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Journal Citation Analysis

the first 6 most recent years is 2410. As (2,564.5 2 2,410) 5 154.5 and
154.5 is 0.51 of 305, the median citation age is 6.51 (rounded in the JCR
to 6.5). The number of articles published during the most recent 6 years
in Scientometrics is 1269 (see row three of Table 6.15). Finally,
0.51 3 129 5 65.79 is added to this number, yielding 1334.79. This is the
denominator for the calculation of the MIF. It is concluded that the 2013
MIF of Scientometrics is 2564.5/1334.79 5 1.921, a value which is smaller
than the corresponding JIF 2 (2.274) for 2013 and also smaller than its
5-year JIF (2.294).

6.20 MATHEMATICAL PROPERTIES OF THE DIACHRONOUS
AND THE SYNCHRONOUS IMPACT FACTOR
In this section we illustrate how one can make elementary mathematical
considerations related to indicators.

6.20.1 Elementary Considerations on Impact Factors
As an example we first use the diachronous impact factor. Recall that this
indicator is defined as:
s1n21 CITðY; Y 1 kÞ
P
s
JDIF ðYÞ 5 k5s (6.6)
n
PUBðYÞ
Clearly, when one or more of the citation data increases, and all other
data stay the same, then the JDIF increases. The same happens when the
number of publications decreases. If all citation data are multiplied by the
same factor, say a, then the JDIF also increases by this same factor:
JDIF- a.JDIF. Similarly, when the number of publications increases by a
factor b then the JDIF becomes (1/b).JDIF. If a 5 b then the JDIF stays
invariant. Note though that thinking in percentages is more difficult. If
each citation data increases by 10% then a 5 1.1 and JDIF also increase by
10%. If however PUB increases by 10% then b 5 1.1 and (1/b) 5 0.91.
Hence an increase of PUB by 10% leads to a decrease of the JDIF by
about 9% (and not 10%!).
What happens if citations come from different pools of citing articles?
We first assume that the total pool of citing articles is subdivided into two
disjoint pools. We denote by CIT j ( j 5 1,2) the number of citations given
by journals belonging to pool j ( j 5 1,2), and use a similar notation for