Differences in Impact of Scientific Publications: Some Indices Derived from a Citation Analysis

A mathematical model is introduced which describes citing as a probabilistic process, while taking into account that in general the probability for a paper to be cited decreases with age.

Abstract

A mathematical model is introduced which describes citing as a probabilistic process, while taking into account that in general the probability for a paper to be cited decreases with age. With the aid of the model it is possible to ascertain what differences in numbers of citations are to be considered statistically significant (i.e. not due to mere chance). Significant differences are supposed to reflect differences in 'impact' (i.e. differences in the overall judgement of the paper by the scientific community). The 'impact' of a paper is thought not only to be determined by its scientific significance, but also by such extrinsic factors as locale of the author, prestige of the journal in which the paper is published, and so on. A parameter is also introduced which measures the decay rate of citations. This parameter may be useful in making quantitative comparisons between the 'dynamics' of various scientific specialties. Finally, indices are proposed to measure the dissemination of scientific work.