Statistical methodology– a system of techniques and methods aimed at studying quantitative patterns manifested in the structure, dynamics and interrelations of socio-economic phenomena.
Statistical research consists of three stages:
1. Statistical observation;
2. Primary processing, summary and grouping of observation results;
3. Analysis of the obtained summary materials.
The passage of each stage of the study involves the use of special methods explained by the content of the work being performed.
1) Statistical observation is a scientifically organized collection of information about the socio-economic processes or phenomena being studied. The obtained data are the source material for performing subsequent stages of statistical research. This data must be processed in a certain way. Such processing is the next stage of statistical research.
2) Summary of initial data to obtain general characteristics of the process or phenomenon under study. The results of the statistical summary and grouping are presented in the form of statistical tables.
3) Statistical analysis – the final stage of statistical research. In its process, the structure, dynamics and relationships of social phenomena and processes are explored. The following main stages of analysis are distinguished:
· Statement of facts and their assessment;
· Establishing the characteristic features and causes of the phenomenon;
· Comparison of a phenomenon with other phenomena;
· Formulation of hypotheses, conclusions and assumptions;
· Statistical testing of proposed hypotheses using special statistical indicators.
General theory of statistics- the science of the most general principles, rules and laws of digital coverage of socio-economic phenomena. It is the methodological basis of all branches of statistics.
Statistics– a set of quantitative characteristics of socio-economic phenomena and processes obtained as a result statistical observation, their processing or corresponding calculations.
Statistical observation- this is a massive, systematic, scientifically organized observation of the phenomena of social and economic life, which consists of recording selected characteristics for each unit of the population. The statistical observation process includes the following steps:
- Preparation of observation. At this stage, scientific and methodological issues are decided (determination of the purpose and object of observation, the composition of features to be registered; development of documents for data collection; selection of the reporting unit and the unit in relation to which the observation will be carried out, as well as methods, means and time for obtaining data, etc.). d.) and organizational issues (determination of the composition of the bodies conducting surveillance; selection and training of personnel for conducting surveillance; drawing up a work schedule for the preparation, conduct and processing of surveillance materials; replication of documents for data collection, etc.).
- Conducting mass data collection.
- Development of proposals to improve statistical observation.
3/ Programme-methodological and organizational issues of statistical observation.
Program and methodological issues determine the goals and objects of observation, signs to be registered, documents for data collection are developed, methods and means of obtaining data are determined, and more.
Organizational issues involve the following types of work: selection and training of personnel; drawing up a work schedule for the preparation and conduct of statistical observation; materials that will be used in statistical observation are processed.
Purpose of observation– obtaining reliable information to identify dependencies in the development of phenomena and processes.
Observation object– a certain statistical aggregate in which the socio-economic phenomena and processes under study occur.
To define an object, it is necessary to determine the boundaries of the population being studied, for which the most important features that distinguish it from other similar populations should be indicated. Each object consists of individual elements, i.e. units of observation that are carriers of characteristics subject to registration.
The reporting unit is the entity from which data about the observation unit is received.
Surveillance program– this is a list of signs (questions) to be recorded during the observation process.
Statistical form– this is a document of a single sample containing the program and observation results. An example could be a census form, survey plan, questionnaire, etc. In this case, two systems of statistical forms are distinguished:
1) Individual (card), which involves recording answers to questions about only one unit of observation.
2) The list method provides answers to questions about several units of observation.
Choosing when to conduct an observation involves resolving two issues:
– establishing a critical moment (date) or time interval.
– determination of the period or period of observation.
Critical moment(date)– a specific day of the year, hour of the day, as of which the registration of characteristics should be carried out for each unit of the population under study.
Duration (period) of observation– this is the time during which statistical forms are filled out, i.e. the time required to conduct mass data collection.
Forms, types and methods of statistical observation.
1) Reporting is the main form of statistical observation, with the help of which statistical authorities, within a certain time frame, receive from enterprises and institutions the necessary data in the form of established reporting documents.
As a rule, reporting is based on primary accounting and is its generalization.
Primary accounting is the registration of various facts and events that occur as they occur.
Registration takes place on a specific social document, while the current statistical reporting is standard and specialized.
The standard one is the same for all enterprises, while in the specialized one the composition of industry indicators changes depending on the characteristics of individual industries.
Reporting can be daily, weekly, fortnightly, monthly, quarterly, annual. All listed, except annual, are current.
2) Specially organized statistical observation.
A striking example is the census - specially organized reporting that is repeated at regular intervals in order to obtain data on the number, composition and condition of an object for a number of characteristics.
Features of the census:
Simultaneous implementation throughout the country
Unity of the statistical observation program
Registration of observation units as of the same critical moment.
This form includes budget surveys that characterize the structure of consumer spending and family income.
3) Register - a system that constantly monitors the state of the observation unit and evaluates the strength of the influence of various factors on the indicators being studied.
Population register is a named and regularly updated list of a country's inhabitants. In this case, the observation program is limited to general characteristics (gender, date and place of birth, date of marriage).
There is such a sign as marital status (variable sign).
A register of enterprises, which includes all types of economic activity and contains the value of the main characteristics for each unit of observation for a certain period or point in time. Contains data on the time of creation or registration of enterprises, name, address, telephone number, legal form, type of economic activity, number of employees, etc., i.e. complete information about the company.
Therefore, a statistical table is usually defined as a form of compact visual presentation of statistical data.
Analysis of tables allows you to solve many problems when studying changes in phenomena over time, the structure of phenomena and their relationships. Thus, statistical tables serve as a universal means of rational presentation, generalization and analysis of statistical information.
Externally statistical table is a system of horizontal rows and vertical columns constructed in a special way, having a common heading, column headings and rows, at the intersection of which statistical data is recorded.
Each figure in statistical tables is a specific indicator characterizing the size or levels, dynamics, structure or relationships of phenomena in specific conditions of place and time, that is, a certain quantitative and qualitative characteristic of the phenomenon being studied.
If the table is not filled with numbers, that is, it has only a general title, column and row titles, then we have a layout of a statistical table. It is with its development that the process of compiling statistical tables begins.
The main elements of a statistical table are subject and predicate tables.
Subject of the table- this is an object of statistical study, that is, individual units of a population, their groups or the entire population as a whole.
Table predicate- these are statistical indicators that characterize the object being studied.
The subject and predicate indicators of the table must be defined very precisely. As a rule, the subject is located on the left side of the table and makes up the content of the rows, and the predicate is located on the right side of the table and makes up the content of the columns.
Usually, when arranging predicate indicators in a table, the following rule is followed: first, absolute indicators characterizing the volume of the population being studied are given, then calculated relative indicators reflecting the structure, dynamics and relationships between the indicators.
Construction of analytical tables
The construction of analytical tables is as follows. Any table consists of a subject and a predicate. The subject reveals the economic phenomenon discussed in this table and contains a set of indicators reflecting this phenomenon. The predicate of the table explains which features reflect the subject.
Some tables reflect changes in the structure of any. Such tables contain information about the composition of the analyzed economic phenomenon both in the base and in the reporting period. Based on these data, the share (specific gravity) of each part in the total population is determined and deviations from the basic specific gravity for each part are calculated.
Separate tables may reflect the relationship between economic indicators based on certain characteristics. In such tables, information on a given economic indicator is arranged in ascending or descending order of numerical values characterizing this indicator.
In economic analysis, tables are also compiled that reflect the results of determining the influence of individual factors on the value of the analyzed generalizing (resultative) indicator. When preparing such tables, information is first placed on the factors influencing the generalizing indicator, then information about the generalizing indicator itself, and finally about the change in this indicator in the aggregate, as well as due to the influence of each analyzed factor. Separate analytical tables reflect the results of calculating reserves for improving economic indicators, identified as a result of the analysis. Such tables show both the actual and theoretically possible size of the influence of individual factors, as well as the possible amount of reserve for growth of the general indicator due to the influence of each individual factor.
Finally, in the analysis of economic activity, tables are also compiled that are intended to summarize the results of the analysis.
The practice of statistics has developed the following rules for compiling tables:- The table should be expressive and compact. Therefore, instead of one cumbersome table for many characteristics, it is better to make several small but visual tables that meet the task of the study.
- The table title, column and line titles should be formulated accurately and concisely.
- The table must necessarily indicate: the object being studied, the territory, and the time to which the data given in the table relates, units of measurement.
- If some data is missing, then in the table either put an ellipsis or write “no information”; if some phenomenon did not take place, then put a dash
- The values of the same indicators are given in the table with the same degree of accuracy.
- The table should have totals for groups, subgroups and overall. If summing the data is impossible, then the multiplication sign “*” is placed in this column.
- In large tables, a space is added after every five rows to make the table easier to read and analyze.
Types of statistical tables
Among the methods, the most common is the tabular method (method) of displaying the digital data under study. The fact is that both the initial data for the analysis and various calculations, as well as the results of the research, are presented in the form of analytical tables. Tables are a very useful and visual form of display. numerical information, used in . In analytical tables in in a certain order contains digital information about the economic phenomena being studied. Tabular material is much more informative and visual compared to textual presentation of the material. Tables allow you to present analytical materials in the form of a single integrated system.
The type of statistical table is determined by the nature of the development of its underlying indicators.
There are three types of statistical tables:- simple
- group
- combinational
Simple tables contain a list of individual units that are part of the totality of the analyzed economic phenomenon. IN group tables digital information in the context of individual components of the data set under study is combined into certain groups in accordance with some characteristic. Combination tables contain separate groups and subgroups into which they are divided, characterizing the economic phenomenon being studied. Moreover, such a division is carried out not according to one, but according to several criteria. in group tables a simple grouping of indicators is carried out, and in combined tables a combined grouping is carried out. Simple tables do not contain any grouping of indicators at all. The last type of tables contains only an ungrouped set of information about the economic phenomenon being analyzed.
Simple tables
Simple tables have a list of units of population, time or territories in the subject.
Group tables
Group tables are those that have the subject grouping of population units according to one characteristic.
Combination tables
Combination tables have the subject grouping of population units according to two or more characteristics.
Based on the nature of the development of indicators of the predicate, they are distinguished:
- tables with a simple development of indicators of the predicate, in which there is a parallel arrangement of indicators of the predicate.
- tables with a complex development of indicators of the predicate, in which there is a combination of indicators of the predicate: within groups formed according to one characteristic, subgroups are distinguished according to another characteristic.
Table with a simple development of predicate indicators
The predicate of this table provides data first on the distribution of students by gender, and then by age, i.e. There are isolated characteristics according to two characteristics.
Table with complex development of predicate indicators
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Branches |
Number of students, people. |
Including |
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of them in age, years |
of them in age, years |
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23 or more |
23 or more |
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Evening |
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The predicate of this table not only characterizes the distribution of students according to each of the two identified characteristics, but also allows us to study the composition of each group, identified by one characteristic - gender, and by another characteristic - student age, i.e. there is a combination of two characteristics.
Consequently, tables with complex development of indicators of the predicate provide greater opportunities for analyzing the indicators being studied and the relationships between them. A table of any type can have a simple and complex development of predicate indicators: simple, group, combinational.
Depending on the stage of statistical research, the tables are divided into:- development(auxiliary), the purpose of which is to summarize information on individual units of the population to obtain final indicators.
- summary, whose task is to show the results for groups and the entire population as a whole.
- analytical tables, the task of which is to calculate general characteristics and prepare information base for the analysis of structure and structural shifts, the dynamics of the phenomena being studied and the relationships between indicators.
So, we examined the tabular method of displaying the digital data under study, which is widely used in the analysis of economic phenomena, statistical data and economic activities of organizations.
Statistical data can be presented in the form of statistical tables, statistical graphs and statistical charts.
Statistical tables are drawn up as a result of summarizing and grouping the available observation data. Statistical tables necessarily contain summary indicators and consist of a subject and a predicate.
Subject of the table shows what the table is about, it is located on the left and represents the contents of the rows.
Table predicate located at the top and represents the content of the graph. The predicate shows what features characterize the subject.
Statistical graphs. The construction of statistical graphs is the final stage of summarizing and grouping statistical data. Graphic representation is the most effective form of presenting statistical data from the point of view of their perception.
Schedule called a conditional, visual representation of statistical quantities and their relationships using geometric lines and figures.
Each graph must include the following elements: a graphic image, a graph field, scale guidelines and a coordinate system.
Graphic image - geometric signs, a set of points, lines, figures with the help of which statistical quantities are depicted.
Graph field represents the space in which geometric signs are placed.
The scale references of a statistical graph are determined by the scale and scale bar.
Statistical graph scale - this is a measure of converting a numerical value into a graphic one,
Scale scale - a line whose specific points can be read as specific numbers. The scale consists of a line (the scale carrier) and a number of points marked on it, arranged in a certain order.
Uniform scale is the length of a segment taken as a unit and measured in some measure.
To place geometric signs in the graph field, a coordinate system is required. The most common system of rectangular coordinates.
According to the method of constructing, graphs are divided into line graphs, diagrams, cartograms, and map diagrams.
The class of linear graphs includes: polygon, cumulate and Lorenz curve.
Polygon called a broken line whose segments connect points X and/j (X j - characteristic value; - frequency).
The polygon is used for a discrete distribution series.
Cumulates- a broken line, compiled from accumulated frequencies or frequencies, the coordinates of the points of which are X ( And f. (X j- value of the characteristic, for an interval series - upper limit of values (X.);/ ( - accumulated frequency).
The starting point of the broken line of the interval distribution series is the lower limit of the value ( X") in the first group.
Lorenz curve, or concentration curve, is called the relative concentration curve of the total value of the attribute. It represents a broken line, the coordinates of the points of which on the abscissa axis are the accumulated relative frequencies, and on the ordinate axis the accumulated (cumulative total) value of the attribute Xj.
The closer the Lorenz curve is to a straight line, the more uniform the distribution of the characteristic is, i.e. concentration is less. The greater the curvature of the curve, the more uneven the distribution, i.e. concentration is greater.
Statistical charts. The class of charts primarily includes a histogram (bar chart), as well as bar charts, ribbon charts, pie charts, linear charts, square charts, pie charts, curly charts, etc.
Histogram - This is a stepped figure consisting of rectangles, the bases of which are equal to the size of the interval in the group, and the heights are equal to the density in the group (absolute or relative).
When constructing bar charts, data is depicted in the form of bars of the same width, but of different heights, depending on the numerical values of the displayed quantities on a certain scale.
A variety of bar charts are strip and strip charts. They depict the dimensions of a feature in the form of horizontally located rectangles of the same width, but of different lengths, in proportion to the depicted values. The beginning of the stripes should be on the same vertical line.
Pie charts It is convenient to use to depict the structure of a phenomenon; in this case, the circle is divided into sectors proportional to the shares of parts of the phenomena. The circle is taken as a whole (100%) and is divided into sectors, the arcs of which are proportional
the values of individual parts of the displayed quantities. The arc of each sector (or the value of the central angle) is determined by the formula
where 360° is the area of the circle;
d- the specific gravity of the depicted phenomenon in percent.
If statistical data is presented in absolute values, then the formula for determining the arc takes the form:
Where b- the magnitude of the depicted phenomenon in absolute values.
To build circular And square diagrams it is necessary to carry out preliminary calculations, since the available statistical data (/)) correspond to the areas of geometric shapes (circles or squares).
To construct a circle, you need to find the radius of the circle using the formula 
To construct a square, you need to find the side of the square based on the formula for the area of a square:
Barbarian Sign used to visually characterize three interrelated quantities - this is a rectangle in which the base is one indicator, the height is another, and the product of the base and the height characterizes the value of the derived third indicator.
Shape charts are constructed in two ways: the compared statistical values (/)) are depicted by figures - symbols different sizes in proportion to the volumes of these aggregates or by different numbers of identical signs-symbols, each of which is given a certain numerical value.
To graphically depict the spatial distribution of any statistical indicator, cartograms are used, which can be background or point.
Cartogram is a combination of a diagram and a geographical map.
On background cartograms, the distribution of the phenomenon under study across the territory is depicted by various territorial colorings
nal units with different densities of color or shading of varying intensity.
On a dot cartogram, the symbols for the graphic representation of statistical data are points located within certain territorial units. Each point is given a specific numerical value.
A cartogram is used in cases where there is a need to show the territorial distribution of any one statistical feature in the aggregate in order to identify the pattern of distribution of this feature.
Automated methods for constructing diagrams. Charts can be created in an automated way based on observation data generated and grouped in a table. To ensure the clarity of the diagram, the data block must meet certain requirements:
- data should be systematized by quantity and by groups, columns and rows;
- data for different categories must be comparable;
- headings of tables, rows, columns should be short and clear so as not to take up much space and ensure a correct understanding of the meanings of the constructed diagram;
- The data should be arranged in one or more rectangular ranges with text labels in the top row and left column.
As part of an integrated package Microsoft Office spreadsheet information is processed using the program Microsoft Excel. A spreadsheet is the computer equivalent of a regular spreadsheet.
Table processor - special program(software package) that provides processing of information presented in tabular form.
Microsoft Excel defines the first row of data, starting with the first cell in the upper left corner of the existing selected non-date data range and ending with the remaining selected rows and columns.
To build diagrams in the spreadsheet processor, it is possible to use a special diagram wizard using a plotter Microsoft Graph. The Chart Wizard is launched by clicking on the icon in the standard toolbar. It is recommended that you first select the range of cells containing the data used to create charts. Diagrams are constructed in four stages:
- 1) choosing the type and type of diagram;
- 2) clarification of the data range and arrangement of rows in rows or columns. The result of constructing a diagram when positioned
series in rows and columns can vary significantly. By default, the window displays the chart view for the selected range of cells. If you have not previously selected the data, you must do this in this window by clicking on the stylized table icon in the field Range and highlighting the data in the table. Tab "row" allows you to add and delete rows, specify the ranges in which the corresponding rows are presented, category axis labels;
- 3) specifying the title of the diagram and completing the necessary signatures;
- 4) placing the diagram on a spreadsheet (on the current or a separate worksheet).
To edit diagram elements, you must double-click, after which you will be taken to the corresponding window for changing the parameters of the selected element. Significant help is provided by a context-sensitive menu that can be called up on individual diagram elements.
Statistical tables.
Plan.
1. The concept of a statistical table. Elements of a statistical table.
2. Types of tables according to the nature of the subject.
3. Types of tables for developing the predicate.
4. Basic rules for constructing tables.
5. Reading and analyzing the table.
1. The concept of a statistical table. Elements of a statistical table.
The results of the summary and grouping of statistical observation materials are, as a rule, presented in the form of tables that make the information visible.
A table is the most rational, visual and compact form of presenting statistical material.
Thus, a statistical table is called, which contains a summary numerical characteristic of the population under study according to one or more essential characteristics, interconnected by the logic of economic analysis. Statistical table- a form of rational and visual presentation of the digital characteristics of the phenomena under study.
Statistical generalization of information and its presentation in the form of summary statistical tables makes it possible to characterize the size, structure and dynamics of the phenomena being studied. Often a statistical table is given a general heading, which indicates the contents of the table, the place and time to which the data given in the table relates, as well as the units of measurement, if they are the same for all the information given.
Elements of a statistical table
The main elements of the statistical table, presented in Fig. 1, form its basis.
Table title * (general title)
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Name of column (top headings) |
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A |
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Line names(side headers) |
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Total line |
Final column |
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* Notes on the table
Rice. 1. The skeleton (base) of the statistical table
The statistical table contains three types of headings:
The general header reflects the contents of the entire table (what place and time it relates to), is located above its layout in the center and is the outer header. The top headings characterize the content of the column (headings of the predicate), and the side headings (headings of the subject) - the term. They are internal headers. Table headings should be short and reveal the content of the indicators.
Digital material can be presented in absolute (population of the Russian Federation), relative (price indices for food products) and average (average monthly income of a commercial bank employee) values.
If necessary, the tables may be accompanied by a note used to explain the headings, the methodology for calculating certain indicators, sources of information, etc.
In terms of logical content, the table is a “statistical sentence”, the main elements of which are the subject and the predicate.
Subject A statistical table is an object characterized by numbers. These can be one or more aggregates, individual units of aggregates (firms, associations) in the order of their list or grouped according to some characteristics (individual territorial units or time periods in chronological tables, etc.). Usually the subject of the table is given on the left side, in the names of the rows.
Predicate The statistical table is formed by a system of indicators that characterize the object of study, i.e. subject of the table. The predicate forms the top headings and makes up the content of the graph with a logically sequential arrangement of indicators from left to right.
The location of the subject and predicate can be swapped, which depends on each individual researcher achieving the most complete and best way to read and analyze the initial information about the population being studied.
2. Types of tables according to the nature of the subject.
The type of statistical table depends on the construction of the subject. From this point of view there are tables:
Simple;
Difficult:
Group;
Combination.
A simple table is called, in which the object of study is not divided into groups. In this case, two options are possible:
1) the table contains data on the population as a whole;
2) the table contains data about each unit of the population.
The latter is justified if the number of units is small. For example, the table shows data for each of the 13 cities with millionaires in the Russian Federation. A table with data about each unit can be used as working material for any subsequent calculations.
In a simple table, the subject gives a simple list of any objects or territorial units, i.e. there is no grouping of aggregate units in the subject. Simple tables can be monographic and list. Monographic tables do not characterize the entire set of units of the object being studied, but only one group from it, identified according to a certain, pre-formed characteristic.
Simple list tables are tables whose subject contains a list of units of the object being studied.
An example of a simple table is table. 1.
Table 1
Volume of basic communication services in the Russian Federation
Source: Social status and standard of living of the population of Russia. Statistical collection. M.: Goskomstat of Russia, 2000. P. 411.
The subject of this table is included in the table header; the table itself is a predicate, and the values of the indicators are given in dynamics.
Group table- this is a table in which the subject, i.e., the object of research, is divided into groups according to any one characteristic (Table 2).
Table 2
Distribution by level of education (according to sample surveys of the population of the Russian Federation on employment issues)
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Education level |
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Including: |
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higher professional |
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incomplete higher professional |
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more harmful than professional |
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average (full) general |
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basic general |
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have no basic commonality |
Source: Social status and standard of living of the population of Russia. Statistical collection. M.: Goskomstat of Russia, 2000. P. 80.
Combination table includes a subject in which the object of study is divided into groups according to two or more characteristics. For example, table. 3 will become combinational if the unemployed are divided into groups not only by level of education, but also by gender. In this case, the following table construction options are possible.
1st option: the subject is located on the left side of the table; groups identified by one characteristic are divided into subgroups by another characteristic. Schematically it looks like this:
2nd option: the subject is located in the left and upper parts of the table. The table looks like:
3. Types of tables for developing the predicate.
The predicate of the statistical table, as already mentioned, contains indicators that are characteristics of the object being studied. This characteristic can be given by a small number of indicators or an entire system of indicators.
Based on the structural structure of the predicate, statistical tables with simple and complex development are distinguished.
At simple predicate development the indicator that defines it is not divided into subgroups, and the final values are obtained by simply summing the values for each characteristic separately, independently of each other. An example of a simple development of a predicate is the following fragment of a statistical table.
After filling out this fragment of the table, a detailed description of privatized enterprises is obtained according to the structure of their subjects - owners. For each company you can obtain information about the number and price conditions for the sale of shares.
Complex predicate development involves dividing the characteristic that forms it into subgroups.
Distribution of shares among employees of privatized industrial enterprises
With complex development of the predicate, a more complete and detailed description of the object is obtained.
The combined development of indicators on the conditions for the sale of shares and their types allows us to deepen the economic and statistical analysis of the share market and its structure for privatized enterprises.
Here, both signs of the predicate (price and type) are closely related to each other. It is possible to analyze not only the number of shares acquired by type and conditions of acquisition by employees of privatized enterprises, but also to determine the number of preferred and ordinary shares acquired under different price conditions. So, with a complex development of the predicate, each group of enterprises or each enterprise separately can be characterized by a different combination of features that form the predicate.
However, complex development of the predicate can lead to an enormous increase in the dimension of statistical tables, which, in turn, reduces their visibility, reading and analysis.
Therefore, when constructing statistical tables, the researcher must be guided by the optimal ratio of predicate indicators and take into account both the positive and negative aspects of the complex development of predicate indicators.
4. Basic rules for constructing tables.
Statistical tables as a means of visual and compact presentation of digital information must be statistically correctly designed.
The main techniques that determine the technique for generating statistical tables are as follows.
1. The table should be compact and contain only those initial data that directly reflect the socio-economic phenomenon under study in statics and dynamics and are necessary to understand its essence.
Unnecessary, secondary, meaningless information related to the given object of study should be avoided. Digital material must be presented in such a way that when analyzing the table, the essence of the phenomenon is revealed by reading the lines from left to right and from top to bottom.
2. The table title and the names of columns and rows must be clear, concise, concise, and represent a complete whole that fits organically into the content of the text.
Must be avoided large quantity dots and commas in the names of tables and columns, making the table difficult to read.
If the table title consists of two or more sentences, a period is placed to separate the sentences from each other, but not after the last one.
Dots in graph headings are allowed only for necessary abbreviations.
The title of the table should reflect the object, sign, time and place of the event. For example: “US dollar exchange rate at MICEX trading in 1997.” But it should be remembered that the more concise and concise the text of the table title, the clearer and more intelligible it is for reading and analysis, naturally, if this is not done to the detriment of its accuracy and cognition. Table, column and row headings are written in full, without abbreviations.
3. The information located in the columns (columns) of the table ends with a summary line. There are various ways connecting the terms of the graph with their total:
the line “Total” or “Total” completes the statistical table;
the final line is located in the first row of the table and is connected to the totality of its terms with the words “Including”.
In group and combination tables it is always necessary to give summary columns and rows.
5. If the names of individual columns are repeated among themselves, contain repeated terms or carry a single semantic load, then they must be assigned a common unifying title.
This technique is used for both the subject and predicate tables.
6. It is useful to number columns and lines. Columns filled with line names on the left are usually designated in capital letters alphabet (A), (B), etc., and all subsequent columns are numbered in ascending order.
7. It is advisable to place interrelated and interdependent data characterizing one of the aspects of the analyzed phenomenon (for example, the number of enterprises and the share of factories (in % of the total), absolute growth and growth rate, etc.) in adjacent columns.
8. Columns and lines must contain units of measurement corresponding to the indicators set in the subject and predicate. In this case, generally accepted abbreviations of units of measurement are used (persons, rubles, kW/h, etc.).
9. It is best to place in tables what is compared during the analysis digital information in the same column, one below the other, which greatly simplifies the process of comparing them.
Therefore, in group tables, for example, it is more appropriate to arrange groups according to the characteristic under study in descending or ascending order of its values while maintaining the logical connection between the subjects and predicates of the table.
10. For ease of use, numbers in tables should be presented in the middle of a column, one under the other: units under units, a comma under a comma, while strictly observing their bit depth.
11. If possible, it is advisable to round numbers. Rounding of numbers within the same column or line should be carried out with the same degree of accuracy (to the whole digit or to the tenth, etc.).
If all the numbers in the same column or line are given with one decimal place, and one of the numbers has two or more decimal places, then numbers with one decimal place should be supplemented with a zero, thereby emphasizing their equal precision.
12. The lack of data on the analyzed socio-economic phenomenon may be due to various reasons, which is noted in different ways in the table:
a) if this position (at the intersection of the corresponding column and line) cannot be filled in at all, then an “X” is placed;
b) when for some reason there is no information, then an ellipsis “…” or “No information.”, or “N. St.";
To display very small numbers, the notation (0.0) or (0.00) is used, suggesting the possibility of the presence of a number.
13. If necessary additional information– explanations – notes may be given to the table.
Compliance with the given rules for the construction and design of statistical tables makes them the main means of presenting, processing and summarizing statistical information about the state and development of the analyzed socio-economic phenomena.
5. Reading and analyzing the table.
The analysis of statistical tables is preceded by a stage of familiarization - reading them.
Reading and analysis of tables should not be carried out chaotically, but in a certain sequence.
Reading assumes that the researcher, having read the words and numbers of the table, has assimilated its content, formulated the first judgments about the object, understood the purpose of the table, understood its content as a whole, and assessed the phenomenon or process described in the table.
Table analysis as a method of scientific research by dividing the subject of study into parts is divided into structural and substantive.
Structural analysis involves analyzing the structure of the table and characterizing those presented in the table:
the totality and units of observation that form it;
signs and their combinations that form the subject and predicate of the table;
characteristics: quantitative or attributive;
correlations between the characteristics of the subject and the indicators of the predicate;
type of table: simple or complex, and the latter - group or combinational;
tasks to be solved - analysis of the structure, types of phenomena or their relationships.
Content analysis involves studying the internal content of the table: analysis of individual groups of the subject according to the corresponding characteristics of the predicate; identification of relationships and proportions between groups of phenomena according to one and different characteristics; comparative analysis and formulation of conclusions for individual groups and for the entire population as a whole; establishing patterns and determining reserves for the development of the object being studied.
Before you begin to analyze numerical information, you need to check its reliability and scientific validity. The researcher must ensure the credibility and reliability of the source of the data information and critically evaluate its numerical values. Logical and counting checks of the data should be performed. Logical check consists in the possibility of determining specific characteristics by certain numerical values (for example, it is absurd if the number of employees in the company was 106.7 people). Account check involves selective calculation of individual characteristic values for a group, or total values of rows or columns, etc.
The analysis of these tables is carried out for each characteristic separately, then in a logical and economic combination of the entire set of characteristics as a whole.
The analysis of individual characteristics and groups must begin with the study of absolute values, then the relative values associated with them. When analyzing data, one should consider the dynamics of each characteristic for the entire period, moving from one to another.
The analysis of tables can be supplemented with calculated relative and average values, if required by the research objectives.
To obtain a more complete and visual representation of the phenomena and processes being studied, graphs, diagrams, etc. are constructed based on data from statistical tables.
Analysis of group and combination tables allows us to characterize the types of socio-economic phenomena, the structure of the population, relationships and proportions between individual groups and units of observation; identify the nature and direction of relationships and interdependencies between various combinations of characteristics, determined by the logic of economic analysis, and the dependence of characteristics - consequences from characteristics - causes.
Compliance with the rules and consistency of working with statistical tables helps the researcher to carry out scientifically based economic and statistical analysis of objects and processes.
Graphic representation of statistical data.
Plan
1. The concept of statistical graphics. Elements of a statistical graph.
2. Classification of types of graphs.
3. Comparison diagrams.
4. Structure diagrams.
5. Dynamics diagrams.
1. The concept of statistical graphics. Elements of a statistical graph.
The technique of compiling statistical graphs was first mentioned in the work of the English economist W. Playfair, “Commercial and Political Atlas,” published in 1786 and which laid the foundation for the development of techniques for graphically depicting statistical data.
Cstatistical graph is a drawing in which statistical aggregates, characterized by certain indicators, are described using conventional geometric images or signs. Presentation of table data in the form of a graph makes a stronger impression than numbers, allows you to better understand the results of statistical observation, interpret them correctly, greatly facilitates the understanding of statistical material, makes it visual and accessible.
When constructing a graphic image, a number of requirements must be observed. First of all, the graph must be quite visual, since the whole point of a graphical representation as a method of analysis is to clearly depict statistical indicators. In addition, the schedule must be expressive, intelligible and understandable. To meet the above requirements, each schedule must include a number of basic elements: graphic image; graph field; spatial references; scale guidelines; operation of the schedule.
Graphic image (graphic basis)– these are geometric signs, i.e. a set of points, lines, figures with the help of which statistical indicators are depicted. Graphic images are those in which the properties of geometric signs - shape, size of lines, arrangement of parts - are essential for expressing the content of the depicted statistical values, and each change in the expressed content corresponds to a change in the graphic image.
Graph field– this is the part of the plane where graphic images are located. The graph field has certain dimensions, which depend on its purpose.
Spatial landmarks graphics are specified in the form of a system of coordinate grids. A coordinate system is necessary to place geometric signs in the graph field. The most common is the rectangular coordinate system.
To construct statistical graphs, usually only the first and occasionally the first and fourth squares are used. In the practice of graphic representation, polar coordinates are also used. They are necessary for a visual representation of cyclic movement in time. In the polar coordinate system (Fig. 2), one of the rays, usually the right horizontal one, is applied as the coordinate axis, relative to which the angle of the ray is determined. The second coordinate is its distance from the center of the grid, called the radius. In radial graphs, the rays represent moments in time, and the circles represent the magnitude of the phenomenon being studied. On statistical maps, spatial landmarks are specified by a contour grid (contours of rivers, coastline m
Rice. 2. Polar coordinate system
Ouray and oceans, state boundaries) and determine the territories to which statistical values relate.
Scale guidelines statistical graphics are determined by the scale and system of scales. The scale of a statistical graph is a measure of the conversion of a numerical value into a graphic one.
Scale bar called a line whose individual points can be read as specific numbers. The scale is of great importance in the graph and includes three elements: a line (or scale carrier), a certain number of points marked with dashes, which are located on the scale carrier in a certain order, and a digital designation of numbers corresponding to individual marked points.
The scale carrier can be either a straight or curved line. Therefore, there are scales straight(for example, a millimeter ruler) and curvilinear– arc and circular (clock dial).
The scale of a uniform scale is called segment length(graphic interval), taken as a unit and measured in any measures.
Graphic and numerical intervals can be equal or unequal.
For the most part, uniform scales are used when equal graphic segments correspond to equal numerical values.
An example of an uneven scale is the logarithmic scale, which is used when there is a large range of indicator levels and the focus, as a rule, is not on absolute, but on relative changes.
The last element of the graph is explication. Each graph must have a verbal description of its contents. It includes its content; captions along the scale bars and explanations for individual parts of the graph.
2. Classification of types of graphs.
Types of graphs. Depending on the field, statistical graphs are divided into statistical charts And statistical maps.
The diagrams, in turn, are as follows:
Comparisons and displays;
Structural;
Speakers;
Special.
Statistical maps reflect the statistical and geographical cross-section of data and show the location of a phenomenon or process in the territory. They are divided into cartograms and map diagrams.
Comparison and display charts. Comparison and display diagrams graphically show the relationship between different statistical populations or units of a statistical population according to some varying characteristic. These charts are in most cases shown on the graph field by an incident chart, a histogram and a polygon.
Structural diagrams. Structural diagrams allow you to compare statistical populations by composition. These are, first of all, diagrams of specific gravity, characterizing the ratio of individual parts of the aggregate to its total volume. By type they are divided into column and sector.
Dynamics diagrams. Time course diagrams are used to show changes in phenomena over time. Such a change can be represented by a bar or bar chart, in which each bar or bar reflects the magnitude of the phenomenon on a certain date or over a certain period of time. Sometimes it is advisable to use pie and square diagrams, in which the magnitude of the phenomenon is displayed by circles or squares, the values of the radii and sides of which are proportional to the square roots of the absolute characteristics.
Communication diagrams (graphics). Communication diagrams are constructed using curves showing the relationship between characteristics, one of which is resultant (dependent), the second is factorial (independent) (Figure 3).
Rice. 3. Dependence of feed consumption per cow per year on productivity
Gilton's ogive and cumulates. Ogiva is called graphic image series of distribution in ascending or descending order of the varying characteristic. Here, as a rule, the values of the characteristic are plotted along the ordinate axis, and the units of the population (by rank) are plotted along the abscissa axis.
From the ogive one can clearly judge the minimum and maximum values of the attribute; from its steepness, one can visually judge the uniformity of distribution and homogeneity of population units (Table 3, Fig. 4).
Table 3
Distribution of work teams No. 21 and No. 32 of Avangard JSC by skill level (categories) and ranks as of July 1, 1998*
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Brigade No. 21 |
Brigade No. 32 |
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personnel number |
personnel number |
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* The example is conditional.
Rice. 4. Distribution of work teams No. 21(a) and No. 32(6) of Avangard JSC by skill level (categories) and ranks as of 07/01/1998:
a) equal intervals
Rice. 4. Continuation
b) unequal intervals
Cumulates is a graph depicting a series of accumulated frequencies. Here, the values of the attribute are plotted along the abscissa axis, and the cumulative totals of frequencies are plotted along the ordinate axis (Fig. 5).
Rice. 5. Cumulative distribution of the population of the Tver region by average per capita monetary income in 1996.
Cartograms. Cartograms, or statistical maps, illustrate the contents of statistical tables, the subject of which is the administrative or geographical division of a population. Here, the field of the graph is represented by geographic maps on which statistical tables (centrograms) are placed, different colors or backgrounds, and conventional symbols are used (Fig. 6).
Rice. 6. Scheme of natural and economic zoning of the Tver region.
3. Comparison diagrams.
Comparison and display diagrams graphically show the relationship between different statistical populations or units of a statistical population according to some varying characteristic.
These charts are in most cases shown on the graph field by an incident chart, a histogram and a polygon.
Case diagram. The incident diagram is a display of a varying characteristic in the sequence in which it is written. Here, the units of the population are placed along the abscissa axis, and the values of the characteristic are placed along the ordinate axis. For example, in Fig. 7, using a diagram of incidents, shows the number of cattle in farms of all categories in the districts of the central zone of the Tver region (districts: 1-Kalininsky, 2-Kalyazinsky, 3-Kimrsky, 4-Konakovsky, 5-Kuvshinovsky, 6-Likhoslavlsky, 7-Maksatikhinsky , 8-Rameshkovsky, 9-Spirovsky, 10-Torzhoksky).
Rice. 7 Dynamics of the number of cattle in farms of all categories in the regions of the central zone of the Tver region.
Histogram. A histogram is a graph in which a distribution series is depicted as adjacent bars. It is used, as a rule, to depict interval distribution series. Here, the intervals of the characteristic are plotted along the abscissa axis, and frequencies are plotted along the ordinate axis.
When constructing histograms, scale breaks are not allowed. If the populations being compared are different in size, then not the frequencies, but the relative frequencies (specific weights or shares of the entire population) are plotted on the ordinate axis. (Fig. 8)
Rice. 8 Distribution of population by per capita size
cash income in 2010 for the first quarter.
Polygon. A polygon is a graph in which a distribution series is depicted as a line diagram. It is used, as a rule, to depict discrete distribution series. Here, the values of the varying characteristic are plotted along the abscissa axis, and frequencies (frequencies) are plotted along the ordinate axis.
In Fig. 9 shows the distribution area for security costs environment in the Russian Federation in 2009 according to table. 4.
Rice. 9 Distribution of environmental protection costs in the Russian Federation in 2009.
Expenditures on environmental protection in the Russian Federation in 2009
(in actual prices; millions of rubles)
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Symbol |
Spent million, rub |
In % of total |
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air protection |
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wastewater treatment |
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waste management |
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protection and rehabilitation of soil, groundwater and surface water |
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conservation of biodiversity and habitats |
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4. Structure diagrams.
Structural diagrams allow you to compare statistical populations by composition. These are, first of all, diagrams of specific gravity, characterizing the ratio of individual parts of the aggregate to its total volume. By type they are divided into columnar (Fig. 10) and sector (circular) (Fig. 11).
1990 1996
Rice. 10. Structure of production fixed assets of agricultural enterprises in the Tver region
Peasant
(farm) farms
Rice. 11. Gross output agriculture Tver region in 1996
When using sector structural diagrams, we must remember that 1% corresponds to 3.6°. In structure diagrams, specific gravities or the structure itself are highlighted by shading or coloring.
5. Dynamics diagrams.
Time course diagrams are used to show changes in phenomena over time. Such a change can be represented by a bar or bar chart, in which each bar or bar reflects the magnitude of the phenomenon on a certain date or over a certain period of time (Figure 12, 13).
1990 1991 1992 1993 1994 1995 1996 1997 Year
Rice. 12. Real wages of workers and employees of the Russian Federation (1990 - 100%)
0 200 400 600 800 1000
Rice. 13. Grain production in the Tver region (in initially capitalized weight)
Sometimes it is advisable to use circular and square diagrams, in which the magnitude of the phenomenon is displayed by circles or squares, the values of the radii and sides of which are proportional to the square roots of the absolute characteristics (Fig. 14).
Rice. 14. Cultivated areas of peasant (farm) farms in the Tver region, thousand hectares
In most cases, the dynamics of the process are displayed by a linear diagram (Fig. 15).
Rice. 15. Share of agriculture in the GDP of the Russian Federation, 1989-1997
One type of diagram is radial, which is used to display phenomena that repeat periodically over time (for example, seasonal fluctuations, Fig. 16).
Rice. 16. Egg production of chickens of the n-th poultry farm by month of the year on average for 1995 - 1997.
To construct radial (radar) diagrams, the circle is divided into parts according to the number of periods. The radius of the circle for each period determines the magnitude (absolute or relative) of the phenomena.
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Statistical observation- it is massive (it covers a large number of cases of manifestation of the phenomenon under study in order to obtain truthful statistical data), systematic (carried out according to a developed plan, including issues of methodology, organization of collection and control of the reliability of information), systematic (carried out systematically, either continuously or regularly), scientifically organized (to increase the reliability of data, which depends on the observation program, the content of questionnaires, the quality of preparation of instructions) observation of the phenomena and processes of socio-economic life, which consists of collecting and recording individual characteristics for each unit of the population.
Stages of statistical observation
- Preparation for statistical observation(solving scientific, methodological, organizational and technical issues).
- determination of the purpose and object of observation;
- determining the composition of features to be registered;
- development of documents for data collection;
- selection and training of personnel to conduct surveillance;
2. Collection of information
- direct filling of statistical forms (forms, questionnaires);
Statistical information is primary data on the state of socio-economic phenomena, formed in the process of statistical observation, which is then systematized, summarized, analyzed and generalized.
The composition of information is largely determined by the needs of society in at the moment. Changes in forms of ownership and methods of regulating the economy led to changes in the policy of statistical observation. If earlier information was available only to government agencies, now it is in most cases publicly available. The main consumers of statistical information are the government, commercial structures, international organizations and the public.
Specially organized surveillanceIt consists of obtaining data that, for one reason or another, was not included in the reporting or to verify reporting data. Represents the collection of data through censuses and one-time counts.
Register surveillanceIt is based on maintaining a statistical register, with the help of which continuous statistical accounting is carried out for long-term processes that have a fixed beginning, stage of development and a fixed end.
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Forms of statistical research |
Types of statistical observations | Methods for obtaining statistical information | |
| by data recording time | by completeness of coverage of population units | ||
| Statistical reporting | Current observation | Continuous observation | Direct observation |
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Specially organized observation:
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Intermittent observation:
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Anecdotal observation:
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Documentary |
| Register surveillance |
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Types of statistical observation
Statistical observations are divided into types according to the following criteria:
- by time of data recording;
- by completeness of coverage;
Types of statistical observation by registration time:
Ongoing (continuous) surveillance— carried out to study current phenomena and processes. Facts are recorded as they occur. (registration of family marriages and divorces)
Intermittent observation- carried out as necessary, with temporary gaps in data recording allowed:
Based on the completeness of coverage of population units, the following types of statistical observation are distinguished:
Continuous observation— represents the collection and receipt of information about all units of the population being studied. It is characterized by high material and labor costs and insufficient information efficiency. It is used in the population census, when collecting data in the form of reporting, covering large and medium-sized enterprises of various forms of ownership.
Partial observation- based on the principle of random selection of units of the population being studied, while all types of units present in the population must be represented in the sample population. It has a number of advantages over continuous observation: reduction of time and money costs.
Continuous observation is divided into:- Selective observation- based on a random selection of units that are observed.
- Monographic observation— consists of examining individual units of a population characterized by rare qualitative properties. An example of monographic observation: characteristics of the work of individual enterprises to identify shortcomings in work or development trends.
- Main Array Method- consists of studying the most significant, largest units of the population, which, according to their main characteristic, have the largest share in the population under study.
- Momentary Observation Method— consists of conducting observations at random or constant intervals of time with notes on the state of the object under study at one time or another.
Methods of statistical observation
Ways to obtain statistical information:
Direct statistical observation- observation in which the registrars themselves, by direct measurement, weighing, and counting, establish the fact to be recorded.
Documentary observation- based on the use of various types of accounting documents.
Includes reporting observation method - in which enterprises submit statistical reports on their activities in a strictly mandatory manner.
The following types of survey exist:Survey- consists of obtaining the necessary information directly from the respondent.
Expeditionary— registrars receive necessary information from the interviewees and record it themselves in the forms.
Self-registration method— the forms are filled out by the respondents themselves, the registrars only hand out the forms and explain the rules for filling them out.
Correspondent— information is provided to the relevant authorities by a staff of voluntary correspondents.
Questionnaire— information is collected in the form of questionnaires, which are special questionnaires, convenient in cases where high accuracy of results is not required.
Private- consists of providing information to the relevant authorities in person.
Errors in statistical observation
Information obtained during statistical observation may not correspond to reality, and the calculated values of indicators may not correspond to actual values.
The discrepancy between the calculated value and the actual value is called observation error.
Depending on the causes of occurrence there are distinguished registration errors and representativeness errors. Registration errors are typical for both continuous and non-continuous observations, and representativeness errors are typical only for non-continuous observations. Registration errors, like representativeness errors, can be random and systematic.
Registration errors- represent deviations between the value of the indicator obtained during statistical observation and its actual value. Registration errors can be random (the result of random factors - for example, strings are mixed up) and systematic (they appear constantly).
Representativeness errors- arise when the selected population does not accurately reproduce the original population. They are characteristic of incomplete observation and consist in the deviation of the value of the indicator of the studied part of the population from its value in the general population.
Control methods:Random errors- are the result of random factors.
Systematic errors- always have the same tendency to increase or decrease the indicator for each observation unit, as a result of which the value of the indicator for the population as a whole will include the accumulated error.
- Counting (arithmetic) - checking the correctness of an arithmetic calculation.
- Logical - based on the semantic relationship between features.
