Working Paper Departamento de Economía

Economic Series 12-06 Universidad Carlos III de Madrid

March 2012 Calle Madrid, 126, 28903 Getafe (Spain)

“THE COMPARISON OF CITATION IMPACT BY ARTICLES IN DIFFERENT SCIENTIFIC SUB-FIELDS”

Juan A. Crespoa, Neus Herranzb, and Javier Ruiz-Castilloc

a Departamento de Economía Cuantitativa, Universidad Autónoma de Madridb Department of Economics, University of Illinois at Urbana-Champaign +

c Departamento de Economía, Universidad Carlos III, Research Associate of the CEPR Project SCIFI-GLOW

Abstract

This paper explores the possibility of making meaningful comparisons of the number of citations received by articles in sub-fields identified with the 219 Web of Science categories distinguished by Thomson Scientific. Such comparisons are instrumented on the basis of: (i) the assumption that articles in the same quantileof any sub-field citation distribution have the same degree of citation impact in their respective sub-field, and (ii) strong similarities found in the behavior of citation distributions in a large quantile interval. Three aims are achieved. Firstly, we answer how many citations for an article in the interval between, approximately, the 75th and the 97th

percentiles in any sub-field are equivalent to a given number of citations in the reference sub-field, Physics, Condensed Matter. The answer, in terms of what we call exchange rates, is very satisfactory for 203 out of 219 sub-fields.

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Secondly, the associated sub-field normalization procedure performs well in that interval. Thirdly, we provide an empirical explanation of why sub-field mean citations can be equally successfully used for both purposes.

Acknowledgements

The authors acknowledge financial support by Santander Universities Global Division of Banco Santander. Ruiz-Castillo acknowledges additional financial support from the Spanish MEC through grant SEJ2007-67436. This paper is produced as part of the project Science, Innovation, Firms and markets in a Globalised World (SCIFI-GLOW), a Collaborative Project funded by the European Commission's Seventh Research Framework Programme, Contract number SSH7-CT-2008-217436. Any opinions expressed here are those of the authors and not those of the European Commission. Conversations with Jesús Carro, Ignacio Ortuño, Juan Romo, Esther Ruiz, Carlos Velasco, and, above all, Pedro Albarrán, are deeply appreciated. All shortcomings are the authors’ sole responsibility.

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I. INTRODUCTION

The notion of scientific “quality” is virtually impossible to operationalize.

The evaluation of the cognitive, methodological, and esthetic quality

components of any research contribution can only be based on intrinsic

scientific criteria assessed by qualified colleague researchers under the peer

review system. However, communication is a crucial aspect of scientific

endeavor. Work of at least some importance provokes reactions of colleagues

that constitute the international forum, the “invisible college” that is permanently

discussing research results. One aspect of successful research performance

consists of actively presenting research findings to other researchers. As a

matter of fact, it can be argued that scientists have a professional obligation

to help in disseminating their results. (Moed et al., 1985). In this view,

together with basic quality, scientific quality includes what we call scientific

influence.

Although scientific influence is essentially an unobservable variable, we

may take into account that members of the invisible college often play their role

as critics by referring in their own work in the periodical literature to earlier

work of other scientists. Although for the founder of the modern sociology of

science citations represent intellectual or cognitive influence on scientific work

(Merton, 1973, Cole, 2000), a large literature has developed which holds that

the probability of being cited depends on many factors that do not have to do

with the accepted conventions of scholarly publishing, to say nothing of

constructivist sociologists of science for whom the cognitive content of articles

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has little influence on how they are received (see Bornmann and Daniel, 2008,

for an excellent survey). For our purposes, we may remain agnostic about the

myriad of citation motives researchers have as long as we are allowed to

assume that citation impact varies monotonically with scientific influence.

Thus, if one paper has greater scientific influence than another one in the

same field, then we expect the former to have also greater citation impact

than the latter.

The problem we confront in this paper is that, due to wide differences in

publication and citation practices, two articles with the same scientific

influence in two different fields will typically have very different number of

citations.1 The reasons are multiple. Think of the differences across scientific

disciplines in size measured by the number of publications in the periodical

literature, the average number of authors per paper, the average paper

length, the average number of papers per author in a given period of time, the

average number of references per paper, the theoretical or experimental mix

and the consequences for the average number of citations, the proportion of

references that are made to other articles in the periodical literature, the

percentage of internationally co-authored papers, or the speed at which the

citation process evolves. Consequently, the comparison of the absolute number

of citations received by articles in different fields is utterly meaningless.

This is, of course, a very well known problem that makes problematic the

evaluation of research units who typically work in a number of closely related but 1 For example, in the dataset used in this paper, consisting of articles in all sciences published in 1998-2002 with a five-year citation window, the mean citation rate in Pure Mathematics is 1.9, about eleven times smaller than in Cell Biology where it is equal to 21.4 citations (see Table A in the Appendix).

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heterogeneous scientific disciplines. The usual practice to overcome this

difficulty in the well-established tradition of relative indicators in

Scientometrics, is to take into account differences in citation practices by

choosing the world mean citation in each area as the normalization factor for

these activities (see inter alia Moed et al., 1985, 1988, 1995, Braun et al.,

1985, Schubert et al., 1983, 1987, 1988, Schubert and Braun, 1986, 1996, and

Vinkler 1986, 2003). More recently, under the universality claim according to

which citation distributions exclusively differ by a scale factor, Radicchi et al.

(2008, 2012) forcefully advocate solving any heterogeneity problem by

choosing as normalization factors the mean citation of the scientific

disciplines involved (see Glänzel, 2010, for another example of normalization

using a single average-based scalar different from the mean). However,

nobody in this tradition has attempted to answer the following question that is

our main aim in this paper: how many citations in any sub-field are equivalent

to 10 citations in a reference sub-field?

Naturally, the possibility of finding a meaningful way of comparing the

number of citations of articles in different scientific fields relies on the actual

behavior of citation distributions. In this respect, this paper takes as a starting

point the following two findings in Albarrán et al. (2011) for 219 sub-fields

identified with the Web of Science (WoS hereafter) subject categories

distinguished by Thomson Scientific. Firstly, the universality claim fails at

both ends of citation distributions. In particular, Albarrán et al. (2011) find

that the existence of a power law cannot be rejected at the top of the upper

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tail in 140 out of 219 sub-fields. On average, power laws represent 2% of all

articles in a sub-field, and account for about 13.5% of all citations. However,

the large dispersion of the power law parameters is a clear indication that

excellence is not equally structured in all citation distributions.2 This seems to

preclude the comparability of the citation impact of articles in different sub-

fields (Waltman et al., 2011 reach the same conclusion with a different

methodology). Secondly, however, the shapes of citation distributions over a

partition into three broad classes are strikingly similar. Consider the size- and

scale-independent statistical technique, known as Characteristic Scores and

Scales, where s1 denotes the mean citation, and s2 the mean citation of articles

above s1. It has been found that the proportion of articles that (i) receive none

or few citations below s1, (ii) are fairly cited, namely, with citations between s1

and s2, and (iii) are remarkably or outstandingly cited with citations above s2

is, approximately, 69/21/10. These three classes of articles account for the

proportions 21/34/45 of all citations (see Table 6 in Albarrán et al., 2011).3

The results of this paper about the comparability of the number of

citations received by articles in different sub-fields depend on a key

2 In addition, consider the possibility of defining a high-impact indicator over the sub-set of articles with citations above the 80th percentile of citation distributions. The distribution of high-impact values for the 219 sub-fields according to an indicator of this type is highly skewed to the right, and it presents some important extreme cases (see Herranz and Ruiz-Castillo, 2012).3 This assessment of mixed results contrasts with the more optimistic view offered by Radicchi et al. (2008) with a methodology that does not inform about how to treat the assignment of articles to multiple sub-fields, omits articles without citations, examines distributions at a limited set of points and, above all, covers only 14 of the 219 sub-fields. Radicchi and Castellano (2012), which is free from other methodological shortcomings, focus on 10 sub-fields within Physics.

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assumption and an empirical regularity. The assumption is that articles in the

same quantileof any sub-field citation distribution have the same degree of

citation impact. Therefore, citation inequality at any quantile can be solely

attributed to differences in citation practices across sub-fields. The regularity

is that these differences are so similar in a wide range of quantiles that the

effect of idiosyncratic citation practices can be rather well estimated.

Consequently, we are able to present precise estimates of what we call

exchange rates that directly answer the question of how many citations in any

sub-field are equivalent to a given number of citations in a certain reference

sub-field for a range of citation impact degrees that goes, approximately, from

the 75th to the 97th percentile. What is truly remarkable is that this strategy

works for most of the 219 sub-fields in both the natural and the social

sciences. By the same token, we are in a position to normalize differences in

citation practices taking the exchange rates as normalization factors. It turns

out that, for reasons that will be explained below, the standard sub-field

normalization procedure that uses mean citation rates leads practically to the

same results.

However, we must recognize at the outset that our procedure is only

partially successful. The reason is that citation distributions are very diverse,

even within the interval in which we are able to exploit their nevertheless

striking similarity. Firstly, we eliminate from about 85% or 90-92% of the

citation inequality attributable to differences in citation practice within the

750, 970 interval. However, given our large dataset the statistical

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significance of our results is rather limited. Secondly, outside of that interval

exchange rates would have to be computed for specific quantiles, and

normalization with a single scalar –our exchange rates or the sub-field means–

yields poor results.

The remaining of this paper consists of two Sections. Section II

introduces the approach and the data, presents the exchange rates, as well as

the results on normalization, and the comparison with the approach that uses

mean citation rates as normalization factors. Section III contains some

concluding comments.

II. EMPIRICAL RESULTS

II. 1. Notation and Assumptions

The smaller the set of closely linked journals used to define a given

research field, the greater the homogeneity of citation patterns among the

articles included must be. This homogeneity guarantees that their number of

citations can measure the relative merit of articles in a given field. Moreover,

when questioned, most scientists would answer that they belong to one, or at

most a few, well-defined research areas. Consequently, one should always

work at the lowest aggregation level that the data allows for. In this paper,

research areas at that level are referred to as sub-fields, are identified with

the 219 WoS categories distinguished by Thomson Scientific in our dataset,

and are indexed by s = 1,…, 219. Consider the partition of the citation

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distribution in any sub-field into quantiles, indexed by = 1,…, . In

practice, we take large, equal to 1,000, and we refer to C = cs as the

(219 x 1,000) quantile citation matrix, where csis the number of citations

corresponding to the -th quantile.4 We denote each of the 219 rows of C by

cs, and each of the columns by c.

Due to differences in citation practices, the number of citations of the i-th

article in sub-field s, csi, cannot be compared with the number of citations of

the j-th article in sub-field t, ctj. However, we will adopt the assumption that

articles at the same quantile of any field citation distribution have the same

degree of citation impact in their respective field.5 This means that the

citations these articles receive in any two sub-fields s and t, csand ct

, are

comparable. Thus, for example, the interpretation of the fact that cs= 2 ct

is that sub-field s uses twice the number of citations as sub-field t to represent

the same underlying phenomenon, namely, the same degree of scientific

influence in both fields. Therefore, for every quantile , the citation inequality

shown by column c is entirely attributable to differences in citation practices

4 Alternatively, we may take the quantile mean citation as representing the quantile itself. We have checked that, for large , the results are very similar (results are available on request).5 Since we assume that in every field citation impact and scientific influence are monotonically related, quantiles of citation impact correspond to quantiles of the underlying scientific influence distribution. Thus, holding constant the degree of citation impact at any level is equivalent to holding constant the degree of scientific influence at that level.

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across the 219 sub-fields.6 Hence, given a reference sub-field R with citations

cR, the exchange rates for each s R defined by

es() = cs/cR

,

(1)

can be reasonably taken to answer the following question: how many citations

for an article at the degree of scientific influence in sub-field s are equivalent

to a given number of citations in reference field R? In the metaphor according

to which a sub-field’s citation distribution is like an income distribution in a

certain currency, exchange rates es() permit to express all citations in the

same reference currency for that .

Naturally, if for many fields es() were to drastically vary with , then we

might not be able to claim that differences in citation practices have a

common element that can be precisely estimated. However, in what follows it

will be established that the coefficient of variation (CV hereafter) by columns

in matrix C is sufficiently constant over a wide range of quantiles to precisely

estimate mean exchange rates for most fields.

II. 2. The Data and Fundamental Regularities

Since we wish to address a homogeneous population, in this paper only

research articles or, simply, articles are studied. The dataset consists of about

6 Welfare economists would surely recognize this approach as Roemer’s (1998) Pragmatic Theory of Responsibility in his model for the inequality of opportunities in the context of income inequality.

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3.6 million articles published in 1998-2002, and the 28 million citations they

receive after a common five-year citation window for every year, namely,

citations received from 1998 to 2002 for articles published in 1998, up to

2002 to 2006 for articles published in 2002. The difficulty is that individual

publications are assigned to sub-fields via the journal in which they have been

published. Many journals are assigned to a single sub-field, but many others

are assigned to two, three, or more sub-fields. This is an important problem.

For example, in the dataset used in this paper 42% of the articles are assigned

to two or more, up to a maximum of six sub-fields. To deal with this situation,

we adopt a multiplicative strategy in which articles classified into several sub-

fields are wholly counted in all of them. We prefer this strategy on the

grounds that in the study of any sub-field all articles should count equally regardless

of the role some of them may play on other sub-fields. In this way, the space of

articles is expanded as much as necessary beyond the initial size in what we

call the sub-field extended count, which amounts to 5,733,512 articles, a total

about 57% greater than the original dataset.7 Table A in the Appendix

presents the number of articles and mean citation rates in the multiplicative

case. For convenience, sub-fields are classified in terms of 20 broad fields,

taken from Albarrán et al. (2011), and these in turn in four large groups: Life

Sciences, Physical Sciences, Other Natural Sciences, and Social Sciences.

7 In the alternative, fractional strategy each publication is fractioned into as many equal pieces as necessary, with each piece assigned to a corresponding sub-field. Fortunately, it turns out that citation characteristics of articles coming from journals assigned to multiple sub-fields do not differ much from those of articles coming from journals assigned to a single sub-field. Thus, the two strategies lead to citation distributions that have many important features in common (see Herranz and Ruiz-Castillo, 2012, for a full discussion of the two strategies).

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Consider matrix C with citations csfor every sub-field s = 1,…, 219 and

quantile = 1, …, 1,000. Panel A in Figure 1 shows mean citation by quantile

over the 219 sub-fields. The mean citation for = 1,000 is very high, and very

low for < 300. Thus, for clarity these quantiles are omitted from Figure 1. It

is observed that mean citation grows smoothly until the final quantiles when

the mean growth dramatically accelerates. This is a very eloquent illustration

of the skewness of science that characterizes every individual citation

distribution.

Figure 1 around here

Panel B in Figure 1 illustrates how citation inequality –measured by the

CV– varies by quantiles. As before, only quantiles in the interval 300, 999 are

shown. Firstly, it is observed that all CVs are rather high, implying that the

standard deviation (SD hereafter) is at least 56% of the column average at

every quantile. Secondly, CVs until 600 and from = 970 onwards are

significantly higher than otherwise. Thus, citation inequality attributable to

the differences in citation practices is particularly high for a wide range of low

quantiles, as well as for a few quantiles at the very upper tail of citation

distributions. Thirdly, CVs are relatively similar in the range (670, 970). Panel

B is clearly consistent with the stylized facts summarized in the Introduction

characterizing citation distributions at the sub-field level: although the

universality claim does not hold at all in a long lower tail and at the very top of

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the upper tail, citation distributions behave very similarly in a wide,

intermediate interval.

II. 3. Methods

It seems possible to choose a quantile interval m, M in the intermediate

range where differences in citation practices –measured by the CV of the

columns in the matrix C– is approximately constant and, therefore, where the

exchange rates es() defined in (1) should be similar independently of the

quantile . In this situation, it seems reasonable to define an average-based

exchange rate over that interval such as

es = 1/(M – m) es().

(2)

The advantage is that we can compute the associated SD:

s = (M – m – 1)-1 (es() – es)21/2.

(3)

The fact that es() es(’) for any , ’ m, M would manifest itself in a

small s, and hence in a small coefficient of variation CVs = s/es. Of course,

the set of exchange rates and SDs provide an answer to the question raised in

the Introduction that constitutes the main aim of this paper: how many

citations in sub-field s in the interval m, M are equivalent to 10 citations in

the reference sub-field R?

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How can we evaluate the reliability of this answer, apart from checking

that the set of CVs is indeed small? A natural direction is to assess the

normalization procedure based on exchange rates whereby the citations

received by any article i in sub-field s, csi, are converted into normalized

citations csi* in terms of the reference sub-field R as follows: csi* = 10csi/es. In

Radicchi et al.’s (2008, 2012) terminology, the fairness of a normalization

procedure is directly quantifiable by looking at its ability to suppress any

potential bias related to the classification of articles in sub-fields. We can

assess the fairness of taking exchange rates as normalization factors in two

steps. In the first place, we compute the CV by columns in the quantile matrix

C of normalized distributions. The closer to zero the CVs, the more the

differences in citation practices have been successfully eliminated. In the

second place, if the bias induced by citation practices is completely corrected,

then we should expect that the number of articles in every sub-field in the

interval m, M of the normalized distributions should be approximately

proportional to sub-field size.

Therefore, we may search for an interval m, M taking into account the

following considerations. Firstly, since we want the exchange rates to be as

representative as possible, we should choose the largest possible interval.

However, we should also be aware that the larger the interval the harder will

be to come up with small SDs. Secondly, the interval should be chosen so as to

achieve the best possible normalization results, namely, the largest reduction

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of the CV by columns in the quantile matrix C of normalized distributions, and

the smallest differences within the interval in question between the number of

articles in the normalized sub-field distributions and the expected number of

articles that should be proportional to sub-field size.

II. 4. Empirical Results on Exchange Rates

Following the above criteria, we find that, for reasons that will be

presently offered, the choice m, M = 750, 970 is a good one. We choose

Physics, Condensed Matter as the reference sub-field. The exchange rates es,

as well as the s, and CVs are in columns 1 to 3 in Table 1. For example, the

first row indicates that 13.9 citations with a standard deviation of 0.5 for an

article in Biology between, approximately, the 75th and the 97th percentile of

its citation distribution are equivalent to 10 citations for an article in that

interval in the reference sub-field.8

Table 1 around here

We find convenient to divide sub-fields into four groups according to the

CVs. Group I (dark green), consisting of 50 sub-fields, has a CV smaller than or

equal to 0.05. This means that the SD of the exchange rate is less than or

equal to five percent of the exchange rate itself. Hence, we consider exchange

8 A minor disadvantage of this procedure is that the ratio es/et for any two sub-fields s and t will be dependent on the reference sub-field R used in their computations. However, we have checked that such ratios are very robust to the choice of reference sub-field (results are available on request).

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rates in this group as highly reliable. Group II (pale green), consisting of 153

sub-fields, has a CV between 0.05 and 0.10. We consider exchange rates in

this group as fairly reliable. Group III (orange), consisting of 13 sub-fields, has

a CV between 0.10 and 0.15. This groups include including some important

sub-fields, such as Multidisciplinary Sciences and Physics, Multidisciplinary

(sub-fields 182 and 88). Some would find exchange rates in this group as

minimally reliable, while others will find them quite unreliable. Finally, Group

IV (red), consisting of 3 sub-fields, has a CV greater than 0.15. Exchange rates

in this group can be considered unreliable.

On average, the interval 750, 970 includes 47.6% of all citations in each

sub-field. Expanding the interval in either direction a larger percentage of

citations would be forthcoming. It turns out that the exchange rates do not

change much. However, they exhibit greater variability. For example, moving

the upper bound M to quantiles 980 or 990 would increase the percentage of

citations to 52.9% and 59.7%. Moreover, the number of sub-fields in Groups I

and II would decrease from 203 in the reference case down to 193 and 185,

respectively. Similarly, moving the lower bound m to quantiles 740, 730, or

720 would increase the percentage of citations to 48.8%, 49.8% and 50.9%.

However, relative to the initial choice, the number of sub-fields in Groups I

and II would decrease from 203 to 202, and 197 in the last two options.

Therefore, we retain the interval 750, 970 in the sequel.

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It should be noted that there is another way f defining an average-based

exchange rate over any interval m, M. We could first compute the mean

citation for every sub-field s by

ms = 1/(M – m) cs, (4)

and then an exchange rate defined by

e*s = ms/mR, (5)

where R is the reference sub-field. The advantage of this procedure is that the

ratio of any two exchange rates e*s/e*t = ms/mt, which serves to express how

many citations in sub-field s are equivalent to 10 citations in sub-field t, is

independent of the reference sub-field R. An important disadvantage is that no

standard deviation (SD hereafter) for every e*s is forthcoming. Using the

interval 750, 970, the information about expression (4) is in column 4 in

Table A in the Appendix while, taking Physics, Condensed Matter as the

reference sub-field, exchange rates e*s defined in expression (5) are in column

4 in Table 1. It turns out that all the new exchange rates e*s are within one SD

of es. Consequently, in the sequel we will exclusively focus on the exchange

rates es.

II. 5. The Normalization Question

Summary results about the CV by columns in the quantile matrix C after

the normalization using exchange rates are in column 2 in Table 2, while the 17

green curve in Figure 2 illustrates the correction achieved. It is observed that

from the median to the 75th percentile the reduction of the CV attributable to

normalization amounts to about 60% or 80% of the original variability. At the

beginning and the end of our interval the reduction amounts to 85%, while in

the interval 796, 945 reaches a maximum of about 90%-93%. In the last three

percentiles normalization results quickly deteriorate.

Table 2 and Figure 2 around here

As previously indicated, if the bias induced by citation practices is completely

corrected, then we should expect that the number of articles in every sub-field

in the 1,261,373 articles in the interval 750, 970 of the normalized

distributions should be approximately proportional to sub-field size. Column 1

in Table B in the Appendix presents the actual number of articles in the

original dataset, while columns 2 and 3 show the expected and the actual

number of articles after normalization. A summary of results is included in

Table 3 and illustrated in Figure 3 (in Panel A, Biochemistry and Molecular

Biology, a sub-field for which the difference is very large and would distort the

picture, is not included). Differences between columns 1 and 2, attributable to

different citation practices, are remarkable (see panel A in Figure 3). In 114

out of 219 sub-fields the absolute difference is greater than 40%, while in only

24 sub-fields that difference is smaller than 10%. On average over the 219

sub-fields, the difference is 43.3%. On the contrary, differences after

normalization by exchange rates are of a small order of magnitude (see Panel

B in Table 3). On average differences in absolute value are 9.9%, and only in 18

27 sub-fields absolute differences are greater than 20%.9 Nevertheless, still in

122 sub-fields differences are between 5% and 10%.

Table 3 and Figure 3 around here

II. 6. The Role of Mean Citations

As indicated in the Introduction, the difficulties of combining

heterogeneous citation distributions into broader aggregates have been

traditionally confronted using sub-field mean citations as normalization

factors. However, no attempt has ever been made to construct exchange rates

based on mean citations to compare citations received by articles in different

sub-fields. One reason might be that, given the high skewness of citation

distributions, it is not clear what mean citation rates do represent (see the

high SDs reported in column 4 in Table A in the Appendix). Be it as it may, the

fact is that –to our knowledge– nobody has suggested a rationale for using

mean citations in this way.

If we denote sub-field s mean citation by s, then we can define the

associated exchange rates by es() = s/R, where R is again the reference sub-

field. Taking Physics, Condensed Matter as reference, such exchange rates

are presented in column 4 in Table 1. It is observed that columns 1 and 4 are

extremely similar. In particular, for 202 out of 219 sub-fields the new

exchange rates are within one standard deviation of our own. Consequently, 9 These include the three articles in Group IV and ten out of 16 in Group III in Table 1 with high CVs, as well as some other important sub-fields such as Chemistry, Organic, and two more sub-fields in Computer Science in addition to sub-field 109 already in Group III. When we eliminate these 27 sub-fields with differences greater than 20%, absolute differences before and after normalization are, on average, 41.9% and 7.9%, respectively.

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the normalization by es() should also lead to very similar results to those

obtained with our es. This is indeed what we find when we compare the

coefficient of variation by columns of the normalized quantile matrix C

(compare columns 2 and 3 in Table 2, as well as the green and the red curves

in Figure 2). On the other hand, the number of articles in the 750, 970

interval after the new normalization is in column 3 in Table 3. It turns out that

in 92 cases the numbers are the same! In 74 cases the absolute differences

between the actual numbers and the expected ones are smaller for our

exchange rates, while in 53 sub-fields the opposite is the case. On average

differences in absolute value are only slightly larger than when normalizing

with our exchange rates. Consequently, the measure of fairness of this

procedure presented in column 4 in Table 4 is only slightly lower than our

own.

The good results obtained when normalization is performed with mean

citations justify both Radicchi et al.’s proposal (2008, 2012), as well as the use

of relative indicators since the mid 1980s. The question is, how can this

similarity of results be accounted for? The explanation is in Albarrán et al.

(2011), where it was found that sub-field mean citations are reached, on

average, at the 68.6 percentile with a SD of 3.7. Thus, the exchange rates es()

are approximately equal to some average of our exchange factors es() for

t649, 723 interval. The fact that, as illustrated in Figure 2, the CV by

columns in the quantile matrix C for this interval and our own 715, 970 are

20

so close to each other provides an empirical explication of the closeness of

both sets of results.

III. CONCLUSIONS

This paper has established that, judging by the effect of differences in

citation practices across a large number of 219 scientific sub-fields, the facts

of the matter can be summarized as follows. Citation inequality attributed to

those differences (i) is first very high and decreases quite rapidly until the

median quantile or beyond; (ii) is relatively constant in an intermediate area,

and (iii) raises rapidly during the last three percentiles. In this scenario, there

is simply no hope of finding a single set of exchange rates that permits to

express the citation of any article in terms of the citation in a reference sub-

field.

The best we can hope for is to find an interval within the intermediate

area in which exchange rates are approximately constant for many sub-fields.

In this paper we suggest that the 750, 970 interval, capturing on average

47.6% of all citations, is a good choice for approximately 203 sub-fields. For

any two articles i and j in that interval in sub-fields s and t in that list

receiving csi and ctj citations, the ratio csi/es is greater than, equal to, or

smaller than the ratio ctj/et, where es and et are taken from Groups I and II in

Table 1, whenever article i in sub-field s has greater than, equal to, or smaller

than scientific influence than article j in sub-field t.

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How reliable are such comparisons? In our view, an answer depends on

two factors. Firstly, on how small are the SD estimated for both sub-fields.

Secondly, on how much of citation inequality attributable to citation practices

is eliminated after taking the exchange rates as normalization factors. In this

paper, we have shown that our procedure eliminates at most 90%-93% of that

citation inequality in the interior of the 715, 970 interval. In turn, differences

between the expected number of articles in that interval under the hypothesis

of complete success in eliminating the bias and the actual number of articles

after normalizing by the exchange rates is vastly reduced –but not completely

eliminated– from an average 43.3% difference to 9.8%. It might be worth

investigating whether these differences are significantly different from zero

(see Radicchi et al., 2008, 2012 for details about the underlying statistical

model).

The paper has also established that using mean citations as normalization

factors leads to very similar results. A long initial tail of articles with no or few

citations is offset by highly cited articles in the upper tail of citation

distributions, so that, as indicated in Albarrán et al. (2011), mean citations for

the entire distribution approximately lie in the649, 723 interval. The CV of

columns in that interval in the quantile matrix C do not differ much from those

of the750, 970 interval, so that the exchange rates based on mean citations

are very close to our own.

It should be noted that the approach described in this paper can be used

to facilitate the comparison of articles belonging to broader, aggregate

22

scientific categories. This can be done in two ways, applying the methodology

(i) either to the original aggregate citation distributions, (ii) or to the sub-field

normalized distributions using as normalization factors the exchange factors

estimated in this paper, or the sub-field mean citation rates as it is usually

done with average-based relative indicators.

On the other hand, it should be stressed that, for uncited and poorly cited

articles below the mean, and for articles in the very upper tail of citation

distributions where excellence is supposed to reside, no convincing answer to

the question motivating this paper can be provided. Since the citation process

evolves at different velocity in different sub-fields, using variable citation

windows to ensure that the process has reached a similar stage in all sub-

fields should improve sub-field comparability at the lower tail of citation

distributions. In any case, the main worry would be how to compare citation

counts in the last three percentiles of citation distributions. Given the fact that

the structure of excellence in citation impact appears to be very diverse

across sub-fields, perhaps this task should not be even attempted. Until we

know more of how differential citation practices operate in these intervals, the

most we can do in the framework developed in this paper is to use exchange

rates es() depending on specific quantiles (970, 1000. Finally, it may be

worth investigating whether using a second set of exchange rates for the (970,

1000 interval improves our normalization results.

This paper has been based on a 3.6 million dataset of articles published in

1998-2002 with a common five-year citation window. The robustness of our

23

results should be explored in two different directions. Firstly, with articles

published in other time periods and/or other common or variable citation

windows indexed either by Thomson Scientific or other sources, such as

Scopus. Secondly, journals cannot unambiguously be classified into journal

categories on the basis of their aggregated citation practices (Leydesdorff,

2006), and WoS categories cannot be taken at all as ideal objects at the lowest

aggregation level (see Boyack et al., 2005, and Rafols and Leydesdorff, 2009

for the problem of erroneous attribution of journals to WoS categories). In

order to better isolate the effect of different citation practices in science, we

must wait for appropriate schemes in which individual articles are assigned to

individual bona fide scientific sub-fields, as in Waltman et al. (2010) by way of

example.

24

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Boyack, K., Klavans, R., and Börner, K. (2005), “Mapping the Backbone of Science”, Scientometrics, 64: 351-374.

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Glänzel, W. and A. Schubert (2003), “A new classification scheme of science fields and subfields designed for scientometric evaluation purposes”, Scientometrics, 56: 357-367.

Herranz, N. and J. Ruiz-Castillo (2012), “Multiplicative and Fractional Strategies When Journals Are Assigned to Several Sub-fields”, accepted for publication in the Journal of the American Society for Information Science and Technology.

Leydesdorff, L. (2006), “Can Scientific Journals Be Classified in Terms of Aggregated Journal-Journal Citation Relations Using the Journal Citation Reports?”, Journal of the American Society for Information Science and Technology, 57: 601-613.

Merton, R. K. (1973), The Sociology of Science: Theoretical and Empirical Investigations, University of Chicago Press, Chicago, Ill.

Moed, H. F., W. J. Burger, J. G. Frankfort, and A. F. J. van Raan (1985), “The Use of Bibliometric Data for the Measurement of University Research Performance”, Research Policy, 14: 131-149.

Moed, H. F., and A. F. J. van Raan (1988), “Indicators of Research Performance”, in A. F. J. van Raan (ed.), Handbook of Quantitative Studies of Science and Technology, North Holland: 177-192.

Moed, H. F., R. E. De Bruin, and Th. N. van Leeuwen (1995), “New Bibliometrics Tools for the Assessment of national Research Performance: Database Description, Overview of Indicators, and First Applications”, Scientometrics, 33: 381-422.

Radicchi, F., Fortunato, S., and Castellano, C. (2008), “Universality of Citation Distributions: Toward An Objective Measure of Scientific Impact”, PNAS, 105: 17268-17272.

Radicchi, F., and Castellano, C. (2012), “Testing the fairness of citation indicators for comparisons across scientific domains: The case of fractional citation counts”, Journal of Informetrics, 6: 121-130.

25

Rafols, I., and Leydesdorff, L. (2009), Content-based and Algorithmic Classifications of Journals: Perspectives on the Dynamics of Scientific Communication and Indexer Effects, Journal of the American Society for Information Science and Technology, 60: 1823-1835.

Roemer, J. (1998), Equality of Opportunities, Harvard University Press.

Schubert, A., and T. Braun (1986), “Relative Indicators and Relational Charts for Comparative Assessment of Publication Output and Citation Impact”, Scientometrics, 9: 281-291.

Schubert, A., and T. Braun (1996), “Cross-field Normalization of Scientometric Indicators”, Scientometrics, 36: 311-324.

Schubert, A., W. Glänzel, and T. Braun (1983), “Relative Citation Rate: A New Indicator for Measuring the Impact of Publications”, in D. Tomov and L. Dimitrova (eds.), Proceedings of the First National Conference with International Participation in Scientometrics and Linguistics of Scientific Text, Varna.

Schubert, A., W. Glänzel and T. Braun (1987), “A New Methodology for Ranking Scientific Institutions”, Scientometrics, 12: 267-292.

Schubert, A., W. Glänzel, and T. Braun (1988), “Against Absolute Methods: Relative Scientometric Indicators and Relational Charts as Evaluation Tools”, in A. F. J. van Raan (ed.), Handbook of Quantitative Studies of Science and Technology: 137-176.

Vinkler, P. (1986), “Evaluation of Some Methods For the Relative Assessment of Scientific Publications”, Scientometrics, 10: 157-177.

Vinkler, P. (2003), “Relations of Relative Scientometric Indicators”, Scientometrics, 58: 687-694.

WaltmanL., N. J. van Eck, and E. Noyons (2010), “A Unified Approach to Mapping and Clustering of Bibliometric Networks”, Journal of Informetrics, 4: 629–635.

Waltman, L, N. J. van Eck, and A. F. J. van Raan (2011), “Universality of Citation Distributions Revisited”, Journal of the American Society for Information Science and Technology, 63:72-77.

26

3003203403603804004204404604805005205405605806006206406606807007207407607808008208408608809009209409609800

10

20

30

40

50

60

70

80

90

100

Figure 1.A. Average Citation Rate of the Quantile Matrix Columns

3003243483723964204444684925165405645886126366606847087327567808048288528769009249489729960

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 1.B. Coefficient of Variation of the Quantile Matrix Columns

27

Table 1. Exchange Rates, Standard Deviations, and Coefficients of Variation

Exchange Standard

Coefficient

Exch. Rates

Alternative

RatesDeviatio

n

of Variatio

nBased on

MeanExch. Rates

Citations

(1) (2) (3) (4) (5)

A. LIFE SCIENCES

I. BIOSCIENCES

1 BIOLOGY 13.9 0.5 0.033 13.5 13.9

2 BIOLOGY, MISCELLANEOUS 6.3 0.4 0.062 6.1 6.3

3 EVOLUTIONARY BIOLOGY 20.8 2.1 0.099 22.5 20.0

4 BIOCHEMICAL RESEARCH METHODS 14.6 0.9 0.062 16.5 14.3

5BIOCHEMISTRY & MOLECULAR BIOLOGY 27.6 1.0 0.036 29.5 27.4

6 BIOPHYSICS 18.4 1.1 0.057 19.6 18.1

7 CELL BIOLOGY 37.3 1.3 0.035 38.6 37.6

8 GENETICS & HEREDITY 26.6 0.9 0.032 28.5 26.6

9 DEVELOPMENTAL BIOLOGY 34.0 1.0 0.029 35.0 33.9

II. BIOMEDICAL RESEARCH

10 PATHOLOGY 15.9 0.5 0.033 16.0 15.8

11 ANATOMY & MORPHOLOGY 10.2 0.8 0.077 10.3 9.9

12 ENGINEERING, BIOMEDICAL 12.1 0.8 0.062 12.2 11.9

13 BIOTECH. & APPLIED MICROBIOLOGY 15.2 0.5 0.035 16.3 15.1

28

14MEDICAL LABORATORY TECHNOLOGY 10.8 0.4 0.039 11.0 10.8

15 MICROSCOPY 10.9 0.7 0.066 11.1 10.7

16 PHARMACOLOGY & PHARMACY 13.9 0.7 0.050 14.5 13.8

17 TOXICOLOGY 12.3 0.9 0.074 12.9 12.0

18 PHYSIOLOGY 18.1 1.8 0.101 18.8 17.5

III. CLINICAL MEDICINE I (INTERNAL)

19CARDIAC & CARDIOVASCULAR SYSTEMS 20.1 1.1 0.054 20.6 20.5

20 RESPIRATORY SYSTEM 17.8 1.0 0.057 18.2 17.5

21 ENDOCRINOLOGY & METABOLISM 21.7 1.5 0.070 23.1 21.2

22 ANESTHESIOLOGY 12.4 0.5 0.041 12.2 12.2

23 CRITICAL CARE MEDICINE 19.2 0.9 0.046 19.4 19.0

24 EMERGENCY MEDICINE 7.5 0.5 0.062 7.4 7.4

25GASTROENTEROLOGY & HEPATOLOGY 18.4 0.5 0.029 18.9 18.3

26 MEDICINE, GENERAL & INTERNAL 17.7 5.4 0.306 22.8 19.8

27 TROPICAL MEDICINE 9.1 0.7 0.080 8.9 8.9

28 HEMATOLOGY 29.3 0.9 0.032 29.7 29.2

29 ONCOLOGY 23.7 0.9 0.040 25.1 23.4

30 ALLERGY 15.7 0.8 0.050 15.4 15.5

31 IMMUNOLOGY 23.9 0.8 0.032 25.3 23.8

32 INFECTIOUS DISEASES 20.2 1.3 0.065 21.0 19.8

IV. CLINICAL MEDICINE II (NON-INTERNAL)

33 GERIATRICS & GERONTOLOGY 14.4 0.9 0.063 14.3 14.1

34 OBSTETRICS & GYNECOLOGY 12.1 0.6 0.052 12.0 11.9

35 ANDROLOGY 9.7 0.9 0.090 10.0 9.4

36 REPRODUCTIVE BIOLOGY 16.4 1.4 0.087 17.2 15.9

37 GERONTOLOGY 13.2 0.7 0.052 12.9 12.9

29

38 DENTISTRY & ORAL SURGERY 9.2 0.6 0.071 9.4 9.0

39 DERMATOLOGY 10.7 0.5 0.046 10.6 10.6

40 UROLOGY & NEPHROLOGY 16.4 0.6 0.039 16.5 16.2

41 OTORHINOLARYNGOLOGY 7.8 0.5 0.070 7.8 7.7

42 OPHTHALMOLOGY 12.4 0.5 0.040 12.5 12.3

43INTEGRATIVE & COMPLEM. MEDICINE 7.8 0.7 0.093 7.8 7.5

44 CLINICAL NEUROLOGY 16.5 0.6 0.035 16.7 16.4

45 PSYCHIATRY 17.2 0.6 0.034 17.3 17.2

46RADIOLOGY, NUCL. MED. & MED. IMAGING 13.6 0.5 0.035 13.8 13.5

47 ORTHOPEDICS 10.2 0.6 0.057 10.3 10.1

48 RHEUMATOLOGY 18.7 0.9 0.049 19.4 18.4

49 SPORT SCIENCES 10.7 0.6 0.057 10.5 10.5

50 SURGERY 11.4 0.5 0.042 11.4 11.3

51 TRANSPLANTATION 12.2 0.5 0.037 12.2 12.1

52 PERIPHERAL VASCULAR DISEASE 27.2 0.8 0.030 27.9 27.1

53 PEDIATRICS 10.2 0.4 0.041 10.3 10.2

V. CLINICAL MEDICINE III

54HEALTH CARE SCIENCES & SERVICES 10.2 0.7 0.064 10.4 10.0

55 HEALTH POLICY & SERVICES 10.8 0.5 0.043 11.3 10.7

56 MEDICINE, LEGAL 7.6 0.5 0.071 7.8 7.5

57 NURSING 5.5 0.5 0.086 5.4 5.3

58PUBLIC, ENVIRON. & OCCUP. HEALTH 12.5 0.6 0.051 12.7 12.3

59 REHABILITATION 7.7 0.5 0.068 7.5 7.5

60 SUBSTANCE ABUSE 12.9 1.2 0.090 13.4 12.5

61EDUCATION, SCIENTIFIC DISCIPLINES 5.3 0.3 0.056 5.1 5.3

62 MEDICAL INFORMATICS 7.4 0.4 0.048 7.5 7.3

30

VI. NEUROSCIENCES & BEHAVIORAL

63 NEUROIMAGING 19.1 0.6 0.033 18.7 19.0

64 NEUROSCIENCES 22.4 0.9 0.038 23.5 22.2

65 BEHAVIORAL SCIENCES 14.3 1.6 0.109 15.7 13.7

66 PSYCHOLOGY, BIOLOGICAL 12.1 1.1 0.091 13.2 11.8

67 PSYCHOLOGY 13.6 1.0 0.075 13.9 13.3

68 PSYCHOLOGY, APPLIED 8.3 0.5 0.065 8.3 8.1

69 PSYCHOLOGY, CLINICAL 13.1 0.7 0.053 13.2 12.9

70 PSYCHOLOGY, DEVELOPMENTAL 13.4 0.8 0.059 13.7 13.2

71 PSYCHOLOGY, EDUCATIONAL 9.5 0.5 0.052 9.1 9.4

72 PSYCHOLOGY, EXPERIMENTAL 13.1 0.7 0.050 13.3 13.0

73 PSYCHOLOGY, MATHEMATICAL 9.2 0.5 0.052 9.2 9.1

74 PSYCHOLOGY, MULTIDISCIPLINARY 8.5 0.6 0.070 8.6 8.7

75 PSYCHOLOGY, PSYCHOANALYSIS 4.9 0.4 0.074 4.6 5.0

76 PSYCHOLOGY, SOCIAL 10.9 0.4 0.041 10.9 10.8

77 SOCIAL SCIENCES, BIOMEDICAL 9.1 0.5 0.055 9.4 9.0

B. PHYSICAL SCIENCES

VII. CHEMISTRY

78 CHEMISTRY, MULTIDISCIPLINARY 16.2 1.1 0.068 15.5 16.5

79 CHEMISTRY, INORGANIC & NUCLEAR 11.9 0.8 0.066 11.9 11.6

80 CHEMISTRY, ANALYTICAL 13.0 0.7 0.056 13.3 12.7

81 CHEMISTRY, APPLIED 9.8 0.7 0.072 9.8 9.6

82 ENGINEERING, CHEMICAL 7.9 0.4 0.052 7.6 7.8

83 CHEMISTRY, MEDICINAL 12.6 0.9 0.073 13.2 12.3

84 CHEMISTRY, ORGANIC 13.7 1.2 0.090 14.3 13.2

85 CHEMISTRY, PHYSICAL 13.5 0.8 0.059 13.9 13.3

86 ELECTROCHEMISTRY 13.1 1.1 0.083 13.4 12.8

87 POLYMER SCIENCE 10.9 0.4 0.036 11.0 10.7

31

VIII. PHYSICS

88 PHYSICS, MULTIDISCIPLINARY 14.5 1.7 0.118 14.8 15.1

89 SPECTROSCOPY 10.2 0.6 0.058 10.2 10.0

90 ACOUSTICS 7.3 0.4 0.060 7.1 7.2

91 OPTICS 9.7 0.4 0.044 9.6 9.6

92 PHYSICS, APPLIED 10.0 0.3 0.029 10.2 10.0

93PHYSICS, ATOMIC, MOLEC. & CHEMICAL 14.6 1.1 0.078 15.3 14.2

94 THERMODYNAMICS 6.1 0.5 0.087 6.1 5.9

95 PHYSICS, MATHEMATICAL 10.1 0.5 0.047 10.2 9.9

96 PHYSICS, NUCLEAR 9.1 0.4 0.040 9.0 9.2

97 PHYSICS, PARTICLES & SUB-FIELDS 15.5 1.1 0.072 16.2 15.8

98 PHYSICS, CONDENSED MATTER 10.0 0.0 0.000 10.0 10.0

99PHYSICS OF SOLIDS, FLUIDS & PLASMAS 12.2 0.9 0.071 12.6 12.0

IX. SPACE SCIENCES

100 ASTRONOMY & ASTROPHYSICS 19.8 0.7 0.035 20.4 19.8

X. MATHEMATICS

101 MATHEMATICS, APPLIED 5.0 0.4 0.073 4.8 5.0

102 STATISTICS & PROBABILITY 7.0 0.5 0.066 8.1 7.2

103

MATHEMATICS, INTERDIS. APPLICATIONS 7.4 0.4 0.053 7.4 7.3

104 SOCIAL SCIENCES, MAth. METHODS 7.3 0.3 0.043 7.3 7.3

105 MATHEMATICS 3.8 0.3 0.079 3.5 3.8

XI. COMPUTER SCIENCE

106

COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE 6.9 0.5 0.071 6.9 7.0

107 COMPUTER SCIENCE, CYBERNETICS 5.0 0.4 0.073 4.6 5.0

32

108

COMP. SC., HARDWARE & ARCHITECTURE 5.5 0.4 0.081 5.5 5.6

109

COMP. SCIENCE, INFORMATION SYSTEMS 5.9 0.7 0.115 6.0 6.1

110 COMP. SC., INTERDIS. APPLICATIONS 7.2 0.5 0.075 8.1 7.4

111

COMP. SCIENCE, SOFTWARE ENGINEERING 5.0 0.4 0.075 4.8 5.0

112

COMPUTER SCIENCE, THEORY & METHODS 4.4 0.4 0.081 4.3 4.5

113 MATH. & COMPUTATIONAL BIOLOGY 12.1 0.5 0.043 15.2 12.1

C. OTHER NATURAL SCIENCES

XII. ENGINEERING

114 ENG., ELECTRICAL & ELECTRONIC 6.4 0.4 0.060 6.3 6.4

115 TELECOMMUNICATIONS 5.1 0.5 0.098 5.0 5.2

116 CONSTR. & BUILDING TECHNOLOGY 4.5 0.4 0.086 4.3 4.4

117 ENGINEERING, CIVIL 4.5 0.3 0.070 4.2 4.5

118 ENGINEERING, ENVIRONMENTAL 11.7 0.5 0.043 11.5 11.6

119 ENGINEERING, MARINE 2.0 0.4 0.196 1.8 2.1

120

TRANSPORTATION SC. & TECHNOLOGY 3.1 0.4 0.129 2.7 3.2

121 ENGINEERING, INDUSTRIAL 4.2 0.3 0.077 3.9 4.2

122 ENGINEERING, MANUFACTURING 4.5 0.4 0.085 4.3 4.4

123 ENGINEERING, MECHANICAL 5.2 0.3 0.061 5.0 5.2

124 MECHANICS 6.8 0.4 0.058 6.6 6.7

125 ROBOTICS 4.7 0.3 0.068 4.5 4.7

33

126

INSTRUMENTS & INSTRUMENTATION 6.9 0.4 0.054 6.6 6.8

127

IMAGING SC. & PHOTOGRAPHIC TECH. 9.5 0.5 0.055 9.4 9.6

128 ENERGY & FUELS 6.6 0.4 0.053 6.2 6.5

129 NUCLEAR SCIENCE & TECHNOLOGY 5.8 0.3 0.055 5.7 5.8

130 ENGINEERING, PETROLEUM 2.3 0.5 0.232 2.0 2.5

131 AUTOMATION & CONTROL SYSTEMS 5.3 0.3 0.053 5.1 5.3

132 ENGINEERING, MULTIDISCIPLINARY 5.1 0.4 0.076 4.8 5.1

133 ERGONOMICS 5.9 0.6 0.098 5.9 5.7

134

OPERATIONS RESEARCH & MANAG. SC. 5.2 0.3 0.064 5.0 5.1

XIII. MATERIALS SCIENCE

135 MATERIALS SCIENCE, BIOMATERIALS 16.3 1.6 0.096 16.9 15.8

136 MATERIALS SCIENCE, CERAMICS 6.8 0.3 0.051 6.1 6.8

137

MATS. SC., CHARACTERIZATION & TESTING 2.9 0.3 0.112 2.6 3.0

138

MATERIALS SCIENCE, COATINGS & FILMS 9.8 0.7 0.071 9.8 9.6

139 MATERIALS SCIENCE, COMPOSITES 4.7 0.3 0.073 4.4 4.7

140

MATERIALS SCIENCE, PAPER & WOOD 4.0 0.3 0.077 3.6 3.9

141 MATERIALS SCIENCE, TEXTILES 3.8 0.3 0.080 3.5 3.7

142

METALLURGY & METALL ENGINEERING 6.2 0.3 0.054 6.0 6.3

143

NANOSCIENCE & NANOTECHNOLOGY 10.0 0.2 0.018 10.4 10.0

XIV. GEOSCIENCES

34

144 GEOCHEMISTRY & GEOPHYSICS 12.9 0.9 0.068 12.9 12.6

145 GEOGRAPHY, PHYSICAL 11.3 1.0 0.090 11.6 10.9

146 GEOLOGY 10.5 0.7 0.070 10.3 10.2

147 ENGINEERING, GEOLOGICAL 4.8 0.5 0.106 4.7 4.7

148 PALEONTOLOGY 8.5 0.5 0.064 8.4 8.4

149 REMOTE SENSING 9.4 0.5 0.056 9.7 9.3

150 OCEANOGRAPHY 13.1 1.3 0.095 13.2 12.7

151 ENGINEERING, OCEAN 5.1 0.4 0.075 4.9 5.1

152

METEOROLOGY & ATMOSPH. SCIENCES 13.8 0.7 0.049 13.9 13.6

153 ENGINEERING, AEROSPACE 3.4 0.3 0.093 3.1 3.5

154 MINERALOGY 9.4 0.6 0.062 9.5 9.2

155 MINING & MINERAL PROCESSING 5.2 0.3 0.061 5.0 5.3

XV. AGRICULTURAL & ENVIRONMENT

156 AGRICULTURAL ENGINEERING 6.0 0.6 0.097 5.9 5.8

157 AGRICULTURE, MULTIDISCIPLINARY 8.9 0.4 0.050 8.5 8.8

158 AGRONOMY 7.7 0.4 0.056 7.5 7.6

159 LIMNOLOGY 12.4 0.9 0.073 12.5 12.1

160 SOIL SCIENCE 8.9 0.8 0.085 8.8 8.7

161 BIODIVERSITY CONSERVATION 11.4 0.6 0.056 11.2 11.3

162 ENVIRONMENTAL SCIENCES 11.3 0.7 0.064 11.6 11.1

35

163 ENVIRONMENTAL STUDIES 6.3 0.5 0.080 6.3 6.1

164 FOOD SCIENCE & TECHNOLOGY 9.1 0.7 0.072 9.1 8.9

165 NUTRITION & DIETETICS 14.7 0.6 0.043 14.9 14.6

166

AGRICULTURE, DAIRY & ANIMAL SCIENCE 7.1 0.4 0.050 6.7 7.1

167 HORTICULTURE 8.1 0.4 0.047 8.0 8.0

XVI. BIOLOGY (ORGANISMIC AND

SUPRAORGONISMIC LEVEL)

168 ORNITHOLOGY 7.2 0.6 0.089 7.4 7.0

169 ZOOLOGY 9.7 0.6 0.066 9.7 9.5

170 ENTOMOLOGY 7.1 0.5 0.074 6.9 6.9

171 WATER RESOURCES 7.8 0.6 0.074 7.8 7.7

172 FISHERIES 9.0 0.9 0.096 9.2 8.7

173 MARINE & FRESHWATER BIOLOGY 10.4 1.1 0.102 10.8 10.0

174 MICROBIOLOGY 18.6 1.4 0.074 19.5 18.2

175 PARASITOLOGY 10.5 0.7 0.071 10.8 10.2

176 VIROLOGY 24.6 2.0 0.081 26.3 23.9

177 FORESTRY 9.1 0.7 0.079 9.4 8.9

178 MYCOLOGY 9.1 0.5 0.059 9.0 9.0

179 PLANT SCIENCES 12.5 0.4 0.031 13.0 12.5

180 ECOLOGY 14.6 1.3 0.088 15.0 14.1

181 VETERINARY SCIENCES 6.9 0.4 0.051 6.5 6.8

36

XVII. MULTIDISCIPLINARY

182 MULTIDISCIPLINARY SCIENCES 5.5 0.6 0.109 5.4 5.7

XVIII. RESIDUAL SUB-FIELDS

183

MATERIALS SCIENCE, MULTIDISCIPLINARY 8.4 0.4 0.047 8.6 8.5

184 CRYSTALLOGRAPHY 6.9 0.3 0.051 7.5 6.9

185 GEOSCIENCES, MULTIDISCIPLINARY 9.5 0.5 0.052 9.4 9.4

186

MEDICINE, RESEARCH & EXPERIMENTAL 22.3 3.1 0.141 24.1 23.5

D. SOCIAL SCIENCES

XIX. SOCIAL SCIENCES, GENERAL

187 CRIMINOLOGY & PENOLOGY 6.7 0.3 0.052 6.2 6.7

188 LAW 6.2 0.4 0.060 6.0 6.2

189 POLITICAL SCIENCE 4.5 0.4 0.085 4.3 4.6

190 PUBLIC ADMINISTRATION 4.7 0.3 0.064 4.5 4.7

191 ETHNIC STUDIES 3.4 0.4 0.121 3.3 3.4

192 FAMILY STUDIES 7.7 0.5 0.060 7.6 7.6

193 SOCIAL ISSUES 4.8 0.3 0.060 4.6 4.8

194 SOCIAL WORK 5.1 0.4 0.075 4.9 5.0

195 SOCIOLOGY 5.7 0.3 0.057 5.4 5.7

196 WOMEN'S STUDIES 5.2 0.3 0.059 5.0 5.2

197

EDUCATION & EDUCATIONAL RESEARCH 4.3 0.3 0.070 4.2 4.3

198 EDUCATION, SPECIAL 6.6 0.4 0.061 6.5 6.6

37

199 AREA STUDIES 2.6 0.2 0.095 2.4 2.6

200 GEOGRAPHY 7.4 0.5 0.063 7.5 7.3

201 PLANNING & DEVELOPMENT 5.6 0.3 0.055 5.6 5.6

202 TRANSPORTATION 6.4 0.5 0.075 6.2 6.2

203 URBAN STUDIES 5.6 0.4 0.064 5.6 5.5

204 ETHICS 4.5 0.3 0.071 4.3 4.4

205 MEDICAL ETHICS 6.8 0.5 0.068 6.8 6.6

206 ANTHROPOLOGY 5.7 0.3 0.055 5.4 5.7

207 COMMUNICATION 5.4 0.4 0.069 5.3 5.3

208 DEMOGRAPHY 7.4 0.4 0.051 7.6 7.4

209 HISTORY OF SOCIAL SCIENCES 2.8 0.3 0.105 2.5 2.7

210

INFORMATION SCIENCE & LIBRARY SC. 5.2 0.5 0.092 5.1 5.3

211 INTERNATIONAL RELATIONS 4.2 0.4 0.103 4.0 4.3

212 LINGUISTICS 7.8 0.4 0.053 7.6 7.8

213

SOCIAL SCIENCES, INTERDISCIPLINARY 4.6 0.4 0.077 4.3 4.6

XX. ECONOMICS & BUSINESS

214

AGRICULTURAL ECONOMICS & POLICY 4.8 0.5 0.097 4.6 4.7

215 ECONOMICS 6.2 0.3 0.053 6.2 6.2

216 INDUSTRIAL RELATIONS & LABOR 6.0 0.6 0.097 5.7 5.9

217 BUSINESS 9.1 0.4 0.039 8.8 9.1

38

218 BUSINESS, FINANCE 8.7 0.6 0.069 8.5 8.9

219 MANAGEMENT 8.5 0.4 0.049 8.2 8.5

39

Table 2. Coefficients of Variation By Columns of the Quantile Matrix Before and After Normalization.

Selected Averages

After Normalization By:

BeforeExchang

e Mean

Normalization Rates

Citation

(1) (2) (3)

Quantiles

63- 262 1.993 1.946 1.939

263 - 362 0.853 0.614 0.609

363 - 462 0.709 0.372 0.364

463 - 512 0.656 0.265 0.254

513 - 562 0.635 0.250 0.242

563- 587 0.618 0.210 0.202

588 - 612 0.605 0.186 0.179

613 - 649 0.595 0.161 0.154

650 - 699 0.586 0.138 0.133

700 - 749 0.574 0.104 0.105

750 - 795 0.568 0.084 0.089

796 - 845 0.562 0.057 0.075

40

846 - 870 0.561 0.041 0.067

871 - 920 0.563 0.042 0.072

921 - 945 0.573 0.063 0.085

946 - 970 0.588 0.098 0.109

971 - 1000 0.674 0.231 0.214

41

3003263523784044304564825085345605866126386646907167427687948208468728989249509760

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Original Dataset

Normal-ized By Exchange Rates

Normal-ized By Mean Ctita-tions

Figure 2. Coefficient of Variation By Quantiles After Normalization By Exchange Rates and Mean Citations

42

Table 3. Actual versus Expected Number of Articles In Each Sub-field In the 750, 970 Interval.

NUMBER OF SUB-FIELDS

After Normalization By:

In the Original Exchange Two Sets of Mean

(Actual – Expected) Total Number Dataset Rates Exch. Rates Citation

of Articles. Absolute Differences In % (1) (3) (4) (5)

0 – 5 11 71 70

5 – 10 13 57 59

10 – 20 26 68 63

20 – 30 34 17 17

30 – 40 21 4 8

40 – 50 16 2 2

50 – 70 80 0 0

> 70 18 0 0

Total 219 219 219

Average Difference

Over the 219 Sub-fields 43.3% 9.9% 10.2%

43

0 5000 10000 15000 20000 25000 30000 350000

5000

10000

15000

20000

25000

30000

35000

40000

45000

Original Data-setBefore Normaliza-tion

Expec-ted

Figure 3. A. Differences Between the Expected Number of Articles in Every Sub-field and the Actual Number in the Original Dataset Before Normalization

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 500000

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

After Normalization By Exchange ra-tes

Expec-ted

Figure 3. Differences Between the Expected Number of Articles in Every Sub-field and the Actual Number After Normalization By Exchange Rates

44

APPENDIX

Table A. Number of Articles Published in 1998-2002, and Mean Citation Rates (with a Five-year Citation Window) for Sub-fields According to the Multiplicative Strategy

Mean Citation

Number Mean Standard Over the 750, 970

Of Articles % Citation Deviation

(1) (2) (3) (4) (5)

A. LIFE SCIENCES

I. BIOSCIENCES

1 BIOLOGY 24,255 0.42 7.50 11.3 17.2

2 BIOLOGY, MISCELLANEOUS 418 0.01 3.41 4.6 7.8

3 EVOLUTIONARY BIOLOGY 10,948 0.19 12.47 15.3 24.8

4 BIOCHEMICAL RESEARCH METHODS 33,519 0.58 9.18 30.4 17.7

5 BIOCHEMISTRY & MOLECULAR BIOLOGY 213,036 3.72 16.34 27.7 33.9

6 BIOPHYSICS 48,733 0.85 10.88 19.9 22.4

7 CELL BIOLOGY 83,279 1.45 21.43 34.8 46.6

8 GENETICS & HEREDITY 61,490 1.07 15.80 26.0 33.0

9 DEVELOPMENTAL BIOLOGY 16,689 0.29 19.41 28.2 42.0

II. BIOMEDICAL RESEARCH

10 PATHOLOGY 28,710 0.50 8.88 13.6 19.6

11 ANATOMY & MORPHOLOGY 5,996 0.10 5.69 7.5 12.3

12 ENGINEERING, BIOMEDICAL 19,273 0.34 6.76 8.9 14.7

13BIOTECHNOLOGY & APPLIED MICROBIOLOGY 62,096 1.08 9.07 20.3 18.7

14 MEDICAL LABORATORY TECHNOLOGY 10,076 0.18 6.08 9.5 13.3

15 MICROSCOPY 3,974 0.07 6.18 7.7 13.3

45

16 PHARMACOLOGY & PHARMACY 100,046 1.74 8.04 11.1 17.0

17 TOXICOLOGY 30,590 0.53 7.14 9.2 14.9

18 PHYSIOLOGY 43,122 0.75 10.42 11.1 21.6

III. CLINICAL MEDICINE I (INTERNAL)

19 CARDIAC & CARDIOVASCULAR SYSTEMS 54,761 0.96 11.42 20.7 25.4

20 RESPIRATORY SYSTEM 28,225 0.49 10.09 13.3 21.6

21 ENDOCRINOLOGY & METABOLISM 48,325 0.84 12.83 17.9 26.2

22 ANESTHESIOLOGY 16,677 0.29 6.79 9.2 15.2

23 CRITICAL CARE MEDICINE 13,106 0.23 10.74 15.4 23.5

24 EMERGENCY MEDICINE 6,627 0.12 4.11 5.9 9.1

25 GASTROENTEROLOGY & HEPATOLOGY 34,796 0.61 10.51 16.8 22.7

26 MEDICINE, GENERAL & INTERNAL 61,992 1.08 12.68 50.7 24.5

27 TROPICAL MEDICINE 6,793 0.12 4.96 6.5 11.0

28 HEMATOLOGY 41,664 0.73 16.50 25.3 36.1

29 ONCOLOGY 80,504 1.40 13.93 23.3 29.0

30 ALLERGY 8,979 0.16 8.57 12.5 19.2

31 IMMUNOLOGY 81,367 1.42 14.02 22.7 29.5

32 INFECTIOUS DISEASES 31,984 0.56 11.68 15.4 24.5

IV. CLINICAL MEDICINE II (NON-INTERNAL)

33 GERIATRICS & GERONTOLOGY 9,333 0.16 7.94 10.1 17.4

34 OBSTETRICS & GYNECOLOGY 32,152 0.56 6.67 9.0 14.7

35 ANDROLOGY 1,419 0.02 5.54 6.9 11.7

36 REPRODUCTIVE BIOLOGY 16,586 0.29 9.54 10.7 19.7

37 GERONTOLOGY 6,795 0.12 7.14 9.6 16.0

38 DENTISTRY & ORAL SURGERY 20,745 0.36 5.21 6.4 11.1

46

39 DERMATOLOGY 21,105 0.37 5.90 8.3 13.1

40 UROLOGY & NEPHROLOGY 33,336 0.58 9.14 14.1 20.1

41 OTORHINOLARYNGOLOGY 17,293 0.30 4.31 5.4 9.5

42 OPHTHALMOLOGY 26,020 0.45 6.93 10.5 15.2

43INTEGRATIVE & COMPLEMENTARY MEDICINE 2,425 0.04 4.33 5.3 9.3

44 CLINICAL NEUROLOGY 66,351 1.16 9.29 14.1 20.3

45 PSYCHIATRY 43,084 0.75 9.58 14.3 21.2

46RADIOLOGY, NUCLEAR MED. & MED. IMAGING 53,889 0.94 7.65 11.9 16.8

47 ORTHOPEDICS 23,943 0.42 5.73 7.9 12.5

48 RHEUMATOLOGY 10,558 0.18 10.74 16.2 22.8

49 SPORT SCIENCES 20,520 0.36 5.85 7.6 13.0

50 SURGERY 103,479 1.80 6.35 9.7 14.1

51 TRANSPLANTATION 21,054 0.37 6.76 10.6 15.0

52 PERIPHERAL VASCULAR DISEASE 36,397 0.63 15.50 25.1 33.6

53 PEDIATRICS 42,315 0.74 5.70 9.2 12.6

V. CLINICAL MEDICINE III

54 HEALTH CARE SCIENCES & SERVICES 13,947 0.24 5.75 8.3 12.4

55 HEALTH POLICY & SERVICES 8,748 0.15 6.26 9.3 13.2

56 MEDICINE, LEGAL 4,152 0.07 4.33 5.9 9.2

57 NURSING 8,769 0.15 2.99 3.9 6.6

58 PUBLIC, ENV. & OCCUPATIONAL HEALTH 49,445 0.86 7.07 9.9 15.2

59 REHABILITATION 13,725 0.24 4.17 5.5 9.3

60 SUBSTANCE ABUSE 7,765 0.14 7.44 8.5 15.4

61 EDUCATION, SCIENTIFIC DISCIPLINES 8,084 0.14 2.84 4.6 6.6

62 MEDICAL INFORMATICS 6,339 0.11 4.14 7.6 9.1

47

VI. NEUROSCIENCES & BEHAVIORAL

63 NEUROIMAGING 6,195 0.11 10.38 16.7 23.6

64 NEUROSCIENCES 109,828 1.92 13.05 17.9 27.5

65 BEHAVIORAL SCIENCES 14,495 0.25 8.73 9.0 17.0

66 PSYCHOLOGY, BIOLOGICAL 3,987 0.07 7.33 8.7 14.6

67 PSYCHOLOGY 16,107 0.28 7.73 9.5 16.4

68 PSYCHOLOGY, APPLIED 8,092 0.14 4.59 5.8 10.1

69 PSYCHOLOGY, CLINICAL 17,770 0.31 7.34 10.3 16.0

70 PSYCHOLOGY, DEVELOPMENTAL 10,034 0.18 7.58 9.9 16.3

71 PSYCHOLOGY, EDUCATIONAL 5,301 0.09 5.08 7.4 11.7

72 PSYCHOLOGY, EXPERIMENTAL 15,641 0.27 7.38 10.0 16.0

73 PSYCHOLOGY, MATHEMATICAL 1,751 0.03 5.10 7.1 11.3

74 PSYCHOLOGY, MULTIDISCIPLINARY 18,505 0.32 4.75 9.4 10.7

75 PSYCHOLOGY, PSYCHOANALYSIS 2,427 0.04 2.54 4.5 6.1

76 PSYCHOLOGY, SOCIAL 9,704 0.17 6.05 8.4 13.4

77 SOCIAL SCIENCES, BIOMEDICAL 6,099 0.11 5.20 7.5 11.1

B. PHYSICAL SCIENCES

VII. CHEMISTRY

78 CHEMISTRY, MULTIDISCIPLINARY 98,455 1.72 8.59 15.4 20.4

79 CHEMISTRY, INORGANIC & NUCLEAR 48,897 0.85 6.58 8.6 14.4

80 CHEMISTRY, ANALYTICAL 67,276 1.17 7.36 10.9 15.8

81 CHEMISTRY, APPLIED 33,898 0.59 5.43 7.4 11.9

82 ENGINEERING, CHEMICAL 58,925 1.03 4.23 6.5 9.7

83 CHEMISTRY, MEDICINAL 24,497 0.43 7.33 9.3 15.3

84 CHEMISTRY, ORGANIC 77,824 1.36 7.91 9.8 16.4

85 CHEMISTRY, PHYSICAL 125,278 2.19 7.73 11.0 16.5

86 ELECTROCHEMISTRY 19,943 0.35 7.45 9.2 15.8

87 POLYMER SCIENCE 55,805 0.97 6.11 9.2 13.3

48

VIII. PHYSICS

88 PHYSICS, MULTIDISCIPLINARY 83,218 1.45 8.21 20.7 18.7

89 SPECTROSCOPY 29,777 0.52 5.66 8.6 12.4

90 ACOUSTICS 14,507 0.25 3.96 5.5 8.9

91 OPTICS 52,712 0.92 5.30 8.9 11.9

92 PHYSICS, APPLIED 125,579 2.19 5.68 10.1 12.4

93PHYSICS, ATOMIC, MOLECULAR & CHEMICAL 60,873 1.06 8.51 10.9 17.6

94 THERMODYNAMICS 17,406 0.30 3.36 4.6 7.3

95 PHYSICS, MATHEMATICAL 33,755 0.59 5.66 9.1 12.3

96 PHYSICS, NUCLEAR 25,305 0.44 5.01 8.8 11.4

97 PHYSICS, PARTICLES & SUB-FIELDS 39,261 0.68 9.01 24.4 19.6

98 PHYSICS, CONDENSED MATTER 106,659 1.86 5.55 9.6 12.4

99 PHYSICS OF SOLIDS, FLUIDS & PLASMAS 24,095 0.42 7.02 8.9 14.8

IX. SPACE SCIENCES

100 ASTRONOMY & ASTROPHYSICS 59,717 1.04 11.32 19.5 24.5

X. MATHEMATICS

101 MATHEMATICS, APPLIED 52,352 0.91 2.64 4.4 6.2

102 STATISTICS & PROBABILITY 23,095 0.40 4.48 23.4 8.9

103

MATH., INTERDISCIPLINARY APPLICATIONS 17,363 0.30 4.10 6.3 9.1

104

SOCIAL SCIENCES, MATHEMATICAL METHODS 5,198 0.09 4.07 6.6 9.1

105 PURE MATHEMATICS 64,657 1.13 1.95 3.2 4.7

49

XI. COMPUTER SCIENCE

106

COMP. SCIENCE, ARTIFICIAL INTELLIGENCE 23,546 0.41 3.84 8.0 8.7

107 COMPUTER SCIENCE, CYBERNETICS 4,393 0.08 2.58 4.8 6.2

108

COMP. SCIENCE, HARDWARE & ARCHITECTURE 12,494 0.22 3.06 7.3 6.9

109

COMPUTER SCIENCE, INFORMATION SYSTEMS 20,554 0.36 3.33 7.8 7.5

110

COMP. SC., INTERDISCIPLINARY APPLICATIONS 27,243 0.48 4.50 21.9 9.2

111

COMP. SCIENCE, SOFTWARE ENGINEERING 17,375 0.30 2.64 4.9 6.2

112

COMPUTER SCIENCE, THEORY & METHODS 32,877 0.57 2.36 5.4 5.5

113

MATHEMATICAL & COMPUTATIONAL BIOLOGY 7,388 0.13 8.45 39.9 15.0

C. OTHER NATURAL SCIENCES

XII. ENGINEERING

114

ENGINEERING, ELECTRICAL & ELECTRONIC 117,411 2.05 3.52 6.7 8.0

115 TELECOMMUNICATIONS 19,724 0.34 2.76 6.3 6.5

116

CONSTRUCTION & BUILDING TECHNOLOGY 8,198 0.14 2.36 3.2 5.5

117 ENGINEERING, CIVIL 21,077 0.37 2.33 3.8 5.5

118 ENGINEERING, ENVIRONMENTAL 19,986 0.35 6.40 10.5 14.4

119 ENGINEERING, MARINE 403 0.01 0.98 1.9 2.5

120

TRANSPORTATION SCIENCE & TECHNOLOGY 5,882 0.10 1.49 3.0 4.0

121 ENGINEERING, INDUSTRIAL 12,809 0.22 2.17 3.2 5.1

50

122 ENGINEERING, MANUFACTURING 13,416 0.23 2.36 3.2 5.5

123 ENGINEERING, MECHANICAL 37,597 0.66 2.80 4.4 6.4

124 MECHANICS 42,797 0.75 3.69 5.4 8.3

125 ROBOTICS 2,906 0.05 2.50 3.7 5.8

126 INSTRUMENTS & INSTRUMENTATION 37,550 0.65 3.67 5.8 8.5

127

IMAGING SCIENCE & PHOTOGR. TECHNOLOGY 4,758 0.08 5.24 9.4 11.9

128 ENERGY & FUELS 23,855 0.42 3.46 6.0 8.1

129 NUCLEAR SCIENCE & TECHNOLOGY 35,795 0.62 3.17 5.2 7.2

130 ENGINEERING, PETROLEUM 6,289 0.11 1.12 2.5 3.1

131 AUTOMATION & CONTROL SYSTEMS 15,992 0.28 2.83 5.1 6.6

132 ENGINEERING, MULTIDISCIPLINARY 20,244 0.35 2.66 5.0 6.4

133 ERGONOMICS 3,029 0.05 3.25 4.0 7.1

134

OPERATIONS RES. & MANAGEMENT SCIENCE 18,431 0.32 2.75 4.1 6.3

XIII. MATERIALS SCIENCE

135 MATERIALS SCIENCE, BIOMATERIALS 6,559 0.11 9.40 10.8 19.5

136 MATERIALS SCIENCE, CERAMICS 19,356 0.34 3.41 5.5 8.4

137

MAT. SC., CHARACTERIZATION & TESTING 6,194 0.11 1.42 3.0 3.7

138

MATERIALS SCIENCE, COATINGS & FILMS 21,987 0.38 5.44 7.2 11.8

139 MATERIALS SCIENCE, COMPOSITES 9,535 0.17 2.45 4.0 5.8

140 MATERIALS SCIENCE, PAPER & WOOD 6,033 0.11 1.97 2.9 4.9

14 MATERIALS SCIENCE, TEXTILES 4,634 0.08 1.94 3.4 4.6

51

1

142

METALL. & METALLURGICAL ENGINEERING 38,465 0.67 3.31 6.4 7.8

143 NANOSCIENCE & NANOTECHNOLOGY 19,165 0.33 5.78 10.2 12.4

XIV. GEOSCIENCES

144 GEOCHEMISTRY & GEOPHYSICS 26,065 0.45 7.13 11.0 15.6

145 GEOGRAPHY, PHYSICAL 8,772 0.15 6.43 7.7 13.5

146 GEOLOGY 7,796 0.14 5.71 7.3 12.7

147 ENGINEERING, GEOLOGICAL 4,624 0.08 2.60 3.6 5.8

148 PALEONTOLOGY 6,596 0.12 4.66 6.5 10.3

149 REMOTE SENSING 4,981 0.09 5.38 8.5 11.5

150 OCEANOGRAPHY 18,972 0.33 7.32 8.7 15.7

151 ENGINEERING, OCEAN 3,332 0.06 2.71 5.1 6.3

152

METEOROLOGY & ATMOSPHERIC SCIENCES 27,338 0.48 7.72 11.6 16.8

153 ENGINEERING, AEROSPACE 11,574 0.20 1.73 2.9 4.3

154 MINERALOGY 7,308 0.13 5.25 7.2 11.5

155 MINING & MINERAL PROCESSING 6,536 0.11 2.77 5.2 6.5

XV. AGRICULTURAL & ENVIRONMENT

156 AGRICULTURAL ENGINEERING 4,379 0.08 3.29 4.2 7.2

157 AGRICULTURE, MULTIDISCIPLINARY 14,593 0.25 4.71 7.5 10.9

52

158 AGRONOMY 23,263 0.41 4.18 6.1 9.4

159 LIMNOLOGY 5,479 0.10 6.94 8.3 15.0

160 SOIL SCIENCE 13,589 0.24 4.87 5.9 10.7

161 BIODIVERSITY CONSERVATION 6,269 0.11 6.21 9.0 13.9

162 ENVIRONMENTAL SCIENCES 69,648 1.21 6.42 9.3 13.8

163 ENVIRONMENTAL STUDIES 9,742 0.17 3.48 4.6 7.6

164 FOOD SCIENCE & TECHNOLOGY 43,023 0.75 5.05 6.7 11.0

165 NUTRITION & DIETETICS 21,575 0.38 8.29 12.2 18.0

166

AGRICULTURE, DAIRY & ANIMAL SCIENCE 21,564 0.38 3.71 5.5 8.7

167 HORTICULTURE 10,014 0.17 4.44 6.4 10.0

XVI. BIOLOGY (ORGANISMIC AND

SUPRAORGONISMIC LEVEL)

168 ORNITHOLOGY 4,334 0.08 4.12 8.1 8.6

169 ZOOLOGY 33,428 0.58 5.41 7.3 11.8

170 ENTOMOLOGY 19,138 0.33 3.85 5.1 8.6

171 WATER RESOURCES 25,164 0.44 4.30 5.5 9.5

172 FISHERIES 15,452 0.27 5.11 5.6 10.8

173 MARINE & FRESHWATER BIOLOGY 32,162 0.56 5.99 6.4 12.4

174 MICROBIOLOGY 55,648 0.97 10.82 13.6 22.5

175 PARASITOLOGY 10,789 0.19 5.97 7.5 12.7

17 VIROLOGY 20,499 0.36 14.62 16.6 29.6

53

6

177 FORESTRY 10,844 0.19 5.20 6.7 11.0

178 MYCOLOGY 5,916 0.10 5.01 8.8 11.1

179 PLANT SCIENCES 63,766 1.11 7.19 11.2 15.5

180 ECOLOGY 39,963 0.70 8.33 10.2 17.5

181 VETERINARY SCIENCES 49,295 0.86 3.62 5.7 8.5

XVII. MULTIDISCIPLINARY

182 MULTIDISCIPLINARY SCIENCES 25,369 0.44 2.99 6.5 7.0

XVIII. RESIDUAL SUB-FIELDS*183

MATERIALS SCIENCE, MULTIDISCIPLINARY 134,872 2.35 4.77 9.0 10.5

184 CRYSTALLOGRAPHY 28,300 0.49 4.17 25.5 8.5

185 GEOSCIENCES, MULTIDISCIPLINARY 45,048 0.79 5.24 7.5 11.6

186 MEDICINE, RESEARCH & EXPERIMENTAL 42,928 0.75 13.35 29.6 29.1

D. SOCIAL SCIENCES

XIX. SOCIAL SCIENCES, GENERAL

187 CRIMINOLOGY & PENOLOGY 3,117 0.05 3.46 5.2 8.3

188 LAW 9,488 0.17 3.33 5.4 7.7

189 POLITICAL SCIENCE 12,008 0.21 2.39 4.6 5.7

190 PUBLIC ADMINISTRATION 3,430 0.06 2.47 3.7 5.8

191 ETHNIC STUDIES 786 0.01 1.82 3.7 4.3

54

192 FAMILY STUDIES 5,018 0.09 4.22 6.0 9.4

193 SOCIAL ISSUES 4,126 0.07 2.53 4.5 5.9

194 SOCIAL WORK 4,795 0.08 2.73 3.6 6.1

195 SOCIOLOGY 12,125 0.21 3.02 5.6 7.0

196 WOMEN'S STUDIES 3,650 0.06 2.80 4.4 6.4

197 EDUCATION & EDUCATIONAL RESEARCH 15,185 0.26 2.33 4.2 5.4

198 EDUCATION, SPECIAL 2,946 0.05 3.63 4.8 8.1

199 AREA STUDIES 3,273 0.06 1.33 2.1 3.2

200 GEOGRAPHY 5,498 0.10 4.18 6.3 9.0

201 PLANNING & DEVELOPMENT 5,835 0.10 3.10 4.8 6.9

202 TRANSPORTATION 1,889 0.03 3.45 4.1 7.7

203 URBAN STUDIES 4,581 0.08 3.10 4.5 6.8

204 ETHICS 3,557 0.06 2.37 3.5 5.5

205 MEDICAL ETHICS 931 0.02 3.76 5.0 8.2

206 ANTHROPOLOGY 6,217 0.11 2.99 4.5 7.1

207 COMMUNICATION 4,766 0.08 2.94 4.2 6.6

208 DEMOGRAPHY 2,061 0.04 4.23 7.2 9.2

209 HISTORY OF SOCIAL SCIENCES 1,297 0.02 1.41 1.9 3.4

210

INFORMATION SCIENCE & LIBRARY SCIENCE 8,734 0.15 2.82 5.7 6.6

211 INTERNATIONAL RELATIONS 6,124 0.11 2.24 4.7 5.3

212 LINGUISTICS 5,499 0.10 4.23 6.0 9.6

55

213 SOCIAL SCIENCES, INTERDISCIPLINARY 8,563 0.15 2.40 3.9 5.7

XX. ECONOMICS & BUSINESS

214 AGRICULTURAL ECONOMICS & POLICY 1,725 0.03 2.56 3.3 5.8

215 ECONOMICS 35,452 0.62 3.47 6.2 7.7

216 INDUSTRIAL RELATIONS & LABOR 2,051 0.04 3.17 4.6 7.3

217 BUSINESS 9,329 0.16 4.90 7.6 11.3

218 BUSINESS, FINANCE 6,162 0.11 4.74 8.1 11.0

219 MANAGEMENT 13,314 0.23 4.57 7.4 10.5

ALL CATEGORIES5,733,512 100.0

Mean 26,180 5.84

Standard Deviation 29,390 3.46

Coefficient of Variation 1.12 0.59

* These are sub-fields whose presence distorts the appearance of a power law among the group of sub-fields to which they in principle belong (see Albarrán et al., 2011, for details).

56

Table B. Number of Articles In the 750, 970 Interval Before Normalization, Expected Number of Articles In the Absence of Any Bias, and Actual Number of Articles After Different Normalization Procedures

After Normalization By:

Before Expected Exchange Mean

Normalization Rates Citation

(1) (2) (3) (4)

A. LIFE SCIENCESI. BIOSCIENCES

1 BIOLOGY 5,823 5,336.1 5,249 5,192

2 BIOLOGY, MISCELLANEOUS 43 92.0 85 85

3 EVOLUTIONARY BIOLOGY 4,776 2,408.6 2,971 2,765

4 BIOCHEMICAL RESEARCH METHODS 9,886 7,374.2 7,851 7,068

5 BIOCHEMISTRY & MOLECULAR BIOLOGY 86,302 46,867.9 47,143 44,879

6 BIOPHYSICS 17,319 10,721.3 12,165 11,087

7 CELL BIOLOGY 32,326 18,321.4 16,490 16,615

8 GENETICS & HEREDITY 23,400 13,527.8 13,003 12,385

9 DEVELOPMENTAL BIOLOGY 6,774 3,671.6 3,590 3,445

II. BIOMEDICAL RESEARCH

10 PATHOLOGY 7,796 6,316.2 5,828 5,828

11 ANATOMY & MORPHOLOGY 1,158 1,319.1 1,363 1,363

12 ENGINEERING, BIOMEDICAL 4,565 4,240.1 4,587 4,587

13BIOTECHNOLOGY & APPLIED MICROBIOLOGY 16,891 13,661.1 13,805 12,509

14 MEDICAL LABORATORY TECHNOLOGY 1,948 2,216.7 2,197 2,197

15 MICROSCOPY 850 874.3 989 989

57

16 PHARMACOLOGY & PHARMACY 26,917 22,010.1 24,060 21,145

17 TOXICOLOGY 7,617 6,729.8 7,651 7,710

18 PHYSIOLOGY 16,858 9,486.8 11,888 11,938

III. CLINICAL MEDICINE I (INTERNAL)

19 CARDIAC & CARDIOVASCULAR SYSTEMS 15,355 12,047.4 10,099 10,172

20 RESPIRATORY SYSTEM 9,435 6,209.5 6,683 6,709

21 ENDOCRINOLOGY & METABOLISM 19,482 10,631.5 11,865 12,005

22 ANESTHESIOLOGY 3,840 3,668.9 3,819 3,819

23 CRITICAL CARE MEDICINE 4,345 2,883.3 2,997 2,997

24 EMERGENCY MEDICINE 775 1,457.9 1,400 1,400

25 GASTROENTEROLOGY & HEPATOLOGY 10,368 7,655.1 7,559 6,906

26 MEDICINE, GENERAL & INTERNAL 9,753 13,638.2 7,414 6,583

27 TROPICAL MEDICINE 1,171 1,494.5 1,637 1,637

28 HEMATOLOGY 15,407 9,166.1 8,920 8,920

29 ONCOLOGY 30,984 17,710.9 18,527 17,312

30 ALLERGY 2,518 1,975.4 2,131 2,115

31 IMMUNOLOGY 29,696 17,900.7 17,808 16,770

32 INFECTIOUS DISEASES 12,306 7,036.5 7,608 7,683

IV. CLINICAL MEDICINE II (NON-INTERNAL)

33 GERIATRICS & GERONTOLOGY 2,663 2,053.3 2,115 2,401

34 OBSTETRICS & GYNECOLOGY 7,438 7,073.4 7,432 7,358

35 ANDROLOGY 266 312.2 372 372

36 REPRODUCTIVE BIOLOGY 5,880 3,648.9 4,334 4,380

37 GERONTOLOGY 1,729 1,494.9 1,516 1,739

38 DENTISTRY & ORAL SURGERY 3,528 4,563.9 5,146 5,146

39 DERMATOLOGY 4,158 4,643.1 4,705 4,705

58

40 UROLOGY & NEPHROLOGY 9,599 7,333.9 7,372 7,372

41 OTORHINOLARYNGOLOGY 2,331 3,804.5 4,172 4,172

42 OPHTHALMOLOGY 5,995 5,724.4 5,979 5,979

43INTEGRATIVE & COMPLEMENTARY MEDICINE 330 533.5 603 603

44 CLINICAL NEUROLOGY 18,994 14,597.2 14,536 14,536

45 PSYCHIATRY 12,599 9,478.5 9,005 9,888

46RADIOLOGY, NUCLEAR MED. & MED. IMAGING 13,106 11,855.6 11,760 11,760

47 ORTHOPEDICS 4,503 5,267.5 5,154 5,154

48 RHEUMATOLOGY 3,587 2,322.8 2,356 2,388

49 SPORT SCIENCES 4,232 4,514.4 4,933 4,933

50 SURGERY 21,342 22,765.4 21,240 24,274

51 TRANSPLANTATION 4,599 4,631.9 4,572 4,572

52 PERIPHERAL VASCULAR DISEASE 13,470 8,007.3 7,618 7,657

53 PEDIATRICS 7,621 9,309.3 8,587 8,587

V. CLINICAL MEDICINE III

54 HEALTH CARE SCIENCES & SERVICES 2,637 3,068.3 3,044 3,044

55 HEALTH POLICY & SERVICES 1,753 1,924.6 2,047 2,047

56 MEDICINE, LEGAL 528 913.4 949 949

57 NURSING 578 1,929.2 2,424 2,424

58PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH 11,726 10,877.9 11,828 11,828

59 REHABILITATION 1,747 3,019.5 3,144 3,109

60 SUBSTANCE ABUSE 2,137 1,708.3 1,902 1,920

61 EDUCATION, SCIENTIFIC DISCIPLINES 583 1,778.5 1,759 1,710

62 MEDICAL INFORMATICS 743 1,394.6 1,273 1,273

VI. NEUROSCIENCES & BEHAVIORAL

63 NEUROIMAGING 1,845 1,362.9 1,284 1,385

59

64 NEUROSCIENCES 41,969 24,162.2 25,529 23,698

65 BEHAVIORAL SCIENCES 4,958 3,188.9 3,836 3,891

66 PSYCHOLOGY, BIOLOGICAL 1,026 877.1 1,042 886

67 PSYCHOLOGY 4,492 3,543.5 4,023 4,023

68 PSYCHOLOGY, APPLIED 1,178 1,780.2 2,088 2,088

69 PSYCHOLOGY, CLINICAL 4,452 3,909.4 3,898 3,898

70 PSYCHOLOGY, DEVELOPMENTAL 2,667 2,207.5 2,373 2,373

71 PSYCHOLOGY, EDUCATIONAL 873 1,166.2 1,158 1,138

72 PSYCHOLOGY, EXPERIMENTAL 3,938 3,441.0 3,471 3,471

73 PSYCHOLOGY, MATHEMATICAL 283 385.2 368 368

74 PSYCHOLOGY, MULTIDISCIPLINARY 2,555 4,071.1 3,855 3,855

75 PSYCHOLOGY, PSYCHOANALYSIS 159 533.9 465 448

76 PSYCHOLOGY, SOCIAL 1,888 2,134.9 2,157 2,157

77 SOCIAL SCIENCES, BIOMEDICAL 969 1,341.8 1,347 1,368

B. PHYSICAL SCIENCES

VII. CHEMISTRY

78 CHEMISTRY, MULTIDISCIPLINARY 22,326 21,660.1 17,945 19,293

79 CHEMISTRY, INORGANIC & NUCLEAR 11,733 10,757.3 11,695 11,695

80 CHEMISTRY, ANALYTICAL 16,932 14,800.7 14,888 14,888

81 CHEMISTRY, APPLIED 6,359 7,457.6 8,930 8,930

82 ENGINEERING, CHEMICAL 7,798 12,963.5 12,931 12,710

83 CHEMISTRY, MEDICINAL 6,365 5,389.3 6,463 5,595

84 CHEMISTRY, ORGANIC 23,202 17,121.3 20,794 20,912

85 CHEMISTRY, PHYSICAL 33,128 27,561.2 29,538 29,783

86 ELECTROCHEMISTRY 5,481 4,387.5 4,881 4,908

87 POLYMER SCIENCE 11,197 12,277.1 12,926 12,926

VIII. PHYSICS

60

88 PHYSICS, MULTIDISCIPLINARY 15,886 18,308.0 13,235 13,235

89 SPECTROSCOPY 5,579 6,550.9 6,423 6,423

90 ACOUSTICS 1,700 3,191.5 3,055 3,845

91 OPTICS 8,833 11,596.6 11,710 11,538

92 PHYSICS, APPLIED 21,283 27,627.4 23,871 23,871

93PHYSICS, ATOMIC, MOLECULAR & CHEMICAL 18,471 13,392.1 14,831 15,021

94 THERMODYNAMICS 1,440 3,829.3 4,012 4,012

95 PHYSICS, MATHEMATICAL 6,155 7,426.1 7,008 7,008

96 PHYSICS, NUCLEAR 3,890 5,567.1 4,965 4,965

97 PHYSICS, PARTICLES & SUB-FIELDS 8,695 8,637.4 7,396 6,762

98 PHYSICS, CONDENSED MATTER 18,609 23,465.0 20,781 24,534

99 PHYSICS OF SOLIDS, FLUIDS & PLASMAS 5,960 5,300.9 6,029 6,075

IX. SPACE SCIENCES

100 ASTRONOMY & ASTROPHYSICS 19,155 13,137.7 13,408 12,320

X. MATHEMATICS

101 MATHEMATICS, APPLIED 3,322 11,517.4 10,863 10,521

102 STATISTICS & PROBABILITY 2,393 5,080.9 4,842 3,960

103 MATH., INTERDISCIPLINARY APPLICATIONS 2,036 3,819.9 3,548 3,548

104

SOCIAL SCIENCES, MATHEMATICAL METHODS 603 1,143.6 995 995

105 MATHEMATICS 2,257 14,224.5 14,594 14,088

XI. COMPUTER SCIENCE

106

COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE 2,455 5,180.1 4,814 4,814

61

107 COMPUTER SCIENCE, CYBERNETICS 285 966.5 864 838

108

COMP. SCIENCE, HARDWARE & ARCHITECTURE 956 2,748.7 2,548 2,548

109

COMPUTER SCIENCE, INFORMATION SYSTEMS 1,769 4,521.9 3,065 3,065

110

COMP. SC., INTERDISCIPLINARY APPLICATIONS 2,948 5,993.5 4,573 4,760

111

COMPUTER SCIENCE, SOFTWARE ENGINEERING 1,152 3,822.5 3,303 3,192

112 COMPUTER SCIENCE, THEORY & METHODS 1,803 7,232.9 5,129 7,336

113

MATHEMATICAL & COMPUTATIONAL BIOLOGY 1,525 1,625.4 1,545 1,192

C. OTHER NATURAL SCIENCES

XII. ENGINEERING

114

ENGINEERING, ELECTRICAL & ELECTRONIC 11,203 25,830.4 23,542 23,121

115 TELECOMMUNICATIONS 1,398 4,339.3 3,567 3,567

116

CONSTRUCTION & BUILDING TECHNOLOGY 373 1,803.6 1,736 2,451

117 ENGINEERING, CIVIL 1,067 4,636.9 4,015 5,612

118 ENGINEERING, ENVIRONMENTAL 4,228 4,396.9 4,142 4,698

119 ENGINEERING, MARINE 4 88.7 62 62

120

TRANSPORTATION SCIENCE & TECHNOLOGY 184 1,294.0 839 1,269

121 ENGINEERING, INDUSTRIAL 524 2,818.0 3,497 3,393

122 ENGINEERING, MANUFACTURING 573 2,951.5 2,826 4,006

123 ENGINEERING, MECHANICAL 2,438 8,271.3 8,902 8,702

124 MECHANICS 4,492 9,415.3 10,383 10,244

125 ROBOTICS 165 639.3 579 579

62

126 INSTRUMENTS & INSTRUMENTATION 4,013 8,261.0 8,991 8,831

127

IMAGING SCIENCE & PHOTOGR. TECHNOLOGY 753 1,046.8 969 969

128 ENERGY & FUELS 2,360 5,248.1 5,181 5,089

129 NUCLEAR SCIENCE & TECHNOLOGY 2,906 7,874.9 7,004 9,415

130 ENGINEERING, PETROLEUM 144 1,383.6 992 929

131 AUTOMATION & CONTROL SYSTEMS 1,109 3,518.2 3,653 3,570

132 ENGINEERING, MULTIDISCIPLINARY 1,395 4,453.7 3,962 3,821

133 ERGONOMICS 226 666.4 679 679

134

OPERATIONS RES. & MANAGEMENT SCIENCE 1,185 4,054.8 4,270 4,270

XIII. MATERIALS SCIENCE

135 MATERIALS SCIENCE, BIOMATERIALS 2,256 1,443.0 1,701 1,719

136 MATERIALS SCIENCE, CERAMICS 2,112 4,258.3 4,366 4,192

137

MATERIALS SC., CHARACTERIZATION & TESTING 160 1,362.7 894 1,405

138 MATERIALS SCIENCE, COATINGS & FILMS 4,081 4,837.1 5,728 5,728

139 MATERIALS SCIENCE, COMPOSITES 521 2,097.7 1,960 1,887

140 MATERIALS SCIENCE, PAPER & WOOD 218 1,327.3 1,460 1,405

141 MATERIALS SCIENCE, TEXTILES 150 1,019.5 1,056 1,024

142

METALLURGY & METALLURGICAL ENGINEERING 3,578 8,462.3 7,445 7,246

143 NANOSCIENCE & NANOTECHNOLOGY 3,306 4,216.3 3,790 3,790

XIV. GEOSCIENCES

63

144 GEOCHEMISTRY & GEOPHYSICS 6,726 5,734.3 5,922 6,777

145 GEOGRAPHY, PHYSICAL 2,029 1,929.8 2,465 2,064

146 GEOLOGY 1,565 1,715.1 1,838 1,821

147 ENGINEERING, GEOLOGICAL 210 1,017.3 1,111 1,094

148 PALEONTOLOGY 1,017 1,451.1 1,723 1,709

149 REMOTE SENSING 829 1,095.8 1,187 1,204

150 OCEANOGRAPHY 5,403 4,173.8 4,791 4,791

151 ENGINEERING, OCEAN 225 733.0 655 655

152

METEOROLOGY & ATMOSPHERIC SCIENCES 7,106 6,014.4 6,394 6,394

153 ENGINEERING, AEROSPACE 357 2,546.3 2,274 2,156

154 MINERALOGY 1,271 1,607.8 1,791 1,791

155 MINING & MINERAL PROCESSING 440 1,437.9 1,404 1,371

XV. AGRICULTURAL & ENVIRONMENT

156 AGRICULTURAL ENGINEERING 355 963.4 981 981

157 AGRICULTURE, MULTIDISCIPLINARY 2,291 3,210.5 3,091 3,686

158 AGRONOMY 2,961 5,117.9 5,075 4,991

159 LIMNOLOGY 1,380 1,205.4 1,385 1,385

160 SOIL SCIENCE 2,276 2,989.6 3,231 3,193

161 BIODIVERSITY CONSERVATION 1,341 1,379.2 1,336 1,548

162 ENVIRONMENTAL SCIENCES 15,190 15,322.6 17,727 16,066

163 ENVIRONMENTAL STUDIES 863 2,143.2 2,268 2,268

64

164 FOOD SCIENCE & TECHNOLOGY 7,283 9,465.1 10,328 10,328

165 NUTRITION & DIETETICS 5,852 4,746.5 4,743 4,778

166 AGRICULTURE, DAIRY & ANIMAL SCIENCE 2,482 4,744.1 5,221 5,119

167 HORTICULTURE 1,348 2,203.1 2,232 2,200

XVI. BIOLOGY (ORG.& SUPRAORG. LEVEL)

168 ORNITHOLOGY 493 953.5 968 977

169 ZOOLOGY 6,177 7,354.2 8,577 8,577

170 ENTOMOLOGY 2,186 4,210.4 5,194 5,194

171 WATER RESOURCES 3,371 5,536.1 6,126 6,126

172 FISHERIES 2,679 3,399.4 3,999 3,999

173 MARINE & FRESHWATER BIOLOGY 7,047 7,075.6 8,500 8,573

174 MICROBIOLOGY 20,608 12,242.6 13,357 13,501

175 PARASITOLOGY 2,234 2,373.6 2,653 2,653

176 VIROLOGY 9,487 4,509.8 5,215 4,904

177 FORESTRY 1,817 2,385.7 2,640 2,659

178 MYCOLOGY 977 1,301.5 1,322 1,322

179 PLANT SCIENCES 14,221 14,028.5 14,236 14,370

180 ECOLOGY 12,426 8,791.9 9,962 10,013

181 VETERINARY SCIENCES 5,360 10,844.9 11,449 11,217

65

XVII. MULTIDISCIPLINARY

182 MULTIDISCIPLINARY SCIENCES 1,995 5,581.2 4,850 4,850

XVIII. RESIDUAL SUB-FIELDS

183 MATERIALS SCIENCE, MULTIDISCIPLINARY 18,386 29,671.8 30,241 30,241

184 CRYSTALLOGRAPHY 3,012 6,226.0 6,650 5,298

185 GEOSCIENCES, MULTIDISCIPLINARY 7,880 9,910.6 10,806 10,806

186 MEDICINE, RESEARCH & EXPERIMENTAL 10,727 9,444.2 6,863 6,557

D. SOCIAL SCIENCES

XIX. SOCIAL SCIENCES, GENERAL

187 CRIMINOLOGY & PENOLOGY 332 685.7 676 665

188 LAW 900 2,087.4 1,780 1,739

189 POLITICAL SCIENCE 696 2,641.8 2,033 2,841

190 PUBLIC ADMINISTRATION 201 754.6 681 681

191 ETHNIC STUDIES 28 172.9 133 133

192 FAMILY STUDIES 632 1,104.0 1,140 1,113

193 SOCIAL ISSUES 246 907.7 789 789

194 SOCIAL WORK 283 1,054.9 1,155 1,155

195 SOCIOLOGY 961 2,667.5 2,828 2,757

196 WOMEN'S STUDIES 239 803.0 861 842

197 EDUCATION & EDUCATIONAL RESEARCH 724 3,340.7 2,693 4,032

198 EDUCATION, SPECIAL 293 648.1 716 716

199 AREA STUDIES 48 720.1 858 807

66

200 GEOGRAPHY 671 1,209.6 1,177 1,177

201 PLANNING & DEVELOPMENT 454 1,283.7 1,433 1,403

202 TRANSPORTATION 181 415.6 469 469

203 URBAN STUDIES 324 1,007.8 1,189 1,189

204 ETHICS 163 782.5 710 1,040

205 MEDICAL ETHICS 100 204.8 239 239

206 ANTHROPOLOGY 530 1,367.7 1,151 1,453

207 COMMUNICATION 325 1,048.5 1,204 1,204

208 DEMOGRAPHY 238 453.4 418 418

209 HISTORY OF SOCIAL SCIENCES 7 285.3 411 411

210

INFORMATION SCIENCE & LIBRARY SCIENCE 627 1,921.5 1,723 1,668

211 INTERNATIONAL RELATIONS 330 1,347.3 1,272 1,272

212 LINGUISTICS 737 1,209.8 1,210 1,192

213 SOCIAL SCIENCES, INTERDISCIPLINARY 494 1,883.9 1,522 2,167

XX. ECONOMICS & BUSINESS

214 AGRICULTURAL ECONOMICS & POLICY 88 379.5 420 412

215 ECONOMICS 3,199 7,799.4 6,717 6,717

216 INDUSTRIAL RELATIONS & LABOR 165 451.2 448 597

217 BUSINESS 1,404 2,052.4 1,835 1,805

218 BUSINESS, FINANCE 853 1,355.6 1,053 1,287

219 MANAGEMENT 1,876 2,929.1 2,906 2,855

67

68