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Science and Society. Assessment of Research Read chapter Read first chapter

2016 | OriginalPaper | Chapter

4. Frequency and Rank Approaches to Research Production. Classical Statistical Laws

Author : Nikolay K. Vitanov

Published in: Science Dynamics and Research Production

Publisher: Springer International Publishing

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Abstract

We discuss several classical statistical laws that are important for understanding characteristics of research production and for its assessment. The statistical laws are grouped in such a way that the two much-used statistical approaches for the study of research systems and especially for the study of research publications (frequency approach and rank approach) are appropriately addressed. We begin with some remarks on the frequency and rank approaches to distributions and discuss why the frequency approach is much used in the natural sciences and the rank approach is widely used in the social sciences. Then the stable non-Gaussian distributions are described, and their importance for statistical methodology of research dynamics is emphasized. The laws of Lotka, Pareto, Zipf, Zipf–Mandelbrot, and Bradford are discussed from the point of view of their application to describing different aspects of scientific production. In addition to the discussion of statistical laws, we discuss two important effects: the concentration–dispersion effect (which reflects the separation of the researchers into a small group of highly productive ones and a large group of researchers with limited productivity) and the Matthew effect in science (which reflects the larger attention to the research production of the highly ranked researchers). In addition, we mention the invitation paradox (many papers accepted in highly ranked journals are not cited as much as expected) and the Ortega hypothesis (the big discoveries in science are supported by the everyday hard work of ordinary researchers). At the end of the chapter we discuss more general questions; relationships between the statistical laws and power laws as informetric distributions.

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previous chapter Additional Indexes and Indicators for Assessment of Research Production
next chapter Selected Models for Dynamics of Research Organizations and Research Production
Footnotes
1
Hyperbolic relationships are relationships of type \(m_i i^{\alpha } = \mathrm{const}\). Such relationships are frequently observed in different areas of science such as biology and physics. They exist also in the area of mathematical modeling of structures, processes, and systems in the area of social sciences.
 
2
Note that the Zipf law and the Zipf–Mandelbrot law give the rank of the researchers (or in general of some source of information) only approximately. The reason for this is that for example, there can be several researchers with the same production. If there are no researchers with the same production, then the laws are again approximate, because we silently changed the sums to integrals in order to obtain the approximate relationships for the final form of the laws.
 
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Metadata
Title
Frequency and Rank Approaches to Research Production. Classical Statistical Laws
Author
Nikolay K. Vitanov
Copyright Year
2016
Book
Science Dynamics and Research Production

Print ISBN: 978-3-319-41629-8

Electronic ISBN: 978-3-319-41631-1

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-41631-1_4

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