In rankings by average metrics, smaller samples are more volatile: They can fluctuate to higher or lower scores more easily than larger samples, which are more stable. The range of these fluctuations depends on two factors: The disparity (variance) of values in the wider population, and sample size. We have used the celebrated Central Limit Theorem (CLT) of statistics to understand the behavior of citation averages (Impact Factors). We find that Impact Factors are strongly dependent on journal size. We explain the observed stratification in Impact Factor rankings, whereby small journals occupy the top, middle, {\it and} bottom ranks; mid-sized journals occupy the middle ranks; and very large journals converge to a single Impact Factor value. Further, we applied the CLT to develop an `uncertainty relation' for Impact Factors, which provides an upper ($f_{max}^{th}(n)$) and lower bound for a journal's Impact Factor given its size, $n$. We confirm the functional form of $f_{max}^{th}(n)$ by analyzing the complete set of 166,498 journals in the 1997--2016 Journal Citation Reports (JCR) of Clarivate Analytics, the top-cited portion of 345,177 papers published in 2014--2015 in physics, as well as the citation distributions of an arbitrarily sampled list of journals. We conclude that the Impact Factor `uncertainty relation' is a very good predictor of the range of Impact Factors observed for actual journals. Because the size-dependent effects are strong, Impact Factor rankings can be misleading, unless one compares like-sized journals or adjusts for these effects.
from cs updates on arXiv.org http://ift.tt/2Fs7epS
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