Page 234 - Becoming Metric Wise

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Indicators

the number of references of article j. In case all articles’ citations are com-
pared with the same threshold, say T,thenformula (7.14) becomes:
n
1 X
c j (7.15)
n T
j51
This average score no longer has a theoretical upper limit. The multi-
plier idea has been proposed by Yanovsky (1981) and by Matsas (2012)
for scientific leadership. Yanovsky’s popularity factor is defined as (the
number of received citations) divided by (the number of references
given). Yanovsky proposed windows of equal length, but that is, of course
not a necessary requirement. Matsas’ indicator for scientific leadership is
known under the name of Normalized Impact Factor (NIF). The NIF of
scientist A in the sense of Matsas is defined as:

n a j51 j c j =n
a
P P n
j51 j c j
NIFðAÞ 5 P n 5 P n (7.16)
b
j51 j r j j51 j r j =n
b
Here n is the number of publications written by scientist A, during a
given period; c j is the number of citations received by article j (again over
a given citation window) and r j is the number of references of article j.
The numbers a j and b j are weighting factors. In the simplest case they are
all equal to one. In a somewhat more complex setup, one may take
a j 5 b j 5 1/ (the number of authors of article j); of course many other
weighting factors are feasible. NIF(A) is the weighted average number of
received citations divided by the weighted average number of references.
Note that here we face the well-known ratio of averages versus average of
ratios problem (Larivie `re & Gingras, 2011). In formula (7.14) we pro-
posed an average of ratios (when dividing by the total number of articles
in the set) while Matsas, formula (7.16), proposed a (weighted) ratio of
averages.

7.9 PERCENTILE RANK SCORE AND THE INTEGRATED
IMPACT INDICATOR (LEYDESDORFF & BORNMANN, 2011)
Suppose that articles in a reference set are subdivided in K disjoint classes.
If an article belongs to class k it receives a score x k . Let now A be a subset
of this reference set, consisting of N documents and let n A (k) be the