Page 235 - Becoming Metric Wise
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226 Becoming Metric-Wise
number of documents in A belonging to class k. Then the percentile rank
score of A, denoted as R(A), is defined as:
K
X n A ðkÞ
RðAÞ 5 x k (7.17)
N
k51
Proposition: The percentile rank score is a strict independent indicator
for average performance.
X K n A ðkÞ
Proof. Suppose that RðAÞ 5 x k . RðBÞ 5
k51 N
K n B ðkÞ
X
x k (for average performance the sets A and B must have
k51 N
an equal number of elements). We take a new element from class j and
add it to A as well as to B,leading to sets A and B .Then
0
0
N 1 N 1
0
RðA Þ 5 RðAÞ 1 x j . RðB Þ 5 RðBÞ 1 x j .This
0
N 1 1 N 1 1 N 1 1 N 1 1
proves that R is a strict independent indicator for average performance.
We note that the independence property does not hold if sets A and B
have a different number of elements. Indeed, let A consist of 2 elements, one
with score 1 and one with score zero. Then its percentile rank score is /2.Let
1
B consist of 10 elements, one with score 3, one with score 2, one with score
1 and 7withscore zero.Thenits percentile rank scoreis 6/10, which islarger
than A’s. Now we add an element with score 1. This leads to a score of 2/3
0
0
for A and for 7/11 for B , reversing the order of the scores for A and B.
Definition: The integrated impact indicator (I3) (Leydesdorff &
Bornmann, 2011)
Leydesdorff and Bornmann argued that impact means: many publica-
tions and many citations. In this sense the term JIF is a misnomer. The
nonnormalized percentile rank score, denoted I3(A) (the integrated
impact indicator) score satisfies this definition. Indeed, I3(A) is defined as:
K
X
I3ðAÞ 5 x k n A ðkÞ (7.18)
k51
Clearly, the I3 indicator too is a strict independent indicator, not only
for average performance but even in general.
7.10 CITATION MERIT
It is always difficult to compare sets with a different number of elements.
A proposal by Crespo et al. (2012) tries to remedy this. These colleagues