The criterion of reproducibility, as well as its functioning in post-non-classical science, are discussed in the Russian methodology of science. At the same time, critics avoid statistical calculations in their arguments. This raises the following questions: “What is reproducibility?” and “What is the mathematical formulation of the reproducibility criterion?” Literature review has identified five indicators of reproducibility, which was proposed by foreign colleagues. These indicators are being tested and discussed. However, there is no General mathematical formulation of the reproducibility criterion (an integral criterion covering these indicators), and these indicators have not yet become a standard. In the present work, we compare two statistical tests, related to one of these five indicators of reproducibility.
Purpose of the study. The aim of this paper is to compare the powers of two tests of statistical significance that can be used to reveal the effect with the requirement of reproducibility of research results. In this case, the reproducibility is estimated by the indicator “significance”. In accordance with the first criterion, the effect is considered to be revealed if the effect size in all studies is significant (i.e. if the significance of the effect size is reproduced in all studies). In accordance with the second criterion, the effect is considered to be revealed if the weighted mean of the effect size obtained as a result of meta-analysis is significant (the significance of the effect size may be absent in individual studies).
Materials and methods. Methods of mathematical statistics are used to achieve this goal. The powers of two tests are compared by two estimates. The first estimate is theoretical. The second one was obtained during a statistical experiment. The powers are calculated: 1) for different values of the Cohen’s effect size: “small”, “medium” and “large”, 2) for different degree of heterogeneity: zero (fixed-effect primary studies (from 2 to 8).

Results. The power of the first test is less or much less than the power of the second one. The power of the first test decreases with the growth of the number of primary studies, and the power of the second one increases. Taking into account the conventional power value equal to 80%, the first criterion is unsuitable for use in the considered values of the parameters of primary studies (that is, if a two-tailed t-test with the significance level of 0.05 and with two samples of the typical length n=25 is used to determine the significance of the effect size in individual studies), while the power of the second test can be increased if necessary by increasing the number of primary studies included in the meta-analysis.

Conclusion. If the criterion of reproducibility, known from the philosophy of science, is intended to confirm the existence of the effect (connection) or, in other words, to reveal the effect, in conditions where there is a significant random component in the measurement process, it is advisable to apply not the first, but the second test.

The purpose of the study in this article is to identify and analyze the potential economic effect from the implementation of comprehensive programs for the development of small historical settlements in Russia. At the present stage of the economic development of our country, in the economic system of these settlements a whole range of problems arises, which are in many ways common to all small towns. The key ones are the massive closure of uncompetitive enterprises, unemployment, mass migration of people to large cities, infrastructural decline and a general decline in population standards of life. In the case of small historical settlements, this situation is also fraught with the loss of the valuable objects of historical and cultural heritage of the peoples of Russia.
The article outlines shortly the main measures, currently used by the executive authorities of the Russian Federation to revitalize the economy of small historical settlements. In particular, the preparation by the Ministry of Culture of the Russian Federation for the implementation of the Concept on the development of historical settlements, supporting and promoting cultural and tourist opportunities, and developing the economy cultural heritage is mentioned. Within the framework of this Concept, it is planned to implement comprehensive programs for the development of small cities and historical settlements; those programs should take into account all aspects of the functioning of such settlements as socio-economic systems. Issues of economic efficiency of such projects are among the most important for making decisions on implementation. This article analyzes the potential economic effects of the implementation of the project for the creation of the tourist and recreation cluster “Kasimovskiy” (town of Kasimov, Ryazan Region). This project is considered by the Ministry of Culture of the Russian Federation as a pilot in the program for the implementation of the above-mentioned Concept. The economic effect analysis (results of which are shown in this article), was carried out in the context of various income and cost items of the city budget, using the methods of budget planning and financial analysis, and is based on a system of coefficients developed by the expert method.

The analysis shows a significant economic effect of the program implementation in a number of areas – in particular, in the elements of the national economy, tax structure, social security system and housing and communal services, as well as in the sphere of employment of the population and subsidized structure. At the same time, it is important to bear in mind that since the implementation of the program implies a widespread use of the mechanism of municipal-private partnerships, the relationship between the costs of budgets at various levels and the economic effect identified should be the focus of a separate case study.

Study purpose. The paper shows the application of statistical methods for the trade credit management in the wholesale Russian companies. In this industry, the companies deal with a huge amount of customers, while trade credit is a common practice. As a result, fast and reasonable choice of trade credit terms becomes especially important for wholesale companies. The main study purpose is to provide the methods to choose the trade credit terms.
Materials and methods. In this paper, the methods for trade credit management are based of the empirical research where binomial logistic model and discriminant analysis were used. The binomial logistic model was used to assess the customers’ reliability, his inclination to violate the terms specified in the contract. The delay period must be chosen when trade credit is provided. In the paper, the discriminant analysis was applied to make the decision. The discriminant functions allow choosing such a period of delay that will be broken with the least probability by the customer with certain financial and non-financial characteristics. The data used refer to 11 Russian companies from the wholesale industry and include 720 observations for 2016-2017.
Results. As a result, the possibility of due repayment may be evaluated and the payment delay may be selected according to individual customers’ characteristics. Eight factors that characterize the liquidity of the purchaser, its profitability, turnover, and non-financial factors became significant to assess the reliability. In conclusion, the paper contains the practical example for four hypothetical purchasers with different characteristics. The higher the reliability of the customer, the more attractive conditions can be offered for him, depending on the propensity to risk of the wholesale company, as well as its financial opportunities.
Conclusion. This article contains the model to evaluate the possibility of due repayment and algorithm to select the payment delay, which are based on the binomial logistic model and classification functions. Although there are a large number of methods to select the terms of trade credit, the majority of them have serious limitations. The most of methods are based only on the professional experience, while statistical analysis, in presence, is based on data of one company because of the confidentiality of necessary information. In contrast, this article is based on the empirical data and includes the delay period selection, which is slightly enlightened in the literature.

The aim of research. Construction belongs to one of types of economic activity and key industry, thereby having significant effect on economy and growth of well-being of nation and its economic entities. However, the crisis conditions of the last few years could not but affect the construction activity. In this regard, the analysis of the existing situation in the sphere of construction and studying of the factors, influencing increase in efficiency of activity of the construction organizations is a relevant task. The goal of this article is to study and analyze construction area by studying individual organizations, which were chosen in database “SPARK”. One of the most important quality indicators, characterizing the organization’s activities is profit, which is the final financial result and allows replenishing the organization’s financial resources. The work has evaluated the effectiveness of the formation and use of profits of the analyzed organizations, identifying existing problems. The profit is a factor that determines productivity of organization, its liquidity, ability to pay, financial sustainability in the modern market. A part of research performs economics and statistics analysis of main economic indicators, characterizing the formation and use of profit in organizations of the construction industry, and financial activity analysis of the two largest construction organizations in part of profit formation and its use.

Materials and methods. Informational background is statistical data and analytical information about financial activity of construction organizations. Methodological basis of the research is statistical methods of data analysis: comparative and dynamical analysis, variational analysis, correlation and regression analysis.
Results. The role of construction area in economics of Russia was analyzed. Construction is the key industry that influences the formation of the national economy. Main indicators that describe efficiency of activity of construction organizations were considered; analysis of number of indicators about activity of construction area was implemented; a group of organizations was chosen by using database “SPARK”; interrelationship between earnings and net profit was studied, comparative analysis between Ltd “Stroyregistr” and Closed Joint Stock Company “SEDO” is implemented. The main types of profit such as gross profit, profit on sales, before-tax profit and net profit were considered. It is worth noting that these types of profit are interrelated, since one category arises from the other depending on the income and expense items inherent in one or another type of profit. Analysis of the state of construction organizations involves the study of factors affecting their activity. For this purpose correlation and regression analysis was used in the work. 
Conclusion. To study the process of forming and using profits as an object of research, Ltd “Stroyregistr”, which operates in Moscow region, was chosen. As the competitor, Closed Joint Stock Company “SEDO”, which is also carrying out activity in Moscow region, was considered. During the analysis of these organizations, it was revealed that the activity of Ltd “Stroyregistr” is more stable and successful compared to Closed Joint Stock Company “SEDO”, which showed a sharp decline in financial indicators in 2016. However, the value of profitability on net profit in Ltd “Stroyregistr” is lower than the industry average value, which is associated with a low value of the net profit.
As a result, the reasons that influenced the low value of net profit were identified. One of the main reasons is the high cost of the rendered services.

Purpose of the study. The digitization of the economy transforms the ways of delivering and consuming goods and services, which in turn affects all spheres of human activity. The field of electronic commerce is a relatively young area of statistical observation, therefore, at present, researchers, government officials, business representatives and other interested persons lack statistical information, which, in turn, helps to study the economic, social and environmental consequences of the digitized world. The purpose of this study is a quantitative description of the development trends and the degree of regional differentiation of electronic commerce in the Russian Federation in the context of international comparisons.
Materials and methods. The article used the official statistical information of Rosstat and Eurostat, on the basis of which the trends in the development of electronic interaction in the business sphere were analyzed and tools were proposed for a quantitative description of regional digital gaps in the regions of Russia and the European Union countries for 2010–2017. As quantitative characteristics of regional differentiation, statistical indicators of variation and localization indicators were used (based on Gini and Lorentz coefficients). 
Results. The analysis conducted in the study showed the consistency of assessments of the regional digital divide based on economic and statistical indicators. This approach expands the possibilities for an in-depth quantitative description of the processes occurring in the field of digital trading. In addition, it was possible to identify the level of development of e-commerce in Russia in comparison with the leading economies of the European Union, as well as identify the scale of penetration of broadband Internet access among organizations, the involvement of Russian regions and European countries in the processes of placing and receiving orders for goods and services in the global network. According to the results of the study, it should be concluded that despite the obvious leading position of some European countries not only in comparison with Russian regions, but also on a global scale, the development of e-commerce in Russia and the European Union occurs at a comparable pace. It should also be noted that in the case of Russia, this development is more homogeneous in terms of regional differentiation.

Conclusion. Despite the fact that digitalization is transforming both business and personal life, there is currently an extremely small amount of information that helps quantify the economic, social and environmental consequences of this phenomenon. In order to further improve the statistical accounting of the digital economy in general and aspects of electronic commerce in particular, at this stage it is necessary: to determine the nature, structure, characteristics, elements, levels of control, movement of the digital economy’s commodity money supply for statistical purposes; identify specific digital technologies, their use in sectors of the economy and their contribution to the gross domestic product; develop a system of statistical indicators on the basis of state programs and strategies, the current methodology of statistical accounting of the information society, international recommendations and development of quantitative measurement of non-governmental organizations.

The purpose of this paper consists in the identification of historical development pattern of the cost-of-living index, which is a significant price indicator of macroeconomic process.
Materials and methods. The analysis of the cost-of-living index conception in dynamics is realized on the base of the foreign (American and West European) periodical data, also on the base of bulletins of U.S. Bureau of Labor Statistics. The methods of research is an analysis of generated conceptions of the cost-of-living index, mathematically well-founded selection of possible formulae of cost-of-living index, empirical justification of hypotheses about the ratio of the cost-of-living index and other indexes, the numerical estimation of bias calculated in relation of the cost-of-living index.
Results. The history of cost-of-living index development was divided into two stages, the boundary between two stages is 1945, when the price index, which was calculated before this moment and named the cost-of-living index, was renamed the consumer price index. The first stage (from the middle of 1910th to 1945) was described by the first accumulation of data and researches. The most part of researches consists of the survey papers and articles estimating the modern methods of cost-of living index assessment. In addition, there are some articles about the conception of cost-of-living index ant its formulae that are the base of researches after 1945. On the second stage when the investigations of cost-of-living index and consumer price index were divided, the most part of articles consists of the mathematical selection and proofs concerning the detection of the sphere of determinant to cost-of-living index of indicators (income and expenditure, used technology, family structure), also concerning the inclusion and connection of cost-of-living index in the context of economics. Empirical works of the second stage confirm some theoretical ideas on the base of national statistics.
Conclusion. The temporal cost-of-living index is the significant indicator not only of price process in the national economy, also dynamics marker of the standard of living. The effort to attract the attention to cost-of-living index will allow methodically enriching the economic researches and generating the ways of this indicator development. Among the ways it needs to mark out the calculating “alternative” consumer price indexes with due regard to approximation to cost-of-living index, realization of econometric investigation on the base of Russian statistics and intensification of the theoretical analysis on the base of conception of the true cost-of-living index by A. Konüs.

Purpose of the study. The main purpose of creating a curriculum is to regulate academic disciplines in accordance with the logic of the learning process, defined by the relationship between the basic concepts of the disciplines. Violation of this logic becomes apparent only directly during the training sessions.
A large variety of quantitative methods uses indicators that do not reveal structural deficiencies in the curriculum. This makes it difficult to improve the curriculum.
The purpose of this work is to demonstrate the application of a general approach to the assessment of the structural inconsistency of systems in relation to the evaluation of the logical structure of the curriculum.
Materials and methods. The paper applies a general approach to the assessment of structural integrity, developed on the basis of the provisions of the general theory of systems and graph theory. The approach involves the construction of three interrelated structural models of the system and using them to determine the initial data for calculating the index of inconsistency of the system structure.
Results. The overall approach to the assessment of structural integrity is adapted to assess the logical structure of the curriculum. Three models of curriculum structure are developed:
Elementary model of interdisciplinary communication;
Curriculum network model;
Hierarchical curriculum model.
Based on the parameters of the hierarchical curriculum model, using three adapted algorithms, the value of the inconsistency index of the curriculum structure in the direction of preparation “Applied Informatics” is calculated. Recommendations on changing the structure of the studied curriculum to reduce the degree of its structural inconsistency are proposed. 
Conclusion. As a result of the research, the methods were proposed that allow identifying possible contradictions in the structure of the curriculum and evaluating its inconsistency. 

As the experiments have shown, it is extremely difficult to study the curricula in a manual manner, the number of disciplines in which exceeds 50. In this regard, the development of a complex of computer programs that will automate the assessment of the inconsistency of large curricula is being completed.

The aim of the study is a probabilistic description of the functioning of the cognitive system, taking into account its internal logic and interaction with the external environment.
Such concepts of cognitive theory as sensory imaginative representations, models, systems are the most common, so the attempt to formalize them is by obtaining the most common results. One of the key concepts of cognitive theory is Gestalt, which is understood in this work as a kind of holistic perception of the sensual image, as well as the sensual image. Formalization (mathematical description) of Gestalt, as well as other concepts of cognitive theory meets the natural difficulties associated with the uncertainty of these concepts. On the other hand, there are well-developed mathematical models of behavior of quite specific organizational systems, allowing obtaining meaningful results. In this regard, the mathematical description of a wide class of cognitive systems, not limited to the specific content of their functioning, is an urgent task. In this study, it is assumed that sensory images occur at random times and affect the cognitive system with certain probabilities. In this regard, one of the adequate mathematical tools are, apparently, probability-theoretic methods, in particular, the application of the theory of Markov processes. 
The method of research within the framework of the adopted model is the application of the theory of Markov processes developing at fixed points in time, i.e. Markov chains. It is believed that the functioning of the cognitive system is described by abstract probabilities of changes in the system states. This approach allows formalizing the processes of representation of sensory images in the cognitive system, taking into account both the internal logic of the system and the interaction of the system with the outside world. The main attention is paid to the study of the influence on the behavior of the system external to her sensual images.

As a result of the study shows that the inclusion of the interactions of the system is achieved by introducing the stochastic matrix of probabilities of the system response to external influences. Taking into account the well-developed theory of Markov chains, analytical expressions for the probabilities of the system in each of the possible states are obtained. The influence on the behavior of the system of elements of the matrix of probability reactions of the system is investigated, the corresponding graphs are presented. The asymptotic behavior of the system is studied with an unlimited increase in the number of steps that change the state of the system, as well as the average characteristics of the system. It is noted that the presented description is formal, operates only with probabilistic characteristics of the system and does not take into account specific signals that can enter the system from its sensors, and generally sensitive elements. In this regard, the further development of the model may be associated with the assessment of the probability of the system response to external influences, taking into account the characteristics of these specific signals, as well as the development of optimal algorithms for decision-making about the presence or absence of impacts on the system from the outside world.