Applied statistics research of dependencies. Addiction research - Ayvazyan

The book logically concludes the reference editions "Applied Statistics: Basics of Modeling and Primary Data Processing" (1983) and "Applied Statistics: Exploring Dependencies" (1985). The problems of object classification, dimensionality reduction are considered. Much attention is paid to exploratory statistical analysis.
For professionals using data analysis methods.

The effect of significant multidimensionality.
The essence of this principle is that the conclusions obtained as a result of the analysis and classification of a set of statistically surveyed (for a number of properties) objects should be based simultaneously on the totality of these interrelated properties, with the obligatory consideration of the structure and nature of their connections. In 15], the nature of the effect of significant multidimensionality is explained using the following example: an attempt to distinguish between two types of consumer behavior of families, based on the consistent application of the Student's homogeneity criterion 112, paragraph 11.2.81, first on one attribute (specific food costs), then on another (specific expenditures on industrial goods and services) did not give a result, while a multidimensional analogue of this criterion, based on the so-called Mahalanobis distance and taking into account simultaneously the values ​​of both mentioned features and the nature of the statistical relationship between them, gives the correct result (i.e., it detects statistically significant difference between the two analyzed sets of families). We find the formulation of the essence of this principle in the aforementioned work of V. I. Lenin.

Opposing the classification of peasant farms in isolation for each of the analyzed characteristics with a focus on their average values, he writes: “The characteristics for distinguishing these types must be taken in accordance with local conditions and forms of farming; If in extensive grain farming it is possible to limit oneself to grouping by sowing (or by draft animals), then under other conditions it is necessary to take into account the sowing of industrial plants, technical processing of agricultural products, sowing of root crops or forage grasses, dairy farming, horticulture, etc.

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• Applied statistics, Basics of modeling and primary data processing, Aivazyan S.A., Enyukov I.S., Meshalkin L.D., 1983

The reader is offered a book that continues the implementation of the authors' intention: to create a multivolume reference manual on modern mathematical methods statistical processing data, including the simultaneous illumination of the necessary mathematical apparatus, corresponding software Computer and recommendations for overcoming computational difficulties associated with the use of the described methods and algorithms. The book is addressed to specialists different spheres human activity, using the methods of mathematical statistics and data analysis in their work.

To understand the material of the book, the reader needs only to have mathematical training in the volume of programs of an economic or technical university, or to familiarize himself with the basic concepts of probability theory and mathematical statistics, described in the first volume of the reference edition. In turn, mastering the material of the proposed book can serve as a reliable and convenient basis for a deeper penetration into the subject of research, based on the study of special monographs and journal articles.

The theme of the book is undoubtedly central to the entire reference edition. It is such both in the depth and variety of the mathematical apparatus developed to date, and in the specific weight of the use of the described methods and models in practical developments of a various profile.

The main goal that the autos set for themselves was to equip the researcher who uses statistical methods in his work with the tools necessary to solve the key problem of any research: how, on the basis of the particular results of statistical observation of the analyzed events or indicators, to identify and describe the relationships existing between them. It is this problem, the problem of statistical study of dependencies, which turns out to be the main one in solving such typical problems of practice as regulation, forecasting, planning, diagnostics, assessment of the characteristics of the analyzed system that are difficult to directly observe and measure, assessing the efficiency of the functioning or quality of an object, regulating the parameters of a process or system. ...

The authors strove for an objectively balanced presentation of the material both in terms of the structure of the book and in its content. However, the breadth and diversity of the problem raised does not allow them to claim a comprehensive coverage of the topic. For example, the topic of statistical analysis of dynamic dependencies is relatively narrowly presented in this volume; there is no description of a very useful, in certain types of problems, apparatus of logical decision rules; did not include in the book material devoted to the topical in the applied plan (especially in the problems of control of technological processes) the topic of planning regression experiments.

The book consists of an introduction and four sections.

The introduction plays a special role in understanding the methods and logic of the entire book described below. We can say that it presents the content and logical connections of all parts of the book in an accessible form for an inexperienced reader. The main formulations of problems and "addresses" (in the book) of their solution are given. The presentation is illustrated with simple examples. Therefore, we recommend that a relatively poorly prepared reader take the time to read the introduction.

Section I is devoted to methods and techniques for answering the questions, is there any connection at all between the studied variables, how to measure their closeness, and what is the structure of the relationships between the indicators of the studied set? In this case, the structure is understood as the nature of all possible pairwise binary relationships of the considered features (of the type "there is a connection" or "there is no connection"), but not the form of dependence of one on the other. The methods described in this section are the content of correlation analysis.

Section II contains a description of methods and models that allow us to investigate the type of dependence of the “output” (or “resulting”) quantitative indicator of interest to us on a set of explanatory variables of a quantitative nature (regression analysis). In a separate chapter (Ch. 12) the case is considered when the role of the explanatory variable is played by “time”.

Section III solves the same problems as in Section II, but in a situation where non-quantitative or simultaneously non-quantitative and quantitative characteristics act as explanatory variables (analysis of variance and covariance).

And finally, Section IV includes a chapter devoted to the description of methods of statistical analysis of the so-called systems of simultaneous econometric equations (i.e., a set of simultaneously fulfilling relations in which the same variables can participate in different ratios: both in the role of the resulting indicator, and in the role of the predictive variable), and the chapter, which provides an overview of the most interesting domestic and foreign software for methods of statistical research of dependencies.

Reading: 1-2 module 3 courses
Prerequisites: Methods of preliminary statistical analysis or knowledge of statistics at a basic level
Labor intensity: 5 credits

76 classroom hours:

• 28 hours of lectures;
• 48 hours of practical training.

Control forms:

• exam;
• 2 homework

Teachers

About the course

Methods for analyzing the type of dependence and the degree of relationship between variables are widely used in various fields of applied statistical research.
The course examines the methods of correlation analysis to assess the presence and degree of statistical relationship between signs of different nature, to determine the structure of the relationship. In the section of regression analysis, the problems of estimating and checking the significance of the parameters of linear and nonlinear regression models, regression models with variable structure, typological regression and binary choice models, systems of simultaneous equations are considered. Dependency modeling is illustrated with examples based on real data.

The knowledge and skills acquired during the course will allow solving a wide range of problems to create an information basis for decision-making in various areas of knowledge and practice.

The study of addictions is the main occupation of experimenters in any field of knowledge. An object under study, especially one as complex as a biological one, cannot be studied in its entirety. It is necessary to single out certain cause-and-effect relationships in it, which are formalized in the form of dependencies. The study examines the dependence of the effects on the causes or the relationship between several effects due to a common cause.

A special case is the dependence of an attribute of an object on time- the study of such dependencies was devoted to Chapter 7. In this (eighth) chapter, on the contrary, will be mainly considered static dependencies, in the description of which time does not participate, and still the subject of this chapter is extremely extensive. Due to the limited scope of the course, only the “skeleton” of the topic under consideration will have to be presented. It is hoped that readers will master the specific issues of studying dependencies in the course of their own research work, using the extensive literature on various aspects of this complex problem, as well as the available software.

Directly considered the topic is devoted, for example, a solid reference edition, difficult for initial acquaintance. A simpler source would be a tutorial. Quite simply and briefly, in an applied sense, the questions of researching dependencies in the brochure are considered. Modern methods of experimental data processing are described in the monograph. However, along with sophisticated statistical methods for analyzing and processing data, in many cases, methods of visual "exploratory analysis" are useful, which will not be considered here, although, of course, they should not be forgotten either.

8.2. General structure of a dependency experiment

In the general formulation of the problem of investigating dependencies, it is assumed (Fig. 8.1) that the object under study is affected by a set factors(in the previous chapter, the term was used in almost the same sense stimulus), and the result of this influence is response, in the general case, also multicomponent. Among the parameters characterizing the components of the impact and response, generally speaking, there can be quantitative, and ordinal, and classification, and, of course, the types of scales used strongly influence the experimental procedure and data processing.

Some of the factors (more precisely - parameters factors, but in the future we will not follow the severity of expressions) can be set or measured; the values ​​of others usually remain unknown - they introduce uncertainty in the object's response to changes in controlled factors. Added to this uncertainty is the measurement (or classification) of the response components. The behavior of the object itself does not have to be completely deterministic either. All this leads to the need to widely use the methods of mathematical statistics.

Thus, we can say that the mathematical apparatus for studying dependencies is aimed at solving the problem: how, on the basis of the particular results of statistical observation of the analyzed events, to identify and describe the stochastic (probabilistic) connections existing between them.

To shorten the formulas in the study of dependencies, one can consider independent ("predictor") variables x 1 … x k as components of the vector x and dependent variables y 1 … y m- as components of the vector y... Quite often, you can limit yourself to researching addiction. one variable y from k vector components x(or consider y 1 … y m separately, as if breaking a single experiment into m private experiments).

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