Page 168 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Unit 12: Research Report Writing

12.5.1 Laws of Bibliometrics Notes

One of the main areas in bibliometric research concerns the application of bibliometric laws.
The three most commonly used laws in bibliometrics are: Lotka’s law of scientific productivity,
Bradford’s law of scatter, and Zipf’s law of word occurrence.
Lotka’s Law

Lotka’s Law describes the frequency of publication by authors in a given field. It states that
“ . . . the number (of authors) making n contributions is about 1/n² of those making one; and
the proportion of all contributors, that make a single contribution, is about 60 percent”
(Lotka 1926, cited in Potter 1988). This means that out of all the authors in a given field, 60
percent will have just one publication, and 15 percent will have two publications (1/2² times
.60). 7 percent of authors will have three publications (1/3² times .60), and so on. According
to Lotka’s Law of scientific productivity, only six percent of the authors in a field will
produce more than 10 articles. Lotka’s Law, when applied to large bodies of literature over
a fairly long period of time, can be accurate in general, but not statistically exact. It is often
used to estimate the frequency with which authors will appear in an online catalog (Potter
1988).

Bradford’s Law
Bradford’s Law serves as a general guideline to librarians in determining the number of core
journals in any given field. It states that journals in a single field can be divided into three
parts, each containing the same number of articles: 1) a core of journals on the subject,
relatively few in number, that produces approximately one-third of all the articles, 2) a
second zone, containing the same number of articles as the first, but a greater number of
journals, and 3) a third zone, containing the same number of articles as the second, but a still
greater number of journals. The mathematical relationship of the number of journals in the
core to the first zone is a constant n and to the second zone the relationship is n². Bradford
expressed this relationship as 1:n:n². Bradford formulated his law after studying a bibliography
of geophysics, covering 326 journals in the field. He discovered that 9 journals contained 429
articles, 59 contained 499 articles, and 258 contained 404 articles. So it took 9 journals to
contribute one-third of the articles, 5 times 9, or 45, to produce the next third, and 5 times
5 times 9, or 225, to produce the last third. As may be seen, Bradford’s Law is not statistically
accurate, strictly speaking. But it is still commonly used as a general rule of thumb (Potter
1988).
Zipf’s Law
Zipf’s Law is often used to predict the frequency of words within a text. The Law states that
in a relatively lengthy text, if you “list the words occurring within that text in order of
decreasing frequency, the rank of a word on that list multiplied by its frequency will equal a
constant. The equation for this relationship is: r x f = k where r is the rank of the word, f is
the frequency, and k is the constant (Potter 1988). Zipf illustrated his law with an analysis of
James Joyce’s Ulysses. “He showed that the tenth most frequent word occurred 2,653 times,
the hundredth most frequent word occurred 265 times, the two hundredth word occurred 133
times, and so on. Zipf found, then that the rank of the word multiplied by the frequency of
the word equals a constant that is approximately 26,500” (Potter 1988). Zipf’s Law, again, is
not statistically perfect, but it is very useful for indexers.

12.5.2 Citation Analysis

Another major area of bibliometric research uses various methods of citation analysis in order
to establish relationships between authors or their work. Here is a definition of citation analysis,

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