How fractional counting of citations affects the impact factor: Normalization in terms of differences in citation potentials among fields of science

The Impact Factors (IFs) of the Institute for Scientific Information suffer from a number of drawbacks, among them the statistics—Why should one use the mean and not the median?—and the incomparability among fields of science because of systematic differences in citation behavior among fields. Can these drawbacks be counteracted by fractionally counting citation weights instead of using whole numbers in the numerators? (a) Fractional citation counts are normalized in terms of the citing sources and thus would take into account differences in citation behavior among fields of science. (b) Differences in the resulting distributions can be tested statistically for their significance at different levels of aggregation. (c) Fractional counting can be generalized to any document set including journals or groups of journals, and thus the significance of differences among both small and large sets can be tested. A list of fractionally counted IFs for 2008 is available online at http://www.leydesdorff.net/weighted_if/weighted_if.xls The between-group variance among the 13 fields of science identified in the U.S. Science and Engineering Indicators is no longer statistically significant after this normalization. Although citation behavior differs largely between disciplines, the reflection of these differences in fractionally counted citation distributions can not be used as a reliable instrument for the classification.