Averaging and globalising quotients of informetric and scientometric data

Based on the particular case of the average impact factor of a subfield versus the impact factor of this subfield as a whole, the difference is studied between an average of quotients, denoted as AQ, and a global average, obtained as a quotient of averages, and denoted as GQ. In the case of impact factors, AQ becomes the average impact factor of a field, and GQ becomes its global impact factor. Many applications in the context of informetrics and scientometrics are given, e.g. the Price index, the text to reference ratio, ageing, the receptivity factor for foreign literature, journal price calculation, discipline influence scores, and fill-rates as measures of library performance, We strongly claim that, in most applications, the global average is the preferred one. It is also shown that, if geometric averages are used instead of arithmetic ones in the definition of AQ and GQ, the difference between the two approaches is eliminated.