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Problems of quantitative analysis of scientific activities: The non-additivity of data. Part II. Corollaries

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

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  24. 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.

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  28. See S. D. HAITUN, op. cit., note 1, Section 7.

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  30. 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.

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  31. 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.

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  32. Z. A. HELLWIG, op. cit., note 30.

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  35. See S. D. HAITUN, op. cit., note 3, Part I, Fig. 1.

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  36. 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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Keywords

  • Quantitative Analysis
  • Distribution Statistic
  • Science Study
  • Scientific Activity
  • Empirical Verification