Turning the tables in citation analysis one more time: principles for comparing sets of documents

We submit newly developed citation impact indicators based not on arithmetic averages of citations but on percentile ranks. Citation distributions are-as a rule-highly skewed and should not be arithmetically averaged. With percentile ranks, the citation score of each paper is rated in terms of its percentile in the citation distribution. The percentile ranks approach allows for the formulation of a more abstract indicator scheme that can be used to organize and/or schematize different impact indicators according to three degrees of freedom: the selection of the reference sets, the evaluation criteria, and the choice of whether or not to define the publication sets as independent. Bibliometric data of seven principal investigators (PIs) of the Academic Medical Center of the University of Amsterdam are used as an exemplary dataset. We demonstrate that the proposed family indicators [R(6), R(100), R(6, k), R(100, k)] are an improvement on averages-based indicators because one can account for the shape of the distributions of citations over papers.