Classification, Powerlaws, and the Logarithmic Transformation

[Loet Leydesdorff]

Classification, Powerlaws, and the Logarithmic Transformation

Loet Leydesdorff & Stephen Bensman

 <http://www.leydesdorff.net/log05/log05.pdf> <click here for the full text>

Abstract

Logarithmic transformation of the data has been recommended by the
literature in the case of highly skewed distributions such as those commonly
found in information science. The purpose of the transformation is to make
the data conform to the lognormal law of error for inferential purposes. How
does this transformation affect the initial analysis? We factor analyze and
visualize the citation environment of the Journal of the American Chemical
Society (JACS) before and after a logarithmic transformation. The
transformation strongly reduces the variance necessary for classificatory
purposes and therefore is counterproductive to the purposes of the
descriptive statistics. We recommend against the logarithmic transformation
when sets cannot be defined unambiguously. The intellectual organization of
the sciences is reflected in the curvilinear parts of the citation
distributions, while negative powerlaws fit excellently to the tails of the
distributions.

  _____

Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
 <mailto:loet at leydesdorff.net> loet at leydesdorff.net ;
<http://www.leydesdorff.net/> http://www.leydesdorff.net/


 <http://www.upublish.com/books/leydesdorff-sci.htm> The Challenge of
Scientometrics ;  <http://www.upublish.com/books/leydesdorff.htm> The
Self-Organization of the Knowledge-Based Society

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