Indices of Literature Dispersion Based on Qualitative Attributes

Abstract

The dispersion or ‘scatter’ of documents over some set of values of a document attribute is usually described by means of a frequency distribution. When the attribute is qualitative an order distribution can be defined, as in the usual descriptions of Bradford's law. A more succinct description is offered by an order statistic, such as Singleton's index. A novel order statistic, the ‘adapted Gini index’, is introduced and related to the conventional form of Bradford's law. Some simple properties of it are described. An alternative index of dispersion, not an order statistic, based on the relative entropy of the frequency distribution is also defined. For sets of bibliographies such indices themselves have distributions, and it is suggested that, in particular, the distribution pertaining to an indexed data base provides an objective characterization of the data base in so far as indexing terms have been applied to the items in it. A variety of experimental data is reported. This includes the distribution of two indices for samples of bibliographies taken from British Technology Index and Index Medicus, and studies of the variation of the indices with time when the attribute is that of journal title. Whether a new area of knowledge becomes less or more dispersed in its journals as it progresses depends in part on which index is chosen to represent the dispersion, and on whether a series of cumulative or cross‐section bibliographies is chosen.

Bradford ranking conventions and their application to a growing literature

“…Bradford graph: Any set of paired numeric values where the number-pairs comprise (1) a rank value attaching to a journal, and (2) a value of the cumulative sum of journal articles for journals ranked up to and including that rank value. 1 'periodical', to revert momentarily to the historical Bradfordian term.) For example, journals in the 'real-world' may split into subseries.…”

“…The primary concern of this paper is to draw attention to the need to specify the ranking convention used when Bradford data are presented and/or modelled. Subsidiary concerns are: (1) to identify what appear to be the main conventions that can be used; (2) to explore some of the effects of and relationships between them, with particular regard to the 'Groos droop' and 'Brookes hooks';and (3) to illustrate some of these effects in the context of an evolving journal literature in the humanities.…”

“…The study reported here arose from an awareness of the limitations of an earlier study by the author [1] in which an attempt was made to characterise literature growth, viewed in terms of the variation of literature dispersion with time, by means of single-valued functions applied to the distribution of journal articles over journals. (The early literature on the maser had been used as a test set for that purpose.)…”

Rational normalization of concentration measures

“…Otherwise stated, if we have a good concentration measure f (with values between 0 and 1) then the measure g = 1 -f is a good dispersion measure. So there is no need for a new theory of dispersion measures once a theory of concentration has been developed (see Heine (1978) and Egghe and Rousseau (1990) for a discussion about explicite relations between dispersion and concentration measures). Hence, in the sequel, we restrict our attention to concentration measures.…”