Abstract
It is examined to what extent the corollaries of the earlier proposed solution to the non-additivity problem are urgent for modern quantitative science studies. The role of non-linear transformations of indicators and closed scales in these studies is discussed. The distribution statistics and the coefficients of interconnection are investigated for their additivity. The possibilities of empirical verification of the proposed conception of additivity are also considered.
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Notes and references
S. D. HAITUN, Problems of quantitative analysis of scientific activities: The non-additivity of data. Part I. Statement and solution,Scientometrics, 10 (1986) 3.
See: S. D. HAITUN, Stationary scientometric distributions. Part I. Different approximations,Scientometrics, 4 (1982) 5–25; Part II. Non-Gaussian nature of scientific activities, Ibid.,Scientometrics 4 (1982) 89–104; Part III. Role of the Zipf distribution, Ibid.,Scientometrics 4 (1982) 181–194; S. D. HAITUN,Naukometriya: Sostoyaniye i perspektivy (Scientometrics: State and Prospects), Nauka, Moscow, 1983. The non-Gaussian nature of the distribution of social variable values as an additivity criterion of the latter is meant only with definite stipulations, see note 14 in Part I of the present article, op. cit., note 1. S. D. HPAITUN, Problems of quantitative analysis of scientific activities: The non-additivity of data. Part I. Statement and solution,Scientometrics, 10 (1986) 3.
D. PELZ, F. ANDREWS,Scientists in Organization. Productive Climates for Research and Development, Wiley, N. Y., 1960, 2nd ed., Michigan, 1976.
J. S. LONG, Productivity and academic position in the scientific career,American Sociological Review, 43 (1978) 889–903.
See note 3.
H. G. SMALL, Multiple citation patterns in scientific literatures: the circle and Hill models,Information Storage and Retrieval, 10 (1974) 393; H. G. SMALL, A co-citation model of a scientific specialty: a longitudinal study of collagen research,Social Studies of Science, 7 (1977) 139.
H. G. SMALL, 1974,op. cit., note 7.
S. D. HAITUN: The “rank distortion” effect and non-Gaussian nature of scientific activities,Scientometrics, 5 (1983) 375.
H. G. SMALL, 1974,op. cit., note 7.
H. G. SMALL, 1974,op. cit., note 7.
See note 3.
A. HARASZTHY, L. SZÁNTÓ, Some problems of research planning: data from Hungary compared to other Round I countries, in:Scientific Productivity, UNESCO, Paris, 1979, p. 155–168.
A. HARASZTHY, L. SZÁNTÓ,op. cit., note 13.
S. D. HAITUN, op. cit., note 1.
M. D. OSBALDISTON, J. S. G. COX, D. E. E. LOVEDAY, Citation and organization in pharmaceuticals R&D,R&D Management, 8 (1978) 165.
See, for example: S. CRAWFORD, Informal communication among scientists in sleep research,Journal of the American Society for Information Science, 22 (1971) 301;Problemy sotsialnogo planirovaniya v nauchnom kollektive (Problems of Social Planning in a Scientific Collective), ISI AN SSSR, Moscow, 1977; K. G. RHOADES, E. B. ROBERTS, A. R. FUSFELD, A correlation of R&D laboratory performance with critical function analysis,R&D Management, 9 (1978) 13; W. D. GARVEY,Communication: The Essence of Science, Pergamon Press, Oxford, 1979; J. ROTHMAN,Social R&D: Research and Development in human Service, Prentice Hall, Englwood Cliffs, New Jersey, 1980.
J. S. LONG, op. cit., note 5.
See: F. N. KERLINGER, E. J. REDHAZUR,Multiple Regression in Behavioral Research, Holt, Rinehart and Winston, N. Y., 1973; I. N. BERNSTEIN, Social control in applied social science: a study of evaluative researchers' conformity to technical norms,Social Science Research, 7 (1978) 24.
See, for example, the opinion ofStevens in: S. S. STEVENS, Mathematics, measurement and psychophysics, in:Handbook of Experimental Psychology, S. S. STEVENS, (Ed.), Wiley, N. Y., 1951, p. 56.
S. D. HAITUN, op. cit., note 3.
See notes 2 and 3.
See Fig. 4 in work by S. D. HAITUN, op. cit., note 3, Part II and Figy, 7–10 in work by S. D. HAITUN, op. cit., note 9. The “rank distortion” effect and non-Gaussian nature of scientific activities,Scientometrics, 5 (1983) 375.
Of these works in which the median is used, we may mention: A. G. KUZNETSOV, Nekotorye elementarnye matematicheskiye raschety pri sotsialnom planirovanii v nauchnom kollektive (Elementary mathematic social planning in the scientific community), in:Problemy sotsialnogo planirovaniya v nauchnom kollektive (Problems of Social Planning in a Scientific Community), ISI AN SSSR, 1977, s. 149–165;Ekspertnye otsenki v nauchno-technicheskom prognozirovanii (Expert Evaluation in Science-Technology Forecasting), Naukova dumka, Kiev, 1974;Communication and Communication Barriers in Sociology, Wiley, N. Y., 1976; N. S. ENDLER, J. P. ROEDIGER, Productivity and scholarly impact (citations) of British, Canadian and US department of psychology (1975),American Psychologist, 33 (1978) 1064; K. E. STUDER, D. E. CHUBIN, The cancer mission: Social contexts of biomedical research, Sage Publ., Beverly Hills (Calif.), 1980; N. W. McGUINNES, B. LITTLE, The impact of R&D spending on the foreign sales of new Canadian industrial products,Research Policy, 10 (1981) 78.
For 170 distributions, such a distribution is shown in Fig. 8 in the work by S. D. HAITUN, op. cit., note 9. A distribution curve for 190 distributions will be given in the next paper of this series dedicated to the non-Gaussian nature of data.
See, for example: P. D. ALLISON, Measures of inequality,American Sociological Review, 43 (1978) 865.
See, for example: P. D. ALLISON, op. cit., note 26 ; P. D. ALLISON, Inequality and scientific productivity,Social Studies of Science, 10 (1980) 163.
See S. D. HAITUN, op. cit., note 1, Section 8.
See S. D. HAITUN, op. cit., note 1, Section 7.
Hellwig (Z. A. HELLWIG, A method for the selection of a “compact” set of variables, in:Social Indicators: Problems of Definition and Selection, UNESCO, Paris, 1974, p. 11–20) uses the coefficient of stochastical dependence\(d^2 = \frac{{1 - \sum\limits_{i,j} {\min (p_{ij} - p_i p_j )} }}{{1 - \frac{1}{{\min \left\{ {t_x ;t_y } \right\}}}}}\) (p ij is the probability of simultaneous occurence of valuesx i andy j of variablesx andy; p i ,p j are the marginal probabilities;t x andt y are the number of rows and columns in the contingency matrix).
Kullback (S. KULLBACK,Theory of Information and Statistics, Nauka, Moscow, 1967) used the entropy coefficient of interconnectionT xy =S x +S y -S xy whereS x is the entropy of the distributionf x (X) andS y is the entropy of the distributionf y (Y), and\(S_{xy} = - \sum\limits_{i,j} {f(x_i ,y_j )} \log _2 f(x_i ,y_j )\) (see W. J. McGILL, Multivariate information transmission,Psichometrika, 19 (1954) 97; R. BOUDON,L'analyse mathematique des faits sociaux, Plon, Paris, 1967, s. 151–157) as the basis for his mathematical statistics. However, this coefficient of interconnection cannot be used as a quantitative value.
Khvostova (K. V. KHVOSTOVA, Nekotorye voprosy primeneniya kolichestvennykh metodov izucheniya sotsialnoekonomicheskikh yavlenii srednevekov'ya (Po materialam vizantiyskikh istochnikov XII–XIV vv.) (Applications of quantitative methods in historical research), in:Mathematicheskiye metody v istoricheskikh issledovaniyakh (Mathematical Methods in History Research), Nauka, Moscow, 1972, s. 15–88) introduces her coefficient of interconnection by normalizing the entropy coefficient\(T'xy = \frac{{T_{xy} }}{{T_{xy}^{max} }}\) where, according toKhvostova, T max xy =S x It can however be shown thatT max xy =∞ (see Part III of the second paper of this series) so that the normalization proposed byKhvostova is incorrect.
Z. A. HELLWIG, op. cit., note 30.
S. S. BLUME, R. SINDAIR, Aspects of the structure of a scientific discipline, in:Social Processes of Scientific Development, Routledge & Kegan Paul, L., 1974, p. 224–241.
M. ALESTALO, Interdisciplinarity in the light of the development of science and the actual research work, in:Sociology of Science and Research, Akadémiai Kiadó, Budapest, 1979, p. 363–396.
See S. D. HAITUN, op. cit., note 3, Part I, Fig. 1.
Miller andBarrington (J. D. MILLER, T. M. BARRINGTON, The acquisition and retention of scientific information,Journal of Communication, 31 (1981) 178. perform factor analysis of sociological indicator (items) on the basis of rank correlation coefficients, but they are also non-additive and their application in factor analysis is also incorrect.
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Haitun, S.D. Problems of quantitative analysis of scientific activities: The non-additivity of data. Part II. Corollaries. Scientometrics 10, 133–155 (1986). https://doi.org/10.1007/BF02026038
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DOI: https://doi.org/10.1007/BF02026038
Keywords
- Quantitative Analysis
- Distribution Statistic
- Science Study
- Scientific Activity
- Empirical Verification