Field-normalization of impact factors: rescaling versus fractionally counted

Two methods for comparing impact factors and citation rates across fields of science are tested against each other using citations to the 3,705 journals in the Science Citation Index 2010 (CD-Rom version of SCI) and the 13 field categories used for the Science and Engineering Indicators of the US National Science Board. We compare (i) normalization by counting citations in proportion to the length of the reference list (1/N of references) with (ii) rescaling by dividing citation scores by the arithmetic mean of the citation rate of the cluster. Rescaling is analytical and therefore independent of the quality of the attribution to the sets, whereas fractional counting provides an empirical strategy for
normalization among sets (by evaluating the between-group variance). By the fairness test of Radicchi & Castellano (2012a), rescaling outperforms fractional counting of citations for reasons that we consider.