| Univariate statistical analysis of environmental (compositional) data: problems and possibilities. | |
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MedLine Citation:
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PMID: 19740525 Owner: NLM Status: MEDLINE |
Abstract/OtherAbstract:
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For almost 30 years it has been known that compositional (closed) data have special geometrical properties. In environmental sciences, where the concentration of chemical elements in different sample materials is investigated, almost all datasets are compositional. In general, compositional data are parts of a whole which only give relative information. Data that sum up to a constant, e.g. 100 wt.%, 1,000,000 mg/kg are the best known example. It is widely neglected that the "closure" characteristic remains even if only one of all possible elements is measured, it is an inherent property of compositional data. No variable is free to vary independent of all the others. Existing transformations to "open" closed data are seldom applied. They are more complicated than a log transformation and the relationship to the original data unit is lost. Results obtained when using classical statistical techniques for data analysis appeared reasonable and the possible consequences of working with closed data were rarely questioned. Here the simple univariate case of data analysis is investigated. It can be demonstrated that data closure must be overcome prior to calculating even simple statistical measures like mean or standard deviation or plotting graphs of the data distribution, e.g. a histogram. Some measures like the standard deviation (or the variance) make no statistical sense with closed data and all statistical tests building on the standard deviation (or variance) will thus provide erroneous results if used with the original data. |
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Authors:
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Peter Filzmoser; Karel Hron; Clemens Reimann |
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Publication Detail:
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Type: Journal Article; Research Support, Non-U.S. Gov't Date: 2009-09-08 |
Journal Detail:
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Title: The Science of the total environment Volume: 407 ISSN: 1879-1026 ISO Abbreviation: Sci. Total Environ. Publication Date: 2009 Nov |
Date Detail:
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Created Date: 2009-10-05 Completed Date: 2009-11-27 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 0330500 Medline TA: Sci Total Environ Country: Netherlands |
Other Details:
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Languages: eng Pagination: 6100-8 Citation Subset: IM |
Affiliation:
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Institute of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstrasse 8-10, Vienna, Austria. P.Filzmoser@tuwien.ac.at |
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| MeSH Terms | |
Descriptor/Qualifier:
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Environmental Monitoring
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methods* Models, Statistical* |
From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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