CLARK, A.L. (1986). Value of tectonic regions in the United States. Mathematical Geology, 18, 375–400.

    Article  Google Scholar 

  • DORIAN, J.P. and JOHNSON, C. (1984). A mineral resource assessment technique for developing countries: The unit regional production value concept. Materials and Society, 8, 83–95.

    Google Scholar 

  • EISENHART, C. (1935). A test for the significance of lithological variations. Journal of Sedimentary Petrology, 5, 137–145.

    Google Scholar 

  • EVERITT, B.S. (2002). The Cambridge dictionary of statistics. 2nd edn., Cambridge, Cambridge University Press.

    Google Scholar 

  • FISHER, R.A. (1925a). Statistical methods for research workers. Edinburgh, Oliver and Boyd.

    Google Scholar 

  • GARRETT, R.G. and GOSS, T.I. (1979). The evaluation of sampling and analytical variation in regional geochemical surveys. In: WATTERSON, J.R. and THEOBALD, P.K. (eds.). Geochemical Exploration 1978. Ontario, Association of Exploration Geochemists, 371–383.

    Google Scholar 

  • GARRETT, R.G. and GOSS, T.I. (1980a). The statistical appraisal of survey effectiveness in regional geochemical surveys for Canada’s uranium reconnaissance program. Journal of the International Association for Mathematical Geology, 12, 443–458.

    Article  Google Scholar 

  • GARRETT, R.G. and GOSS, T.I. (1980b). UANOVA: A FORTRAN IV program for unbalanced nested analysis of variance. Computers & Geosciences, 6, 35–60.

    Article  Google Scholar 

  • GEUX, J. and DAVAUD, E. (1984). Unitary association method: use of graph theory and computer algorithm. Computers & Geosciences, 10, 69–96.

    Article  Google Scholar 

  • GOLDBERGER, A.S. (1962). Best linear unbiased prediction in the generalized linear regression model. Journal of the American Statistical Association, 57, 369–375.

    Article  Google Scholar 

  • GOOGLE RESEARCH (2012). Google Books Ngram Viewer (v. 2.0) [online: https://books.google.com/ ngrams/info].

  • GORDON, T. and MARTIN, G. (1974). File management systems and geological field data. In: Computer use in projects of the Geological Survey of Canada. Geological Survey of Canada Paper 74-60. Ottawa, Geological Survey of Canada, 23–28.

    Google Scholar 

  • GOSS, T.I. and GARRETT, R.G. (1978). A new unbalanced nested ANOVA model in geology – a down-to-earth design. In: Proceedings of the ASA Statistical Computing Section. Alexandria, VA, American Statistical Association, 360–365.

    Google Scholar 

  • GRIFFITHS, J.C. (1967a). Unit regional value as basis for decision-making in selecting an exploration strategy [abstract]. AAPG Bulletin, 51, 467.

    Google Scholar 

  • GRIFFITHS, J.C. (1967b). Unit regional value concept and its application to Kansas [abstract]. AAPG Bulletin, 51, 1688.

    Google Scholar 

  • GRIFFITHS, J.C. (1978a). Mineral resource assessment using the unit regional value concept. Journal of the International Association for Mathematical Geology, 10, 441–472.

    Article  Google Scholar 

  • GRIFFITHS, J.C. (1978b). Some alternate exploration strategies. In: MERRIAM, D.F. (ed.). Geology Contribution 5. Geomathematics: Past, present, and prospects. Syracuse, NY, Syracuse University, 23–36.

    Google Scholar 

  • GRIFFITHS, J.C. and ROSENFELD, M.A. (1954). Operator variation in experimental research. Journal of Geology, 62, 74–91.

    Article  Google Scholar 

  • GUBBINS, D. (2004). Time series analysis and inverse theory for geophysicists. Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • GUEX, J. (1991). Biochronological correlations. Berlin, Springer-Verlag.

    Book  Google Scholar 

  • HAMILTON, W.R. (1849). On quaternions; or on a new system of imaginaries in algebra [arts. 71–81]. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, ser. 3, 34, 425–439.

    Google Scholar 

  • HAMILTON, W.R. [edited by D.R. WILKINS, D.R.] (2000). On quaternions; or on a new system of imaginaries in algebra [Originally published in 18 parts in The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, ser. 3. v. 25–36 (1844–60); online: http://www.maths.tcd.ie/ pub/HistMath/People/Hamilton/OnQuat/OnQuat.pdf].

  • HEAVISIDE, O. ( 1892b). Electrical papers. v. 1. London, Macmillan.

    Google Scholar 

  • HRUŠKA, J. (1976). Current data-management systems: Problems of application in economic geology. Computers & Geosciences, 2, 299–304.

    Article  Google Scholar 

  • HURLEY, P.M. (1950). Distribution of radioactivity in granites and possible relation to helium age measurement. Geological Society of America Bulletin, 61, 1–8.

    Article  Google Scholar 

  • JEFFREYS, H. (1932). An alternative to the rejection of observations. Proceedings of the Royal Society, London, ser. A, 137, 78–87.

    Google Scholar 

  • JEFFREYS, H. (1939). Theory of probability. Oxford, Clarendon Press.

    Google Scholar 

  • JOURNEL, A.G. and HUIJBREGTS, C. J. (1978). Mining geostatistics. London, Academic Press.

    Google Scholar 

  • KAISER, J.F. (1963). Design methods for sampled data filters. In: CRUZ, J.B. Jr. and HOFER, J.C. (eds.). Proceedings. First Annual Allerton Conference on Circuit and System Theory. Nov. 15–17, 1963, Monticello, Illinois. Urbana-Champaign, Department of Electrical Engineering, University of Illinois, 221–236.

    Google Scholar 

  • KING, T. (1996). Quantifying nonlinearity and geometry in time series of climate. Quaternary Science Reviews, 15, 247–266.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1936a). Application of logarithmic moments to size frequency distributions of sediments. Journal of Sedimentary Petrology, 6, 35–47.

    Google Scholar 

  • KRUMBEIN, W.C. and GRAYBILL, F.A. (1965). An introduction to statistical models in geology. New York, NY, McGraw-Hill.

    Google Scholar 

  • LAFFITTE, P. (1968). L’informatique géologique et la terminologie [Geological data processing and terminology]. Mineralium Deposita, 3, 187–196.

    Article  Google Scholar 

  • LAGRANGE, J.-L. (1776). Mémoire sur l’utilité de la méthod de prendre le milieu entre les résultats de plusiers observations. [Memoir on the usefulness of taking the centre of the results of many observations]. Miscellanea Taurinensia, 5, 167–232.

    Google Scholar 

  • LAGRANGE, J.-L. (1788). Méchanique analytique [Analytical mechanics]. Paris, Desaint.

    Google Scholar 

  • LAWRENCE, P.L. (1958). Comments on “The moveout filter”. Geophysics, 23, 854–857.

    Article  Google Scholar 

  • LOEWY, A. (1900). Ueber Scharen reeller quadratischer und Hermitescher Formen [On overlapping of real square and Hermitian forms]. Journal für die reine und angewandte Mathematik, 122, 53–72.

    Google Scholar 

  • LOVEJOY, S. and SCHERTZER, D. (2007). Scaling and multifractal fields in the solid earth and topography. Nonlinear Processes in Geophysics, 14, 465–502.

    Article  Google Scholar 

  • MATHERON, G. (1969). Le Krigeage Universel: Recherche d’estimateurs optimaux en présence d’une dérive. Fascicule 1 [Universal kriging: The search for optimal estimators in the presence of drift. Part I]. Les cahiers du Centre de Morphologie Mathématique, Fontainebleu, École des Mines de Paris.

    Google Scholar 

  • MATHERON, G. (1970). La théorie des variables régionalisées et ses applications. Fascicule 5 [The theory of regionalised variables and its applications. Part 5]. Fontainebleau, Centre de Géostatistique, École des Mines.

    Google Scholar 

  • McBRATNEY, A.B. and WEBSTER, R. (1983). Optimal interpolation and isarithmic mapping of flood deposits. Environmental Geology and Water Sciences, 11, 95–106.

    Google Scholar 

  • McKENZIE, D.P. (1969). The relation between fault plane solutions for earthquakes and the directions of the principal stresses. Bulletin of the Seismological Society of America, 59, 591–601.

    Google Scholar 

  • METROPOLIS, N. and ULAM, S. (1949). The Monte Carlo method. Journal of the American Statistical Association, 44, 335–341.

    Article  Google Scholar 

  • MILLER, J. (ed.) (2015a). Earliest known uses of some of the words of mathematics [online: http://jeff560.tripod.com/mathword.html].

  • MILLER, R.L. and KAHN, J.S. (1962). Statistical analysis in the geological sciences. New York, John Wiley & Sons.

    Google Scholar 

  • MISSAN, H., COOPER, B.R., RABA’A, S.M. EL, GRIFFITHS, J.C. and SWEETWOOD, C. (1978). Workshop on areal value estimation. Journal of the International Association for Mathematical Geology, 10, 433–439.

    Google Scholar 

  • OHM, G.S. (1839). Bemerkungen über Combinationstöne und Stosse [Remarks on combination tones and pulses]. Poggendorff’s Annalen der Physik und Chemie, 47, 463–466.

    Article  Google Scholar 

  • PARK, J., LINDBERG, C.R. and VERNON, R.L. (1987). Multitaper spectral analysis of high-frequency seismograms. Journal of Geophysical Research, 92, 12675–12684.

    Article  Google Scholar 

  • PEARSON, K. (1896b). Mathematical contributions to the theory of evolution – On a form of spurious correlation which may arise when indices are used in the measurement of organs. Proceedings of the Royal Society, London, 60, 489–498.

    Google Scholar 

  • PEARSON, K. (1925). The fifteen constant bivariate frequency surface. Biometrika, 17, 268–313.

    Article  Google Scholar 

  • RAMSEY, M.H., ARGYRAKI, A. and THOMPSON, M. (1995). On the collaborative trial in sampling. Analyst, 120, 2309–2312.

    Article  Google Scholar 

  • ROBINSON, E.A. and TREITEL, S. (1964). Principals of digital filtering. Geophysics, 29, 395–404.

    Article  Google Scholar 

  • SAVARY, J. and GUEX, J. (1999). Discrete biochronological scales and unitary associations: Description of the BioGraph computer program. Mémoires de géologie 34, Lausanne, Section des sciences de la terre, Institut de géologie et paléontologie, Université de Lausanne.

    Google Scholar 

  • SCHERTZER, D. and LOVEJOY, S. (eds.) (1991). Non-linear variability in geophysics. Dordrecht, Kluwer.

    Google Scholar 

  • THOMPSON, M.. and RAMSEY, M.H. (1995). Quality concepts and practices applied to sampling – An exploratory study. Analyst, 120, 261–270.

    Article  Google Scholar 

  • VISTELIUS, A.B. (1980). Osnovy matematičeskoj geologii [Essential mathematical geology]. Leningrad, AN SSSR Izdatel’stvo nauk.

    Google Scholar 

  • WEBSTER, R. and OLIVER, M.A. (2001). Geostatistics for environmental scientists. Chichester, John Wiley & Sons.

    Google Scholar 

  • WEEDON, G.P. (2003). Time series analysis and cyclostratigraphy. Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • WHITE, J.E. (1958). Transient behaviour of patterns. Geophysics, 23, 26–43.

    Article  Google Scholar 

  • YULE, G.U. (1922). On the application of the χ2 method to association and contingency tables, with experimental illustrations. Journal of the Royal Statistical Society, 85, 95–104.

    Article  Google Scholar 

  • SCHERTZER, D., and LOVEJOY, S. (1987). Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. Journal of Geophysical Research: Atmospheres, 92 (D8), 9693–9714.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Earth Sciences, University College London, London, UK

    Richard J. Howarth

Authors
  1. Richard J. Howarth
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Howarth, R.J. (2017). U. In: Dictionary of Mathematical Geosciences . Springer, Cham. https://doi.org/10.1007/978-3-319-57315-1_21

Download citation

Publish with us

Policies and ethics

Search

Navigation