Application of Bradford’S Law to Citation Data of History Doctoral Dissertations Accepted By Kurukshetra University: an Analytical Approach

An insufficient budget and inadequate space are the two serious problems which the libraries are confronting presently. About the paucity of funds, Sengupta and others have observed that libraries get less than 15 percent of the parent body’s total budget and the rate of increase of the average annual production cost of publications ranges from 12 to 15 percent, which is far more than the average 3 percent annual increase granted to the library budget by the administration. The problem of inadequate funds thus getting more serious year after year. In view of such problems as : the publication of large number of journals, provision of insufficient budget, world-wide inflation, and the lack of adequate space in the libraries, it is worthwhile to evaluate the Journals for their quality. It is necessary because the libraries today cannot afford to procure even a small fraction of the total number of Journals available in a particular field. There has been no universal tool for determining the quality of the Journals. However, the application of bibliometric technique in identifying the most used Journals in any field of knowledge is now-a-days a well established and reliable practice. Most used means most important journals. Citation count of a journal usually considered to be a fair index of the scientific significance of the material it publishes in the field under investigation. Citation frequency, as such, reflects the relative importance in the terms of the use made of the journals. Citation count of journals help in assessing the relative merit the highly important journals in a given specialization for deciding what journals to get and for how long to keep them. The direct citation method, originally devised by Garfield, has been used in this study.

The scope of this study is limited to 30 doctoral theses submitted to the Department of History under Kurukshetra University during the year 1998-2007. The study treats references as items and journals as source. This study makes an attempt to test the distribution of references among journals in terms of Bradford’s Law.

The main objectives of the present investigation are: 1. To identify the network of journals for communication in history. 2. To test the appropriateness of verbal and graphical formulation of Bradford’s Law. 3. To examine the relative performance of the two formulations Viz. verbal and graphical of the Bradford’s Law based on bibliographical data for selecting the core journals.

In this study, a total of 60 periodicals containing 534 references collected from 20 doctoral theses were arranged in order of their number of frequencies shared (i.e. in their descending order of productivity). Bradford’s Law of scattering was applied to test the appropriateness of both verbal and graphical formulations. The purpose of this investigation is two fold. First the study serves as a test of the two formulations of Bradford’s Law, verbal and graphical; to determine which one better fits citation data to the Social Science journals. Leimkuhler’s formulas are used.

contributions in a particular subject, out of the total number of primary journals available on that particular subject. As the term core journals is as relative terms in a general way core journals may also be defined as those journals which provide useful information for the broad research community and also easily accessible in libraries. To determine core journals for all the subjects a rank frequency distribution of all journals articles were undertaken. The titles of the journals have been recorded against each journal article in the work sheet. The distribution was ranked in order of journals that most frequently cited.

Table 6.1 gives a rank list of periodicals in History. Among the 60 periodicals cited it is noted that only eleven periodicals account for more than 52.62% of the citations and therefore they may be considered as core periodicals. Among them, the first three most frequently cited periodicals are ‘Indian Antiquary’ (9.36%), ‘Indian Historical Quarterly’ (6.18%) and ‘Indian Quarterly’ (5.99%). It is surprising to note that, the analysis of the ranked list reveals that a large number of citations are from the Indian Journals. There are as many as 60 journals cited in the theses. Kurukshetra University is receiving 16 journals and from these journals only 3 journals are cited (* indicate that the Journal is subscribed by the University Library). Interestingly only 2 out of 3 journals cited face in the ranking list. Implications: The implication of the observed citation pattern is that there is a need for re-examination of the use of the periodicals in History, at the Kurukshetra University Library, and more stress should be given to Indian periodicals.

The current revolution in computer-aided, micro-analytic techniques of information retrieval is largely justified by earlier studies of literature used in scientific research. These studies showed that a researcher’s interest was widely scattered among titles and was much more extensive than the coverage provided by existing bibliographic reviews. The important measures of scatter used in empirical studies is ‘Title dispersion’, which is defined as the degree to which the useful

Of particular interest is the work of Bradford. He studied the title dispersion of useful papers in two areas: applied geophysics and lubrication by arranging the source titles in order of productivity and then dividing them into three approximately equal groups. Bradford concluded that the ratio of the titles in successive zones followed a common pattern, and proposed the following “Law of Scattering”. “If scientific journals are arranged in order of decreasing productivity of articles on given subject, they may be divided into a number of periodicals more particularly devoted to the subject and several groups of zones containing the same number of articles as the nucleus where the number of periodicals in the nucleus and succeeding zones will be 1 : a2 ……….”.In other words, only a small number of journals will be needed to supply the nucleus of paper on a given topic, assuming that the topic is a narrow scientific subject. Beyond the nucleus or first zone however, the number of journals required to produce the same number of paper increases dramatically. For example, if two journals supply 300 articles on a topic, then four additional journals will be needed to supply the next 300 articles, and sixteen journals the next 300 journals. In comparing cumulative periodicals with the cumulative references they yield, Bradford proposed a linear logarithmic approximation. Vickery shows that Bradford’s law is independent of the number of zones chosen, although this value affects the value of the ratio multiplier. A more revealing analysis of title dispersion can be made by first serving the mathematical formula for the distribution of references in an ordered collection of titles, which is implicit in Bradford’s Law. This formula, or model, makes it possible to use standard statistical methods for summarizing empirical data and making tests of hypothesis. Bradford did not conclude his study by simply stating his law verbally, but instead went on to express graphically using experimental data, not noting himself that the graphical expression was not mathematically identical to the verbal formulation. He plotted R (n) (Cumulative total of relevant papers) against log (n) (natural logarithm of the total of productive journals) and found that the data revealed an elongated ‘S’ shaped curve. Part one of the curve, the initial concave portion, represents the higher density of the nuclear zone, part two the linear portion of the curve when data are plotted on a semi log scale, is equivalent to the Zipf distribution, hence the commonly used expression is the Bradford-Zipf Distribution, part three often called the “Groos Droop” shows the departure from linearity for higher values of n, the In the years following the publication of Bradford’s Law, papers by eminent researchers such as Vickery, Brookes, and Leimkuhler contributed to a partial understanding of the Bradford distribution-partially because these contributors did not interpret the law in mathematically identical terms. Vickery extended the verbal formulation to show that it applied to any number of zones of equal yield, not to only the three zones that Bradford had used for his data. Later Leimkuhler expressed the verbal formulation mathematically as is shown in the equation. R (n) – j log (n/t+1) (n>nm) ………….. (1) Where R (n) = Cumulative total of relevant papers found in the first n journals when all periodicals are ranked 1, 2, 3 ……….n in order of decreasing productivity: N = Cumulative number of journals producing R (n) relevant papers: j and t = Constants defined in terms of other variables, and nm = the value of n beyond which the curve becomes linear. Brookes in a study expressed the formula for the graphical version of Bradford’s law beyond the nuclear zone and for N log as is shown in equation (2). R (n) = N log (n/s) (n>nm) ……………. (2) Where N = total number of journals estimated to contain articles relevant to the subject of the search, and s = a constant calculated using experimental data. Vickery in his paper noted that the verbal and graphical formulations were not mathematically identical. Once the disparity between the two formulations was recognized, the questions arise concerning which of the two was more practical to apply to empirical data. Wilkison devised a comparative test between the two formulations utilizing the same bibliographic data for four different subjects Instead it utilized simple formulas for calculating N (the estimated total number of journals containing articles relevant to the subject of the search) and R (N) (the estimated total number of papers produced by N) only ‘P’ (number of journals) the empirical data on semi log paper. Although the value of p could be chosen anywhere in the linear portion of the curve, the point at which the initial concave portion of the curve turned into a linear region (n= m) was arbitrarily chosen to be equal to p and was used in determining the corresponding value of s. By identifying on the plot 2s papers, the corresponding number of journals required to supply 2s, called q, was ascertained. The values obtained for s, p, and q, were then used to calculate N and R (N) for both the verbal and graphical expressions of Bradford’s Law. Wilkinson’s test revealed that, for the data she considered the graphical rather than the verbal formulation was more consistent with the practical situation. Where Graphical Formulation: Where

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Series2Figure 8.1 : Bradford's -Bibliograph History - Kurukshetra University Hypothesis: HO: Data fits with Bradford’s Law of Distribution. H1: Data doesn’t fit with Bradford’s Law of Distribution. Results: The Bradford’s Law as applied to the Data of the History and the relevant statistics were computed using Leimkuhler’s equation which is stated as follows: Where is connected with x as follows: Using trial and error method and from Equation (2) we find the value of = 34.8. For goodness of fit the chi-square test has been applied. Where F(x) Observed values and F (x) Theoretical values. At 5% level of significance for n = 60 the table value of x20.05 for 59 df is 76.778. Therefore calculated x2 < x2 0.05 validity of Bradford’s empirical law of Bibliometrics. The curve has been drawn by taking journals and cumulative citations as abscissa and ordinate respectively. Data for plotting this curve is based on information furnished in Table 8.9.

Goffman and Morries found that the distributions of both circulating periodicals and their users in a medical library seemed to obey Bradford’s Law. Much of the untidiness mentioned by Brookes is attributed to the lack of methods for determining the minimum size or lower limits of a useful library collection, using Bradford’s law; they have suggested a method for establishing such lower limits for the purpose of maintaining a dynamic library collection. Broadford’s law, although an interesting phenomenon, was of little practical use (because of zoning only and the absence of a mathematical equation). It was shown, however that there is a numerical nucleus in the sense of Broadford. That is, a core of journals can be separated from the top of an ordered list of periodicals dealing with a given subject who represents the most significant information sources for that field. This numerical nucleus, moreover, does not necessarily consist of only the most productive periodical, but may contain any number of journals depending on the extent of dispersion of the subject’s literature among the various periodicals. Thus it is possible to set lower bounds on the number of journals which must be contained in a collection devoted to a given subject.

Brookes has also pointed out that Bradford’s law can be expected to arise when selection is made of items, charcterised by some common for an equal period and subject to the “success-breeds-success” mechanism. Hence, Broadford’s law should apply to the use of periodicals in a library as well as to the dispersion of articles among journals. These are both acquisitions processes, namely process of obtaining relevant item by means of selection.

Taking in to consideration that journal circulation obeys Bradford’s law; the following acquisition policy can be derived. In doing so it is important to base the selection of journals on expected future demand – 1. First establish the numerical nucleus and its successive zones of periodicals circulating at various successive time intervals. The length of these intervals will vary from library to library with the density of use. Some libraries may complete the nucleus each month,

2. On the basis of these observations, establish the rate of change of circulation for each periodical circulating in the library. 3. On the basis of these rates of change, establish by any appropriate means of extrapolation the expected circulation at some appropriate future date, say a year in advance. 4. The expected numerical nucleus should then belong to the numerical collection in the library’s inventory at that point in time. As a safety factor it may be good policy for the library not to delete a given journal from its collection until its predicted decline in circulation is verified by fact.

If the budget allows, it may be in the library’s interest to include those periodicals which are of greatest interest to its best customers, provided they do not already appear in the nuclear nucleus of circulating journals. The successive zones of users borrowing about the same number of journals formed a geometric series. We can thus: 1. Establish the numerical nucleus of users of the library. 2. Determine the areas of interest of the members of this nucleus, in terms of, for example, Social Science Citation Index. For Social Science Research Scholars, this can be done by selecting the headings of S.S.C.I. under which their most recent publications have been indexed. For social science research scholars, teachers and students, this may be done by interest profiles. 3. Establish the numerical nucleus for each subject heading represented by the user nucleus. This is done by applying Bradford’s Law to the distribution of articles among journals under each of the subject headings. 4. The totality of such numerical nucleus should then be added to the numerical nucleus of circulating journals for the library’s numerical collection. The expected numerical nucleus of users as well as the expected numerical nucleus of the subject areas of their interest at some appropriate future date can be established by extrapolation, and in this way the library can be in a position to anticipate future demand. In this

1. SENGUPTA (IN), GHOSH (BN) and SENGUPTA (KN). Role of bibliometry in journal selection and library management. IASLIC Bulletin. 25, 2; 1980; 87-92. 2. GARFIELD (Eugene). Citation indexes for science. Science. 122; 1955; 108-11. 3. VICKERY (BC). Bradfrod’s Law of Scattering. Journal of Documentation. 4, 3; 1948; 198-203. 4. ZIPF (GK). Human behaviour and the principle of least effort. 1949. Addison-Wesley; Cambridge. 5. GROSS (OV). Bradford’s Law and the Kelvan-Atherton Data. American Documentation. 18; 1967; 46. 6. BROOKES (BC). Derivation and application of the Bradford Zipf distribution. Journal of Documentation. 24, 4; 1968; 247-265. 7. VICKERY (BC). Op. Cit. No. 3. 8. LEIM KUHLER (FF). The Bradford distribution. Journal of Documentation. 23; 1967; 197-2007. 9. BROOKES (BC). Op. Cit. No. 6. 10. WILKINSON (FA). The ambiguity of Bradford’s Law. Journal of Documentation. 28; 1972; 122-130. 11. GOFFMAN (William) and MORRIS (Thomas G). Bradford’s Law and library acquisitions. Nature. 260; 1970; 922-93. 12. BROOKES (BC). Growth, utility and obsolescence of Scientific periodical Literature. Journal of Documentation. 26; 1970; 283-294. 13. BROOKES (BC). Op. Cit., No. 12.