The Accuracy of Confidence Intervals for Field Normalised Indicators

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Abstract

When comparing the average citation impact of research groups, universities and countries, field normalisation reduces the influence of discipline and time. Confidence intervals for these indicators can help with attempts to infer whether differences between sets of publications are due to chance factors. Although both bootstrapping and formulae have been proposed for these, their accuracy is unknown. In response, this article uses simulated data to systematically compare the accuracy of confidence limits in the simplest possible case, a single field and year. The results suggest that the MNLCS (Mean Normalised Log-transformed Citation Score) confidence interval formula is conservative for large groups but almost always safe, whereas bootstrap MNLCS confidence intervals tend to be accurate but can be unsafe for smaller world or group sample sizes. In contrast, bootstrap MNCS (Mean Normalised Citation Score) confidence intervals can be very unsafe, although their accuracy increases with sample sizes.

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Is Open Access

Power-law distributions in empirical data

Cosma Rohilla Shalizi, Aaron Clauset, M. Newman (2007)

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.