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dc.contributor.author
Limpert, Eckhard
dc.contributor.author
Stahel, Werner A.
dc.date.accessioned
2018-09-20T11:10:06Z
dc.date.available
2017-06-09T13:17:39Z
dc.date.available
2018-09-20T11:10:06Z
dc.date.issued
2011-07-14
dc.identifier.issn
1932-6203
dc.identifier.other
10.1371/journal.pone.0021403
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/38723
dc.identifier.doi
10.3929/ethz-b-000038723
dc.description.abstract
Background The Gaussian or normal distribution is the most established model to characterize quantitative variation of original data. Accordingly, data are summarized using the arithmetic mean and the standard deviation, by ± SD, or with the standard error of the mean, ± SEM. This, together with corresponding bars in graphical displays has become the standard to characterize variation. Methodology/Principal Findings Here we question the adequacy of this characterization, and of the model. The published literature provides numerous examples for which such descriptions appear inappropriate because, based on the “95% range check”, their distributions are obviously skewed. In these cases, the symmetric characterization is a poor description and may trigger wrong conclusions. To solve the problem, it is enlightening to regard causes of variation. Multiplicative causes are by far more important than additive ones, in general, and benefit from a multiplicative (or log-) normal approach. Fortunately, quite similar to the normal, the log-normal distribution can now be handled easily and characterized at the level of the original data with the help of both, a new sign, x/, times-divide, and notation. Analogous to ± SD, it connects the multiplicative (or geometric) mean * and the multiplicative standard deviation s* in the form * x/s*, that is advantageous and recommended. Conclusions/Significance The corresponding shift from the symmetric to the asymmetric view will substantially increase both, recognition of data distributions, and interpretation quality. It will allow for savings in sample size that can be considerable. Moreover, this is in line with ethical responsibility. Adequate models will improve concepts and theories, and provide deeper insight into science and life.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Public Library of Science
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/3.0/
dc.title
Problems with Using the Normal Distribution - and Ways to Improve Quality and Efficiency of Data Analysis
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 3.0 Unported
ethz.journal.title
PLoS ONE
ethz.journal.volume
6
en_US
ethz.journal.issue
7
en_US
ethz.journal.abbreviated
PLoS ONE
ethz.pages.start
e21403
en_US
ethz.size
8 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.nebis
006206116
ethz.publication.place
Lawrence, KS, USA
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
08778 - Stahel, Werner A. (Tit.-Prof.)
en_US
ethz.leitzahl.certified
08778 - Stahel, Werner A. (Tit.-Prof.)
ethz.date.deposited
2017-06-09T13:18:04Z
ethz.source
ECIT
ethz.identifier.importid
imp59364e53d23ee87235
ethz.ecitpid
pub:62383
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-31T15:16:15Z
ethz.rosetta.lastUpdated
2021-02-15T01:49:23Z
ethz.rosetta.versionExported
true
ethz.COinS
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