The paper studies the applicability of Lotka’s law for international business literature. The data included eleven thousand two hundred two (11202) references appended to research articles published in Journal of World Business during 2012-2014. It was found that Lotka’s distribution is applicable to international business literature which was further conformed by using Chi-square and K-S statistics tests

Fatima, Nishat 

Naqvi, Shehbaz  Husain

English

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Annals of Library and Information Studies Vol. 64, December 2017, pp. 253-259       Authorship patterns in international business literature: applicability of  Lotka's Law  Shehbaz Husain Naqvia and Nishat Fatimab  aAssistant Professor, Dr. Zakir Husain Library, Jamia Millia Islamia, New Delhi-110025, E-mail: shnaqvi@jmi.ac.in bAssistant Librarian, High Court of Delhi-Delhi-110003. E-mail: nishat.siddique@ymail.com  Received: 03 February 2017; revised: 06 December 207; accepted: 26 December 2017”  The paper studies the applicability of Lotka’s law for international business literature. The data included eleven thousand two hundred two (11202) references appended to research articles published in Journal of World Business during 2012-2014. It was found that Lotka’s distribution is applicable to international business literature which was further conformed by using Chi square and K-S statistics tests.   Keywords: Lotka’s Law; Author productivity; International Business; Straight Count Method; Chi-Square Test; K-S Test   Introduction Lotka’s law is one of the fundamental laws of bibliometrics. In 1926, Lotka1 proposed his inverse square law correlating contribution of scientific papers to their number of contributions. The law provided fundamental theoretical base for bibliometric studies involving authorships. According to the law, the number of authors making n contributions is about l/n2 of those making one; and the proportion of all contributors, that make a single contribution, is about 60percent. Lotka deduced a general equation for the relation between the frequency distribution ‘y’ of persons making ‘x’ contributions as Xny = c, constant and for the special case n = 2, the constant is 0.6079. The applicability of Lotka’s Law in different disciplines has been studied. The present study test's the applicability of Lotka’s law for literature on international business.  Review of literature A number of studies have been carried out in the past to validate the Lotka’s law. A few of them conform to Lotka’s Law in a particular field, while others either partially or do not conform to Lotka’s Law. Few of the recent studies that study the applicability of Lotka’s Law in a particular subject area are discussed below.  A study was conducted by Singh and Rana2 to conform applicability of Lotka’s Law in the Gandhian literature. The data was collected from periodical articles related to Mahatma Gandhi published in English language up to 2010. In this study it was found that the Lotka’s Law holds good in Gandhian Literature for the particular data set. Another study by Kumar3 on Human Computer Interaction (HCI) also confirms that Lotka’s Law is applicable in the field. The study is based on data collected from SCI for the period 2006-2011.  Shukla, Saxena and Riswadkar4 studied Lotka’s Law in the context of bio-energy literature published during 1982-1986 and found that Lotka’s Law holds good for bio-energy literature. Study conducted by Schorr5 conformed the validity of Lotka’s Law in map librarianship. Nath and Jackson6 also confirmed the applicability of generalized version of Lotka’s Law in the field of management information systems. A few studies partially conformed to the applicability of Lotka’s Law in a particular field. Nishtha's study7 on the publication patterns of PRL scientists for the period 1997-2006 found that Lotka’s law is partially applicable in his study. Rajgoli and ANN. LIB. INF. STU., DECEMBER 2017   254 Laxminarsaiah8 also partially conformed the applicability of Lotka’s law in spacecraft technology literature. Radhakrishnan and Kernizan9 also found some deviations in applications of Lotka’s Law in computer science literature.  Mini Devi10 found that Lotka’ Law is not applicable to toxicology literature. The data for her study was collected from TOXLINE database. Sudhier11 in his paper on authorship pattern in physics literature examined the validity of Lotka’s Law on the journal citations in the doctoral theses of University of Kerala, Thiruvananthapuram. Data set for this study consisted of 1,665 authors in straight count method and 3,367 authors through complete count method and the validity of Lotka’s Law was determined through K-S statistical test and Chi-square test. The study concluded that Lotka’s Law was not applicable in physics literature. Another study conducted by Swain12 on the publication pattern of Library Philosophy and Practice, a peer reviewed e-journal in the field of library & information science also concluded that Lotka’s law is not applicable in the study.  Objectives of the study i) To examine the validity of Lotka’s Law in the field of international business; ii) To apply Chi-square test for the conformity of Lotka’s law to the said field; and iii) To validate the study by using K-S test. Methodology Data for the study were collected in the form of the citations appended to the research articles in Elsevier's Journal of World Business. Analysis was conducted on 11,202 unique citations found in the research articles of Journal of World Business for 2012-2014 using MS-Excel.  Analysis The simplest form to represent Lotka’s Law is  xnXy= c (Equation 1) Where x is number of contribution, y is number of authors; and c is a constant. Determination of value of ‘c’ and ‘n’ The values of ‘c’ and ‘n’ are calculated by using Lotka’s equation “xnXy = c”. Data from Table 1 is used for calculating the values of ‘n’ and ‘c’. When the values of (x) and (y), as given in the row 1 of the Table 1, are inserted in Equation 1, we get: 1nX 4879=c c =4879 When data from second row of Table 1 is used in Equation 1, we get: 2nX 891=4879 2n= 4879/891 2n= 5.47587 Taking log at both sides n log2= log(5.47587) n (0.301)=0.738453 n=2.4533 n= 2.45 Verification of Lotka’s Law From data analysis it was found that 4879 authors have contributed only 1 research article each, 891 authors have contributed 2 research articles, 365 authors have contributed three research articles and so on. It was found that out of 11202 citations, only one author has contributed 46 research articles. Expected number of authors was calculated at n = 2.45 & n = 2.46. It was found that in both the cases (at n = 2.45 and n= 2.46) there is not much variation between the observed and expected number of authors.  From the above calculations it can be said that Lotka’s law is applicable to the present study. Table 1 shows the observed and expected number of authors in the field of international business using n = 2.45 & n = 2.46. Goodness of fit tests There are number of statistical tests that can be used to study goodness of fit. However, Chi-square test and Kolmogrov-Smirnov (K-S) test are commonly used test for this purpose. Chi-square Test The Chi-square test is used to find whether a theoretical distribution such as Lotka’s Law fits the  NAQVI & FATIMA: AUTHORSHIP PATTERNS IN INTERNATIONAL BUSINESS LITERATURE    255  given observations satisfactorily or not on the basis of certain hypotheses or theoretical considerations. If the observed values differ significantly from expected values then the goodness of fit test fails and it is said that null hypotheses is rejected.  Kolmogrov-Smirnov (K-S) Test The test is conducted by finding the theoretical/expected cumulative frequency on the basis of null hypothesis [F(x)] and comparing it with the observed cumulative frequency [Sn(x)]. Then maximum deviation point (D), the point where the theoretical/expected and observed values show the maximum deviation is found and compared with the critical value. The null hypothesis is rejected if the calculated value of D is greater than critical value; otherwise not. Chi square test on author’s productivity Table 2 shows the results of Chi square test on productivity of authors in relation to Lotka’s Law (when expected authors was calculated by using n=2.45). Chi-Square test was calculated at a degree of freedom 10, and level of significance of 0.05 percent. The critical value at 0.05 percent significance level is 30.34,whereas Chi square value from the Chi Table is 18.307. The calculated value is significantly higher than the actual Chi value hence it can be said that Lotka’s law is not applicable to this data set. Table 3 shows the result of Chi-Square test on productivity of authors in relation to Lotka’s Law (when expected authors was calculated by using n=2.46). Chi-Square test was calculated at a degree of freedom 10, and level of significance of 0.05 percent.  Table 1—Observed and expected number of authors Number of Contributions (x) Number of Authors (y)  [Observed] Number of Authors (y)  [Expected] at n = 2.45 Number of Authors (y)  [Expected] at n =2.46 1 4879 4879 4879 2 891 893 887 3 365 331 327 4 183 163 161 5 105 95 93 6 68 61 59 7 35 41 41 8 34 30 29 9 24 22 22 10 13 17 17 11 16 14 13 12 6 11 11 13 6 9 9 14 5 8 7 15 1 6 6 16 4 5 5 17 1 5 5 18 1 4 4 19 2 4 3 20 2 3 3 21 1 3 3 22 1 3 2 23 3 2 2 28 2 1 1 30 1 1 1 42 1 1 0 44 1 0 0 46 1 0 0  ANN. LIB. INF. STU., DECEMBER 2017   256 Table 2—Chi-Square test on observed and expected distribution of authors (when expected authors was calculated by using n=2.45) No. of articles Observed no. of citations (Fi) Expected no. of authors (Pi) Fi-Pi (Fi-Pi)2 (Fi-Pi)2/Pi 1 4879 4879 0 0 0.00 2 891 893 -2 4 0.00 3 365 331 34 1156 3.49 4 183 163 20 400 2.45 5 105 95 10 100 1.05 6 68 61 7 49 0.80 7 35 41 -6 36 0.88 8 34 30 4 16 0.53 9 24 22 2 4 0.18 10 13 17 -4 16 0.94 11 16 14 2 4 0.29 12 6 11 -5 25 2.27 13 6 9 -3 9 1.00 14 5 8 -3 9 1.13 15 1 6 -5 25 4.17 16 4 5 -1 1 0.20 17 1 5 -4 16 3.20 18 1 4 -3 9 2.25 19 2 4 -2 4 1.00 20 2 3 -1 1 0.33 21 1 3 -2 4 1.33 22 1 3 -2 4 1.33 23 3 2 1 1 0.50 28 2 1 1 1 1.00 30 1 1 0 0 0.00 42 1 1 0 0 0.00 44 1 0 1 1 0.00 46 1 0 1 1 0.00  466    X2 = 30.34  Table 3—Chi-Square test on observed and expected distribution of authors (when expected authors was calculated atn=2.46) No. of articles Observed no. of citations (Fi) Expected no. of authors (Pi) Fi-Pi (Fi-Pi)2 (Fi-Pi)2/Pi 1 4879 4879 0 0 0.00 2 891 887 4 16 0.02 3 365 327 38 1444 4.42 4 183 161 22 484 3.01 5 105 93 12 144 1.55 6 68 59 9 81 1.37 7 35 41 -6 36 0.88 8 34 29 5 25 0.86 9 24 22 2 4 0.18 10 13 17 -4 16 0.94 11 16 13 3 9 0.69 12 6 11 -5 25 2.27 13 6 9 -3 9 1.00 14 5 7 -2 4 0.57 15 1 6 -5 25 4.17     Contd— NAQVI & FATIMA: AUTHORSHIP PATTERNS IN INTERNATIONAL BUSINESS LITERATURE    257  The critical value at 0.05 percent significance level is 31.58, whereas Chi square value from the Chi Table is 18.307. In this case also the calculated value is significantly higher than the actual Chi value,therefore it can again be concluded that Lotka’s law is not applicable to this data set. Kolmogrov-Smirnov (K- S) Test To confirm results derived from Chi Square tests, we conducted K-S test on the data. Values of expected authors were calculated by using n = 2.45 and 2.46. The analysis shows that in both cases of n, data fits Lotka’s distribution. In the first step, we calculated Maximum deviation (Dmax.) in case where expected number of authors were derived by using n=2.45. It’s value is found to be 0.0055. The critical value of D in K-S test at 5 % level of significance is 0.565. While comparing the actual value of D, 0.00.55 with critical value 0.565, it is found that the actual value of D falls within the critical value of D. Therefore, it can be said that Lotka’s law fits the author productivity distribution in this data set. The details are shown in Table 4. In second step we calculated Maximum deviation (Dmax.) in case where expected number of authors were derived by using n=2.46. It’s value in this case is found to be 0.0076. The critical value of D in K-S test at 5 % level of significance is 0.565. While comparing the actual value of D, 0.0076 with critical value 0.565, it is found that the actual value of D falls within the critical value of D. Therefore, it can again be inferred that Lotka’s law fits the author productivity distributionfor this data set. Details are given in  Table 5. Conclusion In the present study, maximum number of authors have contributed one paper each. It was observed that with increase in number of contributions, there was a significant decrease in number of corresponding authors contributing to research papers. It was also found that expected number of authors shows a significant association with observed number of authors. The Lotka’s Inverse Square law conforms to the study. Authorship pattern is now considered one of the main aspects of scientometric studies. It includes analysis of types of authors, their collaboration pattern, and number of authors, etc. Such studies will definitely be useful in understanding the development of a subject field.  References 1. Lotka A J, The frequency distribution of scientific productivity, Journal of the Washington Academy of Sciences, 16 (12) (1926) 317-322. 2. Singh S and Rana M S, Lotka’slaw and the pattern of scientific productivity in the Gandhian Literature, In Proceedings of the paper presented at 10th CALIBER, H P University and IIAS Shimla, 12-14 March 2015, p. 134-142. 3. Kumar S, Author productivity in the field of human-computer interaction (HCI) research, Annals of Library and Information Studies, 61(4) (2015) 273-285. 4. Shukla M C, Saksena S and Riswadkar M R, Application of Bradford's and Lotka's distribution to bio-energy literature: A  study based on ten abstracting services, Annals of Library and Information Studies, 48 (1) (2001) 3-30. Table 3—Chi-Square test on observed and expected distribution of authors (when expected authors was calculated atn=2.46)                                         —Contd No. of articles Observed no. of citations (Fi) Expected no. of authors (Pi) Fi-Pi (Fi-Pi)2 (Fi-Pi)2/Pi 16 4 5 -1 1 0.20 17 1 5 -4 16 3.20 18 1 4 -3 9 2.25 19 2 3 -1 1 0.33 20 2 3 -1 1 0.33 21 1 3 -2 4 1.33 22 1 2 -1 1 0.50 23 3 2 1 1 0.50 28 2 1 1 1 1.00 30 1 1 0 0 0.00 42 1 0 1 1 0.00 44 1 0 1 1 0.00 46 1 0 1 1 0.00  466    X2=31.58  ANN. LIB. INF. STU., DECEMBER 2017   258 Table 4—Kolmogrov-Smirnov (K S) Test (when expected authors was calculated by using n=2.45) Number of contributions (x) Number of authors (y) [Observed] Cumulative frequency of observed authors Relative frequency of observed authors Fo Number of authors (y) [Expected] by using n = 2.45 Cumulative frequency of expected authors Fe Relative frequency of expected authors Deviation D = Fe-Fo 1 4879 4879 0.7335 4879 4879 0.7379 0.0044 2 891 5770 0.8674 893 5772 0.8730 0.0055 3 365 6135 0.9223 331 6103 0.9230 0.0007 4 183 6318 0.9498 163 6266 0.9477 -0.0021 5 105 6423 0.9656 95 6361 0.9620 -0.0035 6 68 6491 0.9758 61 6422 0.9713 -0.0045 7 35 6526 0.9811 41 6463 0.9775 -0.0036 8 34 6560 0.9862 30 6493 0.9820 -0.0042 9 24 6584 0.9898 22 6515 0.9853 -0.0044 10 13 6597 0.9917 17 6532 0.9879 -0.0038 11 16 6613 0.9941 14 6546 0.9900 -0.0041 12 6 6619 0.9950 11 6557 0.9917 -0.0034 13 6 6625 0.9959 9 6566 0.9930 -0.0029 14 5 6630 0.9967 8 6574 0.9943 -0.0024 15 1 6631 0.9968 6 6580 0.9952 -0.0017 16 4 6635 0.9974 5 6585 0.9959 -0.0015 17 1 6636 0.9976 5 6590 0.9967 -0.0009 18 1 6637 0.9977 4 6594 0.9973 -0.0005 19 2 6639 0.9980 4 6598 0.9979 -0.0002 20 2 6641 0.9983 3 6601 0.9983 0.0000 21 1 6642 0.9985 3 6604 0.9988 0.0003 22 1 6643 0.9986 3 6607 0.9992 0.0006 23 3 6646 0.9991 2 6609 0.9995 0.0004 28 2 6648 0.9994 1 6610 0.9997 0.0003 30 1 6649 0.9995 1 6611 0.9998 0.0003 42 1 6650 0.9997 1 6612 1.0000 0.0003 44 1 6651 0.9998 0 6612 1.0000 0.0002 46 1 6652 1.0000 0 6612 1.0000 0.0000  6652   6612    Table 5—Kolmogrov-Smirnov (K S) Test (when expected authors was calculated by using n=2.46) Number of contributions (x) Number of authors (y) [Observed] Cumulative frequency of observed authors Relative frequency of observed authors Fo Number of authors (y) [Expected] by using n = 2.46 Cumulative frequency of expected authors Fe Relative frequency of expected authors Deviation D = Fe-Fo 1 4879 4879 0.7335 4879 4879 0.7404 0.0069 2 891 5770 0.8674 887 5766 0.8750 0.0076 3 365 6135 0.9223 327 6093 0.9246 0.0023 4 183 6318 0.9498 161 6254 0.9490 -0.0008 5 105 6423 0.9656 93 6347 0.9631 -0.0024 6 68 6491 0.9758 59 6406 0.9721 -0.0037 7 35 6526 0.9811 41 6447 0.9783 -0.0028 8 34 6560 0.9862 29 6476 0.9827 -0.0035       Contd—  NAQVI & FATIMA: AUTHORSHIP PATTERNS IN INTERNATIONAL BUSINESS LITERATURE    259 5. Schorr A E, Lotka's Law and Map Librarianship, Journal of American Society for Information Science, 26 (3) (1975) 189–190. 6. Nath R and Jackson W M, Productivity of management information systems researchers: Does Lotka'slawapply?  Information Processing & Management, 27 (2) (1991) 203-209. 7. Nishtha A K, Publication pattern of scientists of physical research laboratory (PRL), Ahmedabad, India, Library Philosophy and Practice (e-journal), 2013. Paper No. 901. Available at http://digitalcommons.unl.edu/cgi/viewcontent-.cgi?article=2163&context=libphilprac (Accessed on 14 November 2017). 8. Rajgoli I U and  Laxminarsaiah A, Authorship  pattern and collaborative  research  in the field of  spacecraft technology, The Electronic Library, 33 (4) (2015) 625– 642.  9. Radhakrishnan T and Kernizan R, Lotka's Law and computer science literature, Journal of American Society for Information Science, 30 (1) (1979) 51-54. 10. Devi B Mini, Lokta’s Law revisited in Toxicology Literature, Library Philosophy and Practice (e-journal), 2013. Paper No. 1019..Available at http://digitalcommons.unl.edu/-cgi/viewcontent.cgi?article=2163&context=libphilprac (Accessed on 14 November 2017). 11. Sudhier K G P, Lotka's law and pattern of author productivity in the area of physics research, DESIDOC Journal of Library & Information Technology, 33 (6) (2013) 457-464. 12. Swain D K, Library philosophy and practice, 2004-2009: A Scientometric appraisal, Library Philosophy and Practice (e-journal), 2011. Paper 556. Available at http://digital-commons.unl.edu/cgi/viewcontent.cgi?article=1587&context=libphilprac(Accessed on 14 November 2017).  Table 5—Kolmogrov-Smirnov (K S) Test (when expected authors was calculated by using n=2.46)                            —Contd Number of contributions (x) Number of authors (y) [Observed] Cumulative frequency of observed authors Relative frequency of observed authors Fo Number of authors (y) [Expected] by using n = 2.46 Cumulative frequency of expected authors Fe Relative frequency of expected authors Deviation D = Fe-Fo 9 24 6584 0.9898 22 6498 0.9860 -0.0037 10 13 6597 0.9917 17 6515 0.9886 -0.0031 11 16 6613 0.9941 13 6528 0.9906 -0.0035 12 6 6619 0.9950 11 6539 0.9923 -0.0028 13 6 6625 0.9959 9 6548 0.9936 -0.0023 14 5 6630 0.9967 7 6555 0.9947 -0.0020 15 1 6631 0.9968 6 6561 0.9956 -0.0012 16 4 6635 0.9974 5 6566 0.9964 -0.0011 17 1 6636 0.9976 5 6571 0.9971 -0.0005 18 1 6637 0.9977 4 6575 0.9977 0.0000 19 2 6639 0.9980 3 6578 0.9982 0.0001 20 2 6641 0.9983 3 6581 0.9986 0.0003 21 1 6642 0.9985 3 6584 0.9991 0.0006 22 1 6643 0.9986 2 6586 0.9994 0.0007 23 3 6646 0.9991 2 6588 0.9997 0.0006 28 2 6648 0.9994 1 6589 0.9998 0.0004 30 1 6649 0.9995 1 6590 1.0000 0.0005 42 1 6650 0.9997 0 6590 1.0000 0.0003 44 1 6651 0.9998 0 6590 1.0000 0.0002 46 1 6652 1.0000 0 6590 1.0000 0.0000          6652   6590     

Authorship patterns in international business literature: applicability of Lotka's Law

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Authorship patterns in international business literature: applicability of Lotka's Law

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