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.
M.Kunz's criticism of the concept of non-Gaussian nature of scientific activities is discussed. The following points of the concept are analyzed: transformations of closed scales into open scales, the dependence of moments of non-Gaussian distributions on the samples size, the non-Gaussian nature of Man-dwelt upon byKunz. Arguments based on statistical analysis of Kunz's article are put forward againstKunz.
A viewpoint is given, according to which, addivitity may be defined only at the intuition level and quantitative latent variables are origin additive. The proposed solution to the non-additivity problem consists in restricting quantitative indicator scales by the so-called natural, in particular, open scales.
It is shown that in natural sciences, interdependences between variables are determined regardless of the distributions of variable values, whereas in science studies, distributions should be used as a starting point. This difference is due the nature of measuring instruments: in natural sciences, measurements are performed with the use of devices, while science of science uses human devices adapting themselves to the measured objects. Practical inferences are drawn.
Stationary distributions, i.e. distributions involving no time dependence, are analysed. The rank and frequency forms of statistical distributions are considered. On the basis of this consideration the approximations of stationary scientometric distributions are reviewed.
Stationary distributions, i.e. distributions involving no time dependence, are considered. It is shown that all these distributions in scientometrics can be approximated by the Zipf distribution at high values of variables. The sample moments appear to depend significantly on the sample size. Accordingly, the approximation of these observational data by probability distributions converging to a stable distribution different from the normal one proves to be the only correct approximation. The conclusion is formulated that the use of non-Gaussian statistics is necessary in the science of science and other social sciences.
The non-Gaussian character of scientific activity is discussed. This character makes correct only non-Gaussian approximations of stationary distributions of scientific activity. Deviation of different non-Gaussian approximations from the Zipf distribution can be explained in some cases by distortion introduced by the observer. The hypothesis that latent stationary distributions of scientific (and generally human) activity for separate person are always described by the Zipf distribution is formulated using the considerations connected with the variational entropy and the Zigler principles.
The rank distortion of statistical distribution and its effect on the non-Gaussian nature of scientific activities is discussed. Examples are presented and in particular, the dispersion of publications by journals (the Bradford distribution) is discussed in detail. The data supporting the thesis of non-Gaussian nature of science are reexamined, and the empirical basis of the thesis is extended.
Metric models, i.e. formalisms describing relationships between indicators and latent variables, are discussed. In modern metric models, a latent is regarded as independent of the measuring person. It is suggested that this defect of metric models be avoided if the latent is assignment a priori by fixing a form of latent distribution.