Scientometrics

, Volume 93, Issue 1, pp 135–150

Gender bias in journals of gender studies

Authors

    • Faculty of Business Administration/Business ComputingUniversity of Applied Sciences
    • COLLNET Center
  • Ramesh Kundra
  • Donald deB. Beaver
    • Williams College
  • Theo Kretschmer
    • COLLNET Center
Article

DOI: 10.1007/s11192-012-0661-5

Cite this article as:
Kretschmer, H., Kundra, R., Beaver, D.d. et al. Scientometrics (2012) 93: 135. doi:10.1007/s11192-012-0661-5

Abstract

The causes of gender bias favoring men in scientific and scholarly systems are complex and related to overall gender relationships in most of the countries of the world. An as yet unanswered question is whether in research publication gender bias is equally distributed over scientific disciplines and fields or if that bias reflects a closer relation to the subject matter. We expected less gender bias with respect to subject matter, and so analysed 14 journals of gender studies using several methods and indicators. The results confirm our expectation: the very high position of women in co-operation is striking; female scientists are relatively overrepresented as first authors in articles. Collaboration behaviour in gender studies differs from that of authors in PNAS. The pattern of gender studies reflects associations between authors of different productivity, or “masters” and “apprentices” but the PNAS pattern reflects associations between authors of roughly the same productivity, or “peers”. It would be interesting to extend the analysis of these three-dimensional collaboration patterns further, to see whether a similar characterization holds, what it might imply about the patterns of authorship in different areas, what those patterns might imply about the role of collaboration, and whether there are differences between females and males in collaboration patterns.

Keywords

Gender biasCo-operationSocial networksCo-authorshipCollaboration patterns

Mathematical Subject Classification (2000)

62689194

JEL Classification

C0C02C3C31C46

Introduction

The scientific and scholarly systems reflect a strong gender bias favoring men which makes it more difficult for women researchers to fully develop their potential and careers. The causes of that gender bias are complex and related to overall gender relationships in most of the countries of the world. An as yet unanswered question is whether in research publication gender bias is equally distributed over scientific disciplines and fields or if that bias is reflects a closer relation to the subject matter.

Because we expected that gender bias might vary with respect to subject matter, we analysed 14 journals of gender studies using several methods and indicators. Our results are reported in three sections:
  • Bibliometric indicators of gender co-operation

  • Author order in the by-line and concentration measures

  • Three-dimensional collaboration patterns of the journals “PNAS”, “Psychology of Women Quarterly” and of the mixed bibliography of 14 journals of gender studies

The special methods and indicators are explained in each section.

Data

Bibliometric analysis of the indicators in the 14 journals of gender studies (cf. Table 1) is based on a data sample of 8,649 papers published during the years 1976–2011 written by 12,691 authors in all; 10,867 of them are females and 1,823 males.
Table 1

Titles of the 14 journals

Journal

Number of papers

Number of authors

Affilia

620

1,058

Feminism and psychology

666

999

Gender and society

704

1,034

Gender technology and development

230

319

Men and masculinities

298

433

Psychology of women quarterly

1,111

2,473

Sexualities

427

536

Signs

1,396

1,676

Social politics

283

364

Women’s studies international forum

1,631

2,056

European journal of women studies

366

454

Feminist theory

228

258

Indian journal of gender studies

291

373

Feminist economics

398

658

SUM

8,649

12,691

Bibliometric indicators of gender co-operation

Naldi and Parenti (2002) introduced three new bibliometric indicators and have used these indicators in order to process publications produced by co-operation among authors of different gender:
Participation

counts the number of publications with at least one author of a given gender

Contribution

measures the involvement of each gender in the production of a publication assuming that each author contributed the same amount

Number of authors

total count of the authors of a given gender in each publication

Table 2 exemplifies the calculation of the three indicators in the case of a publication produced by four authors (Table 2 according to Naldi et al.).
Table 2

Calculation of female participation, contribution and total count

Gender

Female participation

Female contribution

Female total count

F

M

M

M

1

1/4

1

F

F

M

M

1

2/4

2

F

F

F

M

1

3/4

3

F

F

F

F

1

4/4

4

Table 3 shows the results from three studies:
Table 3

Bibliometric indicators of gender co-operation

 

Participation of women in %

Participation of men in %

Contribution of women, in%

Number of female authors in %

Naldi et al.

45.8

94.7

19.5

22.2

COLLNET bibliometric

65.3

76

45

47.9

14 Journals of gender studies

91.6

17.3

87.5

85.6

  • Naldi et al. (2004)—Science and Technological Performance by Gender

  • COLLNET (COLLNET-Collaboration Network in Science and in Technology: www.collnet.de)

  • Journals of Gender Studies (Kretschmer, Kundra, Beaver and Kretschmer)

The COLLNET results in comparison with the results by Naldi et al. have already been published by Kretschmer and Aguillo (2004).

The bibliometric study of Naldi and Parenti (2002) is based on a data sample of 10,000 items published during the year 1995 in scientific journals of international relevance and written by 35,000 authors from six European countries. Women’s Participation amounted to only 45.8% of all items as opposed to the much greater male Participation of 94.7%. Women’s Contribution amounted to about 1/5 (19.5%), approximately the same as the Number of female authors, 22.2% of all authors. Although there are differences in these results related to disciplines and countries, in general the low position of women in co-operation is striking.

The bibliometric study of 64 COLLNET members from 20 countries examined lifetime productivity until June 2003. This study is based on a data sample of 223 multi-authored publications between at least two COLLNET members. Women’s Participation amounted to 65.3% of all items and men’s Participation 76%. Although the difference between the participation of women and the participation of men is statistically significant (χ2 test, p < 0.01) it is clearly less than in the Naldi and Parenti study. Women’s Contribution, 45%, almost equalled the Number of female authors, 47.9%. In sum, female and male COLLNET members are rather equally distributed in co-operation.

The results of the analysis of the co-operation among COLLNET members differ strongly from those of gender studies in the natural sciences (Naldi et al.) which show a very low participation rate of women in collaboration activities. Female COLLNET members’ collaboration patterns are nearly equally as distributed as male members’. But further, the new results found in Journals of Gender studies even surpass the COLLNET results, insofar as female collaboration is concerned.

Bibliometric analysis of 14 journals of gender studies shows that Women’s Participation amounted to 91.6% of all papers as opposed to the much lesser male Participation of only 17.3%. As before, women’s Contribution, 87.5%, and the Number of female authors, 85.6%, were approximately equal. Although there are some minor differences in these results related to each journal individually, the very high position of women in co-operation is striking and most probably related to the subject matter of the journals.

Author order in the by-line and concentration measures

The order of the authors in the by-line is taken into consideration with help of concentration measures. The concentration of females (COF) in position x (x = 1, 2, 3, 4…) in the by-line is defined here as the ratio between the percentage of females in position x and the percentage of females in total (in the present study of gender studies’ journals: Number of female authors as a percentage of all authors = 85.6%).

If there is equal concentration by gender, the expected percentage of females in position x of the by-line should be equal to the percentage of females in total: COF = 1. If, for example, COF is higher than 1 in position 1 (first author), then females are relatively overrepresented as first authors, and vice versa if lower.

By analogy, the concentration of males (COM) in position x in the by-line is defined here as the ratio between the percentage of males in position x and the percentage of males in total (in the present study of gender studies’ journals: Number of male authors as a percentage of all authors = 14.4%).

The results are presented in Fig. 1. In all of the journals the female scientists are relatively overrepresented on the first place in the by-line. This result confirms the above mentioned results obtained by bibliometric indicators of gender co-operation. However, on the contrary, from the second place on men are relatively overrepresented. Their slight downturn and the women’s slight upturn for positions 4 or higher result from the very few collaborative papers with 7 or more authors, all of which are women.
https://static-content.springer.com/image/art%3A10.1007%2Fs11192-012-0661-5/MediaObjects/11192_2012_661_Fig1_HTML.gif
Fig. 1

Concentration measure values of females (black: open circle) and males (grey: plus) according to author order in the by-line (1 first place, 2 second, 3 third, 4 fourth and higher order). Female scientists are relatively overrepresented in the first place in the by-line. However, from the second place on the men are relatively overrepresented

Three-dimensional collaboration patterns of the journals PNAS, “Psychology of Women Quarterly” and of the mixed bibliographies of 14 journals

For about a decade social network analysis (SNA) has been used successfully in the information sciences, as well as in studies of collaboration in science. A variety of applications of SNA is available (Wasserman and Faust 1994; Otte and Rousseau 2002) both for studies in large and in small networks.

Special structures can be found in many networks, for example power-laws and others. In the present paper we present three-dimensional special network structures that also occur in many networks.

“Many investigations of scientific collaboration are based on statistical analyses of large networks constructed from bibliographic repositories. These investigations often rely on a wealth of bibliographic data, but very little or no other information about the individuals in the network, and thus, fail to illustrate the broader social and academic landscape in which collaboration takes place” (Pepe et al. 2009, p. 1).

In other words, in investigations of large networks information about “Who is collaborating with whom” is mostly missing.

However, the model of well-ordered three-dimensional distributions of co-author pairs’ frequencies in networks (Kretschmer and Kretschmer, 2007, 2009) says that, depending on the personal characteristics of collaborators (for example, author productivity or others), a special fundamental principle of social group formation is a determining factor in shaping preferences in co-authorship between individual scientists. This principle is based on similarities/dissimilarities and the corresponding consideration of this and other complementarities are a crucial determinant of the mathematical model.

Consequently, fundamental principles of social group formation produce well-ordered structures (called “Social Gestalts”) with different shapes depending on changing personalities and situations. This model has already been applied to 52 large co-authorship networks (Kretschmer and Kretschmer 2009). For 96% of them the squared multiple R is larger than 0.98 and for 77% of the 52 networks even larger than 0.99.

Method of counting co-author Pairs, based on SNA

For the purposes of analysis, a social network can be considered as consisting of two sets, a set of n nodes (individuals) and a set of m edges (undirected relations) between pairs of the nodes. The degree of a node Fx with x (x = 1, 2…n) is equal to the number of nodes (or edges) that are attached to the node Fx. In co-authorship networks between two authors (nodes) Fx and Fy, there exists an edge if both have published at least one publication together.

An author’s productivity is measured by his number of publications. The number of publications i per author Fx or j per possible co-author Fy, respectively, are determined by using the ′normal count procedure′. Each time the name of an author appears, it is counted.

The n authors Fx are grouped according to their productivities i or j, respectively. The co-author pairs of authors Fxi, (who have the number of publications i) in co-authorship with authors Fyj (who have the number of publications j), are counted. The resulting sum of co-author pairs Nij is equal to the sum of degrees of the authors Fxi to the co-authors Fyj. Therefore, the matrix of Nij is symmetrical (cf. Table 4).
Table 4

Artificial table of co-author pairs Nij

i/j

1

2

3

Ni

1

30

20

10

60

2

20

25

5

50

3

10

5

2

17

Nj

60

50

17

N = 127

Note\( N_{\rm i} = \mathop \sum \nolimits_{\rm j} N_{ij} \) is the sum of co-authors of all authors with i publications per author

\( N_{\rm j} = \mathop \sum \nolimits_{\rm i} N_{ij} \) is the sum of co-authors of all authors with j publications per author

N = Total sum of degrees of all nodes in a network, equal to the total sum of pairs including Fx each, with x (x = 1, 2…n)

In other words: Nij is equal to the sum of co-author pairs of authors who have the number of publications i in co-authorship with authors who have the number of publications j. N is equal to the total sum of degrees of all n nodes (all authors Fx) in a network, equal to the total sum of pairs.

Logarithmic binning procedure

Distributions of this kind of co-author pairs’ frequencies (Nij) have already been published (Kretschmer and Kretschmer 2007; Kundra et al. 2008; Hanning et al. 2008). However, these distributions were restricted to imax = 31.

Usually the stochastic noise increases with higher productivity because of the decreasing number of authors. We intend to overcome this problem in this paper with help of the logarithmic binning procedure. Newman has already proposed in 2005 using the logarithmic binning procedure for the log–log scale plot of power functions. To get a good fit of a straight line (log–log scale plot of power functions, for example Lotka’s distribution), we need to bin the data i into exponentially wider bins. Each bin is a fixed multiple wider than the one before it. For example, choosing the multiplier of 2 we receive the intervals 1–2, 2–4, 4–8, 8–16, etc… For each bin we have ordered the corresponding first value of i (or j) to this bin. Thus, the sequence of bins i’ or j’ is:

i’ (i’ = 1, 2, 4, 8, 16, 32, 64, 128, 256…). The same holds for the bins j’. The sizes or widths of the bins (∆i’) are: 1, 2, 4, 8, 16 etc… The same holds for (∆j’).

However, because of the bivariate presentation the width of a bin (celli’j’) in the matrix is the product of ∆i’ and ∆j’ = (∆i’ · ∆j’). The sum of co-author pairs in a bin (celli’j’) is called NijS, cf. Tables 5, 6 and 7. The total sum of NijS is equal to the total number of co-author pairs N of a co-authorship network:
$$ N = \sum\nolimits_{ij} {N_{ij}^{\text{S}} } . $$
Table 5

Matrix of NijS (PNAS) with N = 634,014

i’(bin)/j’(bin)

1

2

4

8

16

32

64

Sum

1

13,2068

77,429

41,720

18,484

6,847

1,954

196

278,698

2

77,429

54,516

30,168

14,087

5,564

1,708

192

183,664

4

41,720

30,168

17,390

8,203

3,184

1,021

105

101,791

8

18,484

14,087

8,203

3,718

1,371

428

52

46,343

16

6,847

5,564

3,184

1,371

528

153

16

17,663

32

1,954

1,708

1,021

428

153

24

3

5,291

64

196

192

105

52

16

3

0

564

Sum

27,8698

18,3664

10,1791

46,343

17,663

5,291

564

N = 634,014

Table 6

Matrix of NijS (Psychology of Women Quarterly) with N = 4,324

i’(bin)/j’(bin)

1

2

4

8

Sum

1

2,228

499

186

143

3,056

2

499

154

53

52

758

4

186

53

34

24

297

8

143

52

24

12

231

Sum

3056

758

297

231

N = 4,342

Table 7

Matrix of NijS (mixture of 14 journals in women’s and gender studies) with N = 11,996

i’(bin)/j’(bin)

1

2

4

8

16

Sum

1

6,332

1,415

424

205

44

8,420

2

1,415

574

204

69

31

2,293

4

424

204

160

50

8

846

8

205

69

50

22

3

349

16

44

31

8

3

2

88

Sum

8,420

2,293

846

349

88

N = 11,996

Method of visualizing the original data

For visualizing the original data we use the sum of co-author pairs in a bin (celli’j’), i.e. NijS directly in dependence on i’(bin) and j’(bin), (cf. Tables 5, 6 and 7). Because log 0 is not given, we are using the value “0” for presentation of NijS in the tables (cf. Tables 5, 6 and 7) but not for regression analysis.

Method of visualization the three-dimensional collaboration patterns

As the next step in the logarithmic binning procedure: NijS of a cell (celli’j’) has to be divided by the width of the bin: (∆i’·∆j’). In other words, the new value in a bin is simply the arithmetic average of all the points in the bin. This new value is called the average co-author pairs’ frequency Nij’.

Using the log–log–log presentation after the logarithmic binning procedure, the sequence of log i’ (rows) is as follows: log i’(log i’ = 0, 0.301, 0.602, 0.903, 1.204, 1.505, 1.806, …); the same holds for log j’ (columns).

In three-dimensional presentations log i’ is placed on the X-axis, log j’ on the Y-axis and logNij’ on the Z-axis, cf. Figure 2 in the paragraph headed Results.
https://static-content.springer.com/image/art%3A10.1007%2Fs11192-012-0661-5/MediaObjects/11192_2012_661_Fig2_HTML.gif
Fig. 2

Well-ordered distributions of co-author pairs’ frequencies (Z-axis: log Nij) determined by the productivities of the co-authors (the logarithmic binning procedure is used: X-axis: log i’ and Y-axis: log j’). The leftmost patterns in each row are rotated clockwise as viewed from the top 90 degrees twice in succession, resulting in three patterns per row. First row: Distribution based on data obtained from the journal PNAS (1980–1998) Total number of co-author pairs (N) = 634,014; Authors: 80,058; Articles: 32,486, Regression analysis: R2 = 0.998. Second row: Journal “Psychology of Women Quarterly” (1976–2011). N = 4,342; Authors: 2,569; Articles: 1,146; R2 = 0.998, Third row: Mixture of 14 journals in women’s and gender studies (1976–2011); N = 11,996; Authors: 16,493; Articles: 5,990; R2 = 0.996

The mathematical function for describing the three-dimensional distribution of co-author pairs’ frequencies (Nij or Nij after logarithmic binning) is a special case derived from Kretschmer’s mathematical model for the intensity function of interpersonal attraction (cf. “Appendix”).

We use this mathematical model of social Gestalts for describing co-author pairs’ frequencies (Kretschmer and Kretschmer 2007, 2009) in form of the log–log–log presentation after logarithmic binning:
$$ \log N'_{ij} = c + \alpha \cdot \log \left( {\left| {X - Y} \right| + 1} \right) + \beta \cdot \log \left( {4 - \left| {X - Y} \right|} \right) + \gamma \cdot \log \left( {X + Y + 1} \right) + \delta \cdot \log (7 - X - Y) $$
with X = logi’ and Y = logj’ and with c = constant.

For visualizing the theoretical patterns (Social Gestalts) we use the Function Plot of SYSTAT and the Scatterplot for the empirical patterns.

After regression analysis we obtain four parameters α, β, γ, and δ plus a constant c which are entered into the Function Plot (Z is the dependent variable and X and Y are the independent):
$$ Z = c + \alpha \cdot \log \left( {\left| {X - Y} \right| + 1} \right) + \beta \cdot \log \left( {4 - \left| {X - Y} \right|} \right) + \gamma \cdot \log \left( {X + Y + 1} \right) + \delta \cdot \log (7 - X - Y) $$
Scale Range: The maximum and minimum values to appear on the axis are specified. Any data values outside these limits will not appear on the display. The minimum for the X-axis is specified as 0 ((log i’)min = 0) and the maximum is equal to (log i’)max of the empirical data (For example, in Table 5: (log i’)max = log 64). The same holds for the Y-axis (log j’). The minimum and maximum values for the Z-axis are selected according to the minimum and maximum values of the whole Gestalt produced by the function. In case there are empirical values greater or less than these two theoretical values, the minimum or maximum of the Z-axis has to be extended accordingly. The Surface and Line Style dialog box is used to customize the appearance of lines or surfaces. The used XY Cut Lines are in two directions. The number of cuts in the grid has to be specified by the number of bins i’ (or j’, respectively) minus 1 in the data set. For example, a special data set has 7 bins as in Table 5 (PNAS); the number of cuts in the grid is specified by 7 − 1 = 6. The resulting number of lines of the theoretical pattern (Gestalt) is equal to the double of the number of bins i’ (2 × 7 = 14, cf. Fig. 2, first row in the paragraph Results). The number of points where two of the lines intersect, is equal to the square of the number of bins i’ (72 = 49). The Scale Range of the empirical pattern has to be about equal to the theoretical Gestalt.

After the overlay of the empirical distribution and the theoretical pattern into a single frame the goodness-of-fit is highest in the case where the empirical values (dots) are directly placed on the points where two of the theoretical lines intersect. As the distance between the intersection points and the dots increases, the goodness-of-fit decreases.

Results

The results of the application of the model to three networks are shown in Fig. 2.

Three different well-ordered shapes of distributions of co-author pairs’ frequencies (Z-axis: log Nij) reflecting the relative productivities of the co-authors (X-axis: log i’ and Y-axis: log j’ with i’ or j’-number of publications of co-authors) are presented:
  • The journal PNAS (1980–1998)

  • Journal “Psychology of Women Quarterly” (1976–2011)

  • Mixed bibliographies of 14 journals in women’s and gender studies (1976–2011) are the source for this current study

All of these three-dimensional distributions are well-ordered with changing shapes. The shapes depend on the accentuation of either similarities or, vice versa, dissimilarities, cf. Fig. 2. Whereas the convex distribution in the first row obtained from the data of the journal PNAS (19801998) shows the accentuation of similarities of the co-authors regarding their productivities, the concave distribution in the second row obtained from the data of the journal “Psychology of Women Quarterly” (19762011) shows on the other hand the accentuation of dissimilarities of the co-authors. The shape of the distribution in the third row (source: Mixed Bibliographies of 14 Journals) falls in the middle between those of the PNAS and the journal “Psychology of Women Quarterly”.

Explanation: In convex distributions (as in PNAS) the co-author pairs’ frequencies between authors with the same number of publications are higher than those with different numbers of publications. Thus, accentuation of similarities is expressed by convex distributions.

On the contrary in concave distributions (like in the Psychology of Women Quarterly) the co-author pairs’ frequencies between authors with the same number of publications are lower than those with different numbers of publications. Consequently, accentuation of dissimilarities is expressed by concave distributions.

An example for the theoretical predictions for the places of the empirical values in the theoretical patterns is also shown in Fig. 2. The lines of the theoretical patterns are obtained from the mathematical model. The points where two of the lines intersect are the theoretical predictions for the empirical values at those coordinates. The goodness-of-fit is highest in the case where the empirical values correspond exactly to the points obtained from the theoretical Gestalt (under these conditions we obtain after regression analysis: R2 = 1). In Fig. 2 the empirical values are presented in form of dots.

Conclusion

In accordance with our expectations that potential gender bias may be related to the subject matter of journals, we have analysed fourteen journals of gender studies using several methods and indicators. We have obtained the following results:
  1. 1.

    The very large percentage of women in co-operation is striking and most probably related to the subject matter of the journals.

     
  2. 2.

    Female scientists are relatively overrepresented as first authors. This result confirms the above mentioned results obtained by bibliometric indicators of gender co-operation. In contrast to the women, however, from the second place on in the by-line men are relatively overrepresented.

     
  3. 3.

    The three-dimensional collaboration patterns are well-ordered, however, the shape is different from the well-ordered shape of PNAS. Collaboration behaviour in gender studies is different from that in the natural sciences. The accentuation of similarities in productivity of co-authors is shown in PNAS but the accentuation of dissimilarities can be observed in gender studies, especially in the Journal “Psychology of Women Quarterly”

     

The results confirm our expectation that the strength of gender bias is related to the subject matter of journals, and that it is less expressed in the journals of gender studies.

It would be interesting to extend the analysis of three-dimensional collaboration patterns further, to see whether such a characterization continues to hold, what it might imply about the patterns of authorship in different fields, what those patterns might imply about the role of collaboration, and whether there are differences between females and males in collaboration patterns.

Acknowledgment

Part of this work by one of the authors (Kretschmer H) was supported by the 7th Framework Program by the European Commission, SIS-2010-1.3.3.1. Project full title: “Academic Careers Understood through Measurement and Norms “, Project acronym: ACUMEN.

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012