Impact Factors and the Central Limit Theorem
نویسنده
چکیده
We explore the relevance of the celebrated Central Limit Theorem (CLT) of statistics to citation averages, namely, Impact Factors (IF). The CLT predicts that, first, due to random fluctuations, the range of IF values that are statistically available to a journal of size n, follows a 1/ √ n behavior. Large journals (high-n), whose IF’s vary within a narrower range, are thus penalized in IF rankings because they cannot achieve high IF’s. Second, a scale-dependent stratification of journals is expected from the CLT in IF rankings, whereby small journals occupy the top, middle, and bottom ranks; mid-sized journals occupy the middle ranks; and very large journals converge to a single IF value characteristic of the wider population of papers being sampled. Third, we apply the CLT to arrive at the ‘Impact Factor uncertainty relation,’ a mathematical expression for the range of IF values expected at a given journal size. We have confirmed all these three predictions of the CLT by analyzing the complete set of 166,498 journals listed in the 1997–2016 Journal Citation Reports (JCR) of Clarivate Analytics, the top-cited portion of 276,000 physics papers published in 2014–2015, as well as the citation distributions of an arbitrarily sampled list of physics journals. We have also used the Impact Factor uncertainty relation to explain the individual IF variations from year to year for the ∼13,000 unique journals in the 1997–2016 period. We conclude that the CLT—via the Impact Factor uncertainty relation—is a good predictor of the range of IF values observed in actual journals, while sustained deviations from the expected IF range is a mark of true, i.e., non-random, citation impact. Due to the strength of scale dependent effects, Impact Factor rankings are misleading unless one compares like-sized journals or adjusts for these effects, and we suggest one way to do that here.
منابع مشابه
The Local Limit Theorem: A Historical Perspective
The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملDensity Estimators for Truncated Dependent Data
In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...
متن کاملIndividual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state
The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing m-almost everywhere convergence, where m...
متن کاملA central limit theorem for random ordered factorizations of integers
Write an integer as finite products of ordered factors belonging to a given subset P of integers larger than one. A very general central limit theorem is derived for the number of ordered factors in random factorizations for any subset P containing at least two elements. The method of proof is very simple and relies in part on Delange’s Tauberian theorems and an interesting Tauberian technique ...
متن کامل