impact of productivity increase on the distribution pattern of journals

Scientometrics, Vol. 17, ?Cos 1-2 (1989) 97-109

IMPACT OF PRODUCTIVITY INCREASE ON THE DISTRIBUTION PATTERN OF JOURNALS

VESNA OLUI~-VUKOVI~

Referral Centre of the University of Zagreb , P. O.Box, 327 41001 Zagreb, Croatia (Yugoslavia)

(Received October 19, 1988)

In this study an attempt to examine the dependence between the productivity of core journals and the shape of the distribution curve in the upper section is made. For this purpose, the impact of the core journal productivity increase over an extended time interval was investigated. As a referent point in relation to which the changes were followed, equalized inverse relationship between the core and periphery in terms of the number of journals and the number of papers published in them in a given subject field has been hypothesized. The degree to which a particular set of data conforms to that relationship expressed as #, is taken as an indicator of the changes in the core/periphery relation. The applicability of Lotka's exponent in the journal productivity context is also discussed.

Introduction

A common characteristic of many journal productivity distribution patterns is that the

data in the upper end of the distribution curve (when they are displayed in semilo-

garithmic plot) fall short of the linear prediction of Bradford's law. A similar pheno-

menon occurs in a wide variety of distributions e.g., papers over authors, citations

over authors and over publications etc. The nonlinear section at the end of the dis-

tribution was first interpreted to be due to an incomplete search and it was suggested

that further searching would restore the sagging empirical graph to strict linearity. 1

Although in many cases this explanation was accepted as the most appropriate, a

few authors disagreed with such a claim. First of all was O'Neil contending that the

extent of the characteristic droop is dependent on the sample s ize) Namely, he

pointed out that data on large collections of journals tended to have more of an

S-shape with a pronounced convex droop in the upper section of the curve. On the

other hand Praunlich and Kroll noted that when the data sets are characterised by

a small average productivity and a large number of journals in each subsection, the

shape at the end is not too different from the linear predic t ion) Although at first

glance each of these statements explained two different situations they both argue

for an alternative explanation of the shape of the distribution curve. Furthermore,

Scientometrics 17 (1989) Elsevier, Amsterdam-Oxford-New York- Tokyo A kad~miai Kiad6, Budapest

V. OLUIC-VUKOVIC: DISTRIBUTION PATTERN OF JOURNALS

Drott and Griffith explicitly indicated that the correspondence of a particular set of data to Bradford law is the reflection of some intrinsic feature not related to the

characteristics o f the search mechanism or the nature of the literature .4 However, it

appears that no rigorous proof has been published to support this conjecture in spite of the great research interest in the last ten years. Two concerns have occupied

most of the efforts to explain the factors influencing the shape of the Bradford-type

curve: an emphasis on a priori models of the relationships between the number or the

rank of journals and cumulative production 3,s ,6 and a search for theoretical propo-

sitions based on empirical characteristics of data.7, 8 Nevertheless, it seems that the

nature of the underlying process which causes the Bradford-type distribution deserves closer scrutiny if the results of journal productivity are to be understood. 9

In this study an experimental attempt is made to find out whether the changes in

the productivity of journals from a particular segment are reflected on the other parts

of the distribution curve. Special attention is given to the extreme parts of the curve

(the first and the last segment) and to the extent to which they are interdependent.

General remarks

According to the first theorethical statement of Bradford's law 1 o a geometrically

increasing number of journals is required in the successively less productive zones in

order to generate a production equal to that of the core R ( n l ) . If the number of journals in the first zone is nl then the number of journals in the k' th zone is:

nk n k = a k - 1 X nl or - a k - '

nl

From this follows that the number of journals in any zone is proportional to the

number of journals in the first zone. As the production of the core journals increases, the number of journals required to provide this production increases geo-

metrically, or more low productivity journals are necessary to provide the production equal to the one of the high productivity journals. Therefore, it becomes obvious that the productivity of the few first ranked journals governs the productivity and the number of journals in the succeeding zones. Finally, it seems plausible to presume that also the form of the upper end of the distribution curve is influenced

by the productivity of journals constituting the core.

98 Scientometrics 17 (1989)

v. OLUI(~-VUKOVI~: DISTRIBUTION PATTERN OF JOURNALS

The core/periphery relation

If the presumption about the core/periphery dependence is valid then the changes

in the productivity of the core journals would reflect On the upper end of the dis-

tribution curve. In testing such a claim, the primary step was to choose an appropriate

indicator. Since in the journal productivity context the two mutually dependent variables are the number of journals and the number of papers it seems logical to

relate both variables in studying the core/periphery relation.

Indicator choice and definition

As a starting point a hypothetical assumption that all papers are evenly distributed over the groups of journals or, more precisely, that each group of journals produces

R(n l ) papers on the subject, was considered. In this case there would be p l =

p2 =, . . . . . , = pk papers in each group. Since the number of journals required to provide these papers increases geometrically from the first to the last group (nl , nxa,

nl a k - 1) the mean productivity of journals in the sequential groups would decrease

in the same fashion (p l /n l , p l /n la , p x / n l a k - 1 ) . As can be seen the mean producti-

vity of journals in a particular group is inverse, ty proportional to the rank. If the mean

productivity of journals in the first group is ~1 then the mean productivity of k'th

group is:

~/1 P l

/,/k - - a t _ 1 o r - - = a k - 1

Pk

Starting from this in the even distribution case the core/periphery relation in terms

of the number of journals and their productivity can be expressed as follows:

lat nk

Pk nl

If such relation is satisfied the curve R(n) vs. log n for large values of n is appro-

ximately a straight line. However, in dealing with the actual data certain divergencies from the above relation can be expected because the number of papers in the sequential groups (especially in the last orie) is not likely to be even. The usual pattern

is that a considerably higher percentage of papers comes from a very small number of journals. If the relation between the concentration of papers in the few first ranked journals and their diffusion over peripheral journals is equalized the above relation

between the core/periphery ratios is satisfied. But, if the concentration of papers is

Seientometrics 17 (1989) 99

V. OLUI(~-VUKOVI0: DISTRIBUTION PATTERN OF JOURNALS

higher than their diffusion or vice versa, the following relation exists:

I~ nk

- - ~ _ - - @_.13

I~k nl

where 13 represents the extent of the deviation from the hypothesized equalized inverse relationship.

The closer these two ratios are to each other, the smaller is the practical difference between the concentration/diffusion effect and accordingly the value of 13 tends to 0. Consequently, it seems plausible to use 13 as an indicator of the changes in the core/ periphery relation affected by the journal productivity increase.

The simplest assumption about the core/periphery relation leads us to the concept that the increase of the positive value of 13 will reflect higher depression from the linear prediction. The validity of this concept strongly depends on the form in which the division of the collection into groups has been made.

Methodological approach

Bearing in mind that the stated level of journal productivity relates only to the single time interval and, that the proportion of the core journals to periphery as was stated by Bradford 1~ is variable, it seems reasonable to expect that the increase of the period of observation would reflect on both, the productivity of core journals and on the proportion of core journals to periphery. Starting from this, a distribution of papers published in jour.nals during two different periods of time (t; t + At) was analysed. The main assumption underlying the analysis was that the mean productivity

(p) of journals is positively related to the increase of the observation period, but that the increase of productivity per journal (Ap/]) differs from one zone to another. Since the first and the last zone of the distribution are most disparate in terms of journal productivity it might be expected that these zones would be sensitive enough to the changes in productivity influenced by At.

The approach applied involves a three-step process: 1. Data definition; 2. Full data analysis; 3. Truncated data analysis.

1. Data definition. In choosing an appropriate data source for this analysis, research output in the humanities of authors from Croatia was used to compile full biblio-

graphic references for two different periods of time.

1 O0 Scientometrics 17 (1989}


Sample A consists of 2821 papers published in 442 journals during the interval t

(1971-78). Sample B consists of 4206 papers published in 511 journals during the

period t + At (1971-80). 2.a Determination o f the core and the succeeding zones. In view of the lack of

any theoretical basis upon which the core journals can be determined and the fact that the core can be chosen freely 1 o,11-14 graph oriented approach was applied. The

main reason supporting such decision arose from the concept that the shape of the

distribution curve depends (in each particular case) on the scattering pattern of papers

among journals and thus closely reflects actual situation.

For the purpose of this study relation between the quantity and the yield of

journals constituting the rising curve of the graph and those from the nonlinear sec-

tion in the upper end of the distribution (periphery) will be emphasized.

An additional test including several distinct divisions of empirical data into the

equal productivity zones will be also performed. 2.b Distribution o f Ap among journals. Starting from the assumption that the in-

crease of papers per journal over an extended period of time, differs from one pro-

ductivity segment to another, Ap/j was analysed for: - each of the three segments of the distribution separately,

-.groups containing the same number of journals as the core in sample A.

2.c Core~periphery analysis. In order to see how the core/periphery relation

actually depends on journal productivity increase, the core/periphery ratios in terms

of the number of journals and their productivity were calculated for both samples.

Also the proportion between the first and the second segment of the distribution

during interval t and t + At was determined. 2.d Application o f Lotka's exponent. The fact that the a exponent used in Lotka's

law applications represents a certain measure of inequality in the productivity of sci-

entists from different productivity levels I s and the theoretical support that the laws

of Bradford and Lotka are mathematically equivalent under certain conditions and are

in that sense different viewes of the same phenomena ~ 6,1 7 allow us to use a exponent in the journal productivity context as well. Moreover, Egghe using Lotka's taw to derive the law of Bradford pointed out that the a exponent plays a crucial

role in determining the shape of the curve in the upper section. 13 For this purpose frequency approach was applied based on direct counting of the

number of journals with a given productivity. The a exponent is calculated by Hewlett-Packard mathematics program (least

squares curve fit) adapted for IBM PC. 3. Truncated data analysis. Following our initial assumption about the core/periphery

dependence, an artificial test on the behaviour of the last segment is performed by ex-

cluding:

Scientometrics 17 (1989) 101

V. OLUIC-VUKOVI(~: DISTRIBUTION PATTERN OF JOURNALS

(a) core j ou rna l s f rom b o t h samples ,

(b ) new jou rna l t i t les f r o m sample B.

The t r u n c a t i o n o f da ta f rom the h ighly p roduc t ive end o f the d i s t r ibu t ion offers an

o p p o r t u n i t y to examine the s i tua t ion oppos i te to the h igh c o n c e n t r a t i o n case and, its

e f fec t on the co r e / pe r i phe r y re la t ion .

In (b ) by way o f i l lus t ra t ion we cons ide red a h y p o t h e t i c a l case in which the to ta l

n u m b e r o f jou rna l s is f ixed for b o t h periods.

To achieve cons i s tency w i t h the full da ta analysis and to enab le compar i son , the

co r e /pe r i phe ry rat ios, the value o f fl and the a e x p o n e n t were ca lcu la ted on t r u n c a t e d

da ta too .

Results

Over the pe r iod o f t w o years an increase o f 1385 papers (Ap) and 69 new jou rna l

t i t les (A]) occurs. As a consequence the m e a n p roduc t i v i t y o f journa l s ~ ) i n c r e a s e s

f rom 6 .28 in the in terval t to 8 .23 in the in terval t + At.

Table 1 Distribution of journals into zones: a) graphical determination - core, linear part, droop section;

b) divison into zones containing approximately the same numbex of papers (k = 3, 4, 5)

Sample A Sample B

Zone No. of No. of ratm No. of No. of ratio

journals papers (a) jourrt~s papers (a)

a core 23 993 - 22 1488 - linear part 64 1004 2.78 62 1495 2.82 droop ~ct ion 355 824 5.85 427 1225 6.80

b 20 909 - 20 1393 - k = 3 52 946 2.60 51 1410 2.55

370 966 7.11 440 1405 8.63

14 716 - 14 1086 - 28 713 2.00 26 1051 1.85 k = 4 70 740 2.50 67 1074 2.57

330 652 4.71 404 997 6.03

10 568 - 10 864 - 18 556 1.80 17 841 1.70

k = 5 28 533 1.55 30 841 1.76 71 587 2.53 73 838 2.43

315 5 7 7 4.43 381 824 5.22


V. OLUI~-VUKOVIt~: DISTRIBUTION PATTERN OF JOURNALS

A e -

r r

420s

400(i

38~

360~

340'

3200

3000

2800

2600

2400 2200

2000

1800

1600

B

1400 -

1200 -

1000 -

800 -

600 -

400~ 200

0 ! 3 5 7 ~0 30 5070100 300500

log n

Fig. 1. Journal productivity distributions for two time intervals: t (curve A) and t+ At (curve B). Dashed line in the upper section of the curve B illustrates the change in the distribution pattern of journals from sample B after removal of the new journal titles

By plotting the cumulative total of papers R(n) against the log n for both samples typical S-shaped curves are obtained (Fig. 1). The linear trend is attained only in part and the droop sets in after n has reached 87 (curve A) and 84 (curve B).

Several distinct divisions into the groups of equal productivity revealed that the

ratio (a) is not constant in any of the analysed situations, but increases (Table 1).

These differences are attributed to the irregularities in the studied collections, cor-

responding to the deviation from the basic requirements of Bradford's law. Probably,

with more divisions (k > 5) these differences can be reduced. As the intention of

this study was not to define the smaller fraction of journals for Which the ratio

between the sequential groups varies at least, the division into the three productivity segments based on graphical data analysis is prefered.

Journal composition accross the first and the second segments shows reasonable

uniformity over both periods (the overlap is greater than 0.8) allowing comparison


V. O L U I 6 V U K O V I ~ : DISTRIBUTION PATTERN OF JOURNALS

A 1400 ~_ 1200

6oo " 4 0 0

0 ~ D , - 0 46 92 138384230276322 368414460506

Journots

F~. 2. Distr ibution of papers (~p) published in journals during the period At (2 years) in the groups containing the same number of journals (23). The groups are arranged in descending order o f journal productivi ty

3oooL n-" 2800- m

2600 240O 2200 200O

1800 - ATR

1600

1400

1200

1000

80O

6OO

4OO

2OO

0 ~. 3 5 7 10 30 5070100 300 500

tog n

Fig. 3. Journal productivi ty distributions after removal o f the core journals from sample A and B

104 Scientometrics ] 7 (1989)


Table 2 Characteristics of full and truncated data involving the ratios between the zones

in terms of the number of journals and their productivity, the values of 13, the c~ exponent and the mean productivity of the samples/7

Data n~ n~ n 3 /~l N1 N1

sources nj n~ n~ U~ Us U~

Full data Sample A 1 : 2.78 : 15.43 1 : 2.75 : 18.60 3.17 1.25 6.38 Sample B 1 : 2.82 : 19.41 1 : 2.81 : 23.65 4.24 1.04 8.23

Truncated data Sample Atr 1 : 2.59 : 10.86 1 : 2.41 : 11.38 0.52 1.45 4.36 Sample Btr 1 " 2.60 : 12.70 1 : 2.60 : 14.63 1.93 1.37 5.56 Sample Blt r 1 : 2.82 : 16.27 1 : 2.80 : 22.03 5.76 1.02 9.24

with respect to Ap. A significant change occurs only in the last segment due to the

increase of low productive journals in the interval t + At.

The analysis of Ap/] for each of the three segments of the distribution separately

yielded the following relation: core: linear part: periphery = 23.5:7.1:0.84

Figure 2 is a graphical illustration of the distribution of Ap among groups contain-

ing the same number of journals as was the number of core journals in sample A.

It was found that 39% of the total @ is accumulated in the first 23 journals (4% of

the total number of journals).

In Figure 3 the distributions of the truncated data are presented (curves Atr and

Btr). As can be seen, journals were reranked after the core journals were excluded.

The effect of new journal title elimination (sample Bl t r ) can be seen in Fig. 1

(dashed line in the upper section of curve B).

For each version of data (full and truncated data) the core/periphery ratios, the

values of/3 and the a exponent' are summarized in Table 2. In the fifth column the

corresponding mean productivity of samples is given.

In Fig. 4 the relationship between the ~ and the value of/3 and the a exponent is

presented.

Discussion

Although the period of two years appears to be very short, the obtained results

indicate that the mean productivity, the productivity of the core, the value of the

a exponent, the core/periphery ratios etc., are heavily influenced by At. As was ex-

pected the mean journal productivity is positively related to the increase of the



period of observation, but there is some variability in the underlying rate of produc-

tion between journals from different productivity segments. Namely, the results

obtained by the analysis of Ap/j for each of the three segments of the distribution

separately, explicitly indicate that the increase of papers is positively associated with the rank of journals or in other words the increase of papers per journal follows the Bradford distribution. This is in agreement with Morse's statement that the probabi-

lity of journals to publish a new paper depends on the number of papers that have

already been published) 8 Consequently, it seems that the state of the system

(journals-papers) on interval t + At is a function of the state in which the system was at time t. Although it is far from clear why such a pattern occurs, it seems that the authors' preference to submit their papers to those journals that had published more papers in their speciality in the past is the crucial one)8

Indeed, by increasing the period of observation, gradually more and more papers

appear in highly productive journals. This is clearly evident in Fig. 2 where an initial

strong cumulation of Ap in the few first ranked journals and a considerably less increase in the succeeding groups occur. Although the rank of a particular journal changes over time indicating thot the distribution of journals as a process is rather dynamic, on

the group scale it is evident that the higher Ap is allocated to approximately the same journals. This additionally supports the statement that the productivity of journals

increases with time in some predetermined fashion. On the other hand, there is no large difference in a number of journals in a particular segment over an extended period of time, except for the last one where slight trend for the number of journals to increase

as t increases occurs. But this trend does not appear to be strong enough to minimize

the impact of the higher increase of papers in the core journals.

Due to the unequal distribution of z~o among journals, the concentration of papers

in the most productive journals is significantly higher than their diffusion over peri-

pheral journals. As a consequence, the gap between the productivity of the first and the last segment of the distribution increases. This behaviour exhibits certain pecu-

liarity which can be seen in Fig. 1. In the upper section of curve B stronger depres-

sion from the linear prediction occurs supporting our initial assumption that the

changes in the productivity of the core journals would be reflected on the upper end

of the distribution curve.

Quantifying this phenomenon by core/periphery ratios is thus interesting from two points of view: (1) for testing the sensitivity of/3 to the concentration/diffusion disparity influenced by journal productivity increase and, (2) for the sake of com-

parison with respect to the degree to which the core/periphery ratio in a particular set of data conforms or not conforms to the hypothesized equalized relationship.

Core/periphery ratio analysis shows that/3 is positive in both cases but it is higher for the period t + At (Table 2). Although the proportion of core to periphery in terms


V. OLUI~-VUKOVIC: DISTRIBUTION PATTERN OF JOURNALS

of the number of journals is smaller for sample B, its productivity is significantly higher than it was in the interval t. Due to this, the value of/3 increases indicating higher concentration effect and consequently, higher deviation from the linear prediction. At the same time the ratios between the productivity and the number of journals

in the first and the second zone (I.tl/I.t2, n 2 / n l ) a r e approximately the same for sample A and B indicating that the strong middles are established in both periods.

As far as the core/periphery ratios are taken into consideration our assumption that the increase of positive value of/3 would reflect higher deviation from the linear

prediction is supported. The results obtained by two artificial tests further support the findings achieved

on full data. The apparent consequence of the removal of the core journals is that

the curves in both cases exhibit smaller deviation in the upper section, escpecially curve A (Fig. 3). In this context, it becomes meaningless to consider the extent of

deviation from the linear prediction as an indication of the incompleteness of data. The inspection of/3 discloses that its value decrease for truncated data and, for

sample Atr is near zero (Table 2) being thus a valuable indicator of the changes in

the core/periphery relation. On the contrary, by removing the new journal titles from sample B (Table 2, sample Bltr), an increase in the value of/3 occurs due to the resulting higher concentration. As a conseqU'ence a small decrease in the upper

section of curve B occurs (Fig. 1, dashed line). The main findings of the analysis described above could be summarized: (1) devia-

tion from the linear prediction increases as the productivity of core journals increases, (2) an increase of positive value of/3 is accompanied with the higher depression in the upper end of the distribution curve and, (3) an increase of new journal

titles only slightly influences the shape of the curve in the upper section. Another indicator that is of interest with respect to the core/periphery relation

is Lotka's exponent a. According to Yablonsky I s the increase of a is accompanied

by the increase of the low productive journals. Starting from this an increase of o~ during interval t + At can be expected due to the increase of low productive journals. The inspection of data, however, indicates that a is smaller for sample B (Table 2). This fact is additionally used as an indication of the changes influenced by the increase of core journal productivity. Namely, although the portion of low productive journals in sample B is higher, their productivity (on the group scale) with regards to the productivity of the core is smaller than it was in sample A. Due to this the new jorunal titles only partly influence the. shape of the curve in the upper section. The results obtained by calculation of a for fixed collection of journals further con- firmed this fact. As can be seen, only a slight decrease from 1.04 to 1.02 in the value of o~ is observed after the new journal titles were excluded (Table 2, sample

Scientometrics 17 (1989] 107

V. OLUI~-VUKOVII~: DISTRIBUTION PATTERN OF JOURNALS

Bltr). On the contrary, after the core journals were excluded (Table 2, sample Atr

and Btr) the a exponent increases in both cases.

A comparison of the ct exponent obtained from each particular set of data (in full

and truncated form) with the corresponding values of fl and/~ (Fig. 4) indicates a

slight tendency for a to decrease as the concentration increases. On the other hand

f~

8 -

6

2

0 '

Fig. 4. Dependence of samples

a)

4 6 8 lo ;5

OE

4--

3

2

I -

2

b)

i l , I F I , I ~,. 6 8 lOp

the value of ~ (a) and the a exponent (b) on the mean productivity of the

the value of/3 increases proportionally with ~. This is not unexpected due to the fact that the higher increase of g in the interval t + At is mainly attributed to the

increase of the core journal productivity. In conclusion, the following can be discerned: (1) the higher the ~ the more con-

centrated the data, the value of/3 is higher and consequently the deviation from the

linear prediction increases, (2) the smaller the ~ the higher the portion of the low productive journals, the value of o~ exponent increases and the deviation from the

linearity decreases. On the basis of the results presented, it can be suggested that tile shape of the

curve in the upper section is really affected by the core/periphery relation. The in-

crease of the concentration/diffusion disparity influenced by the higher concentration effect during interval t + At and its manifestation on the upper end of the distribution curve speaks in favour of this fact. Finally, although our intention was

not to examine the impact of time component per se, the results obtained in this study indicate that the core/periphery relation as well as many other characteristics of the distribution pattern of journals, depend upon the length of time interval. From this point of view, it is reasonable to presume that a longer time period may alter the pattern recorded for the two year interval due toa higher increase of low productive journals on the one hand and, the effect of the saturation of the highest productive journals 19 on the other.


V. OLUI~-VUKOVI~: DISTRIBUTION PATTERN OF JOURNALS

The author is very grateful to Dr. M. Kr~ak for computer software support.

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Scientometncs 17 (1989) 109

impact of productivity increase on the distribution pattern of journals

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