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Environmental Geology

, Volume 39, Issue 9, pp 1001–1014 | Cite as

Normal and lognormal data distribution in geochemistry: death of a myth. Consequences for the statistical treatment of geochemical and environmental data

  • C. Reimann
  • P. Filzmoser
Research article

Abstract

All variables of several large data sets from regional geochemical and environmental surveys were tested for a normal or lognormal data distribution. As a general rule, almost all variables (up to more than 50 analysed chemical elements per data set) show neither a normal or a lognormal data distribution. Even when different transformation methods are used more than 70 % of all variables in every single data set do not approach a normal distribution. Distributions are usually skewed, have outliers and originate from more than one process. When dealing with regional geochemical or environmental data normal and/or lognormal distributions are an exception and not the rule. This observation has serious consequences for the further statistical treatment of geochemical and environmental data. The most widely used statistical methods are all based on the assumption that the studied data show a normal or lognormal distribution. Neglecting that geochemcial and environmental data show neither a normal or lognormal distribution will lead to biased or faulty results when such techniques are used.

Key words Normal distribution Lognormal distribution Geochemistry Exploratory data analysis Multivariate normal distribution Robust methods Non-parametric methods Median 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • C. Reimann
    • 1
  • P. Filzmoser
    • 2
  1. 1.Geological Survey of Norway, N-7491 Trondheim, Norway e-mail: Clemens.Reimann@ngu.noNO
  2. 2.Department of Statistics, Probability Theory and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstr. 8–10, A-1040 Vienna, Austria e-mail: P. Filzmoser@tuwien.ac.atAT

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