Statistical properties of Bibliometric indicators: Research group indicator distributions and correlations

In this article we present an empirical approach to the study of the statistical properties of bibliometric indicators on a very relevant but not simply "available" aggregation level: the research group. We focus on the distribution functions of a coherent set of indicators that are used frequently in the analysis of research performance. In this sense, the coherent set of indicators acts as a measuring instrument. Better insight into the statistical properties of a measuring instrument is necessary to enable assessment of the instrument itself. The most basic distribution in bibliometric analysis is the distribution of citations over publications, and this distribution is very skewed. Nevertheless, we clearly observe the working of the central limit theorem and find that at the level of research groups the distribution functions of the main indicators, particularly the journal-normalized and the field-normalized indicators, approach normal distributions. The results of our study underline the importance of the idea of "group oeuvre," that is, the role of sets of related publications as a unit of analysis.