  The ISI-Impact Factors 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 counting
citation weights fractionally instead of using whole numbers in the numerators?
(i) 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. (ii) Differences in the resulting distributions can be tested
statistically for their significance at different levels of aggregation. (iii)
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 Impact
Factors for 2008 is available online at
http://www.leydesdorff.net/weighted_if/weighted_if.xls. The in-between group
variance among the thirteen fields of science identified in the U.S. Science
and Engineering Indicators is not statistically significant after this
normalization. Although citation behavior differs largely between disciplines,
the reflection of these differences in fractionally counted citation
distributions could not be used as a reliable instrument for the
classification.
