The precision of the arithmetic mean, geometric mean and percentiles for citation data: An experimental simulation modelling approach
Mike Thelwall
TL;DR
This study uses extensive simulation to compare the precision of arithmetic mean, geometric mean, and percentile-based citation metrics, recommending the geometric mean for more reliable international comparisons.
Contribution
It provides a comprehensive simulation-based analysis of citation metrics, identifying the geometric mean as the most precise indicator for comparing citation impacts.
Findings
Geometric mean is the most precise citation indicator.
Percentile in top 50% is reliable for comparisons.
Percentile in top 1% is highly imprecise.
Abstract
When comparing the citation impact of nations, departments or other groups of researchers within individual fields, three approaches have been proposed: arithmetic means, geometric means, and percentage in the top X%. This article compares the precision of these statistics using 97 trillion experimentally simulated citation counts from 6875 sets of different parameters (although all having the same scale parameter) based upon the discretised lognormal distribution with limits from 1000 repetitions for each parameter set. The results show that the geometric mean is the most precise, closely followed by the percentage of a country's articles in the top 50% most cited articles for a field, year and document type. Thus the geometric mean citation count is recommended for future citation-based comparisons between nations. The percentage of a country's articles in the top 1% most cited is a…
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