Citation averages, and Impact Factors (IFs) in particular, are sensitive to sample size. We apply the Central Limit Theorem (CLT) to IFs to understand their scale-dependent behavior. For a journal of $n$ randomly selected papers from a population of all papers, we expect from the CLT that its IF fluctuates around the population average $μ$, and spans a range of values proportional to $σ/\sqrt[]{n}$, where $σ^2$ is the variance of the population's citation distribution. The $1/\sqrt[]{n}$ dependence has profound implications for IF rankings: The larger a journal, the narrower the range around $μ$ where its IF lies. IF rankings therefore allocate an unfair advantage to smaller journals in the high IF ranks, and to larger journals in the low IF ranks. We expect a scale-dependent stratification of journals in IF rankings, whereby small journals occupy top, middle, and bottom ranks; mid-sized journals occupy middle ranks; and very large journals have IFs that asymptotically approach $μ$. We confirm these predictions by analyzing (i) 166,498 IF \& journal-size data pairs in the 1997--2016 Journal Citation Reports of Clarivate Analytics, (ii) the top-cited portion of 276,000 physics papers published in 2014--2015, and (iii) the citation distributions of an arbitrarily sampled list of physics journals. We conclude that the CLT is a good predictor of the IF range of actual journals, while sustained deviations from its predictions are a mark of true, non-random, citation impact. IF rankings are thus misleading unless one compares like-sized journals or adjusts for these effects. We propose the $Φ$ index, a rescaled IF adjusted for size, which can be generalized to account also for different citation practices across research fields. Our methodology applies also to citation averages used to compare research fields, university departments or countries in various rankings.
Why it has become more difficult to predict Nobel Prize winners: a bibliometric analysis of Nominees and Winners of the Chemistry and Physics Prizes (1901-2007)
Knowledge Independence Breeds Disruption but Limits Recognition
College of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）；Computer Science, Science Division, New York University Abu Dhabi（纽约大学阿布扎比分校科学系计算机科学）；College of Computer and Information Science, Chongqing Normal University（重庆师范大学计算机与信息科学学院）
