Stages of statistical research. Methods and main stages of statistical research Statistics stages of statistical research

The result of the first stage of statistical research - statistical observation - is information characterizing each unit of the statistical population. However, the ability to reflect patterns and trends in the dynamics of the phenomena being studied using even the most complete characterization of individual facts is limited. Such data is obtained only as a result of statistical summaries. A summary is the arrangement, systematization and generalization of statistical data obtained during statistical observation. Only proper processing of statistical material allows us to identify the essence of socio-economic phenomena, character traits and essential features of individual types, to discover patterns and trends in their development. There are simple and group reports, or reports in the narrow and broad sense. A simple summary is the calculation of the overall results in groups and subgroups and the presentation of this material in tables. As a result of a simple summary of statistical data, it is possible to determine the number of enterprises, the total number of personnel, and the volume of products produced in monetary terms. These overall results are primarily for informational purposes. They provide a generalized characteristic of the population in the form of absolute values.

Group summary, or summary in a broad sense, is a complex process of multilateral processing of primary statistical data, i.e. data obtained as a result of observation. It includes grouping statistical data, developing a system of indicators to characterize groups, calculating group and overall results, and calculating generalizing indicators. The task of the statistical summary as the second stage of statistical research is to obtain general indicators for information, reference and analytical purposes. The summary of mass statistical data is carried out according to a pre-developed program and plan. During the program development process, the subject and predicate of the summary are determined. The subject is the object of study, divided into groups and subgroups. Predicate - indicators that characterize the subject of the summary. The summary program is determined by the objectives of the statistical study.

The statistical summary is carried out according to a pre-drawn plan. In terms of summaries, questions are addressed about how to carry out the work of summarizing information - manually or mechanically, and about the sequence of individual summation operations. The deadlines for completing each stage and the summary as a whole are established, as well as methods for presenting the results of the summary. These can be distribution series, statistical tables and statistical graphs.

The concept of studying the quantitative aspects of objects and phenomena was formed a long time ago, from the moment a person developed basic skills in working with information. However, the term “statistics”, which has come down to our time, was borrowed much later from Latin language and comes from the word “status”, which means “a certain state of things”. “Status” was also used in the meaning of “political state” and was fixed in almost all European languages in this semantic meaning: the English “state”, the German “Staat”, the Italian “stato” and its derivative “statista” - an expert on the state.

The word “statistics” received widespread use in the 18th century and was used to mean “state science.” Statistics is a branch of practical activity aimed at collecting, processing, analyzing and providing for public use data about phenomena and processes of social life.

Analysis is a method scientific research object by considering its individual aspects and components.

Economic statistical analysis is the development of a methodology based on the widespread use of traditional statistical and mathematical-statistical methods in order to control the adequate reflection of the phenomena and processes under study.

Stages of statistical research. Statistical research takes place in three stages:

1) statistical observation;
2) summary of the data obtained;
3) statistical analysis.

At the first stage, primary statistical data is collected using the mass observation method.

At the second stage of statistical research, the collected data undergoes primary processing, summary and grouping. The grouping method allows you to identify homogeneous populations and divide them into groups and subgroups. A summary is the obtaining of results for the population as a whole and its individual groups and subgroups.

The grouping and summary results are presented in the form of statistical tables. The main content of this stage is the transition from the characteristics of each observation unit to the summary characteristics of the population as a whole or its groups.

At the third stage, the obtained summary data is analyzed by the method of generalizing indicators (absolute, relative and average values, variation indicators, index systems, methods mathematical statistics, tabular method, graphical method, etc.).

Basics of statistical analysis:

1) approval of facts and establishment of their assessment;
2) identifying the characteristic features and causes of the phenomenon;
3) comparison of the phenomenon with normative, planned and other phenomena that are taken as the basis for comparison;
4) formulation of conclusions, forecasts, assumptions and hypotheses;
5) statistical testing of the put forward assumptions (hypotheses).

Analysis and generalization of statistical data is the final stage of statistical research, the ultimate goal of which is to obtain theoretical conclusions and practical conclusions about the trends and patterns of the socio-economic phenomena and processes being studied. The objectives of statistical analysis are: determining and assessing the specificity and characteristics of the phenomena and processes being studied, studying their structure, relationships and patterns of their development.

Statistical analysis of data is carried out in inextricable connection with a theoretical, qualitative analysis of the essence of the phenomena under study and the corresponding quantitative tools, the study of their structure, connections and dynamics.

Statistical analysis is the study of the characteristic features of the structure, relationships of phenomena, trends, patterns of development of socio-economic phenomena, for which specific economic-statistical and mathematical-statistical methods are used. Statistical analysis concludes with the interpretation of the results obtained.

In statistical analysis, signs are divided according to the nature of their influence on each other:

1. Result trait - the trait analyzed in this study. The individual dimensions of such a feature in individual elements of the population are influenced by one or more other features. In other words, the result-attribute is considered as a consequence of the interaction of other factors;
2. Sign-factor - a sign that influences the characteristic under study (sign-result). Moreover, the relationship between the factor-attribute and the result-attribute can be quantitatively determined. Synonyms for this term in statistics are “factor characteristic”, “factor”. It is necessary to distinguish between the concepts of factor-attribute and weight-attribute. A weight feature is a feature that must be taken into account in calculations. But the weight trait does not affect the trait being studied. A factor attribute can be considered as a weight attribute, i.e., taken into account in calculations, but not every weight attribute is a factor attribute. For example, when studying in a group of students the relationship between the time to prepare for an exam and the number of points received on the exam, the third characteristic should also be taken into account: “The number of people certified for a certain score.” The last feature does not affect the result, however, it will be included in the analytical calculations. It is this kind of attribute that is called a weight attribute, and not a factor attribute.

Before starting the analysis, it is necessary to check whether the conditions are met to ensure its reliability and correctness:

- Reliability of primary digital data;
- Completeness of coverage of the population being studied;
- Comparability of indicators (by accounting units, territory, calculation method).

The main concepts of statistical analysis are:

1. Hypothesis;
2. Decisive function and the decisive rule;
3. Sample from the general population;
4. Assessment of characteristics of the general population;
5. Confidence interval;
6. Trend;
7. Statistical relationship.

Analysis is the final stage of statistical research, the essence of which is to identify relationships and patterns of the phenomenon being studied, formulate conclusions and proposals.

1. STAGES OF STATISTICAL RESEARCH

The process of studying socio-economic phenomena through a system of statistical methods and quantitative characteristics - a system of indicators - is called statistical research.

The main stages of conducting a statistical study are:

1) statistical observation;

2) summary of the data obtained;

3) statistical analysis.

If necessary, a statistical study may contain an additional stage - a statistical forecast.

Statistical observation is a scientifically organized collection of data about the phenomena and processes of social life through registration according to a pre-developed program for observing their essential features. Observation data represents primary statistical information about the observed objects, which is the basis for obtaining their general characteristics. Observation acts as one of the main methods of statistics and as one of the most important stages of statistical research.

Conducting a statistical study is impossible without a high-quality information base obtained during statistical observation. Therefore, since the change in ideas about statistics as a descriptive science, special rules for conducting observations and special requirements for its results - statistical data - have been developed. That is, observation is one of the main methods of statistics.

Observation is the first stage of statistical research, the quality of which determines the achievement of the final objectives of the study.

1.1. Observation is carried out according to a specially prepared program.

The program includes a list of characteristics of the research object, data about which must be obtained as a result of observation.

When preparing an observation, it is necessary to determine in advance:

1. An observation program in which:

a) the object of observation is determined, i.e. that set of units of a phenomenon that needs to be investigated. Moreover, it is necessary to distinguish the observation unit from the reporting unit. A reporting unit is a unit providing statistical data; it may consist of several population units, or may coincide with a population unit. For example, in a population survey, the unit might be the household member and the reporting unit might be the household.

b) the boundaries of the observation object are determined.

c) the characteristics of the object of observation are identified, information about which must be obtained as a result of observation.

2. Time of observation of an object - the time as of which or for which information about the object being studied is recorded.

3. Timing of observation. That is, the period of time for data collection and the date of completion of observation are determined. The observation period affects the completion time of the overall statistical study and the timeliness of its conclusions.

4. Funds and resources required for monitoring: number of qualified specialists; material resources; means for processing observation results.

5. Requirements for statistical data. The main requirements are: a) reliability, i.e. information about the object of research should reflect its real state at the time of observation; b) comparability of data, i.e. information obtained as a result of observation must be comparable, which is ensured by a unified methodology for collecting and analyzing data, by units of measurement, etc.

1.2. There are several types of statistical observation.

1. By coverage of population units:

a) solid;

b) non-continuous (selective, monographic, based on the bulk method)

2. According to the time of registration of facts: a) current (continuous); b) discontinuous (periodic, one-time)

3. By the method of collecting information: a) direct observation; b) documentary observation; c) survey (questionnaire, correspondent, etc.)

Summary is the process of bringing the received data into the system, processing it and calculating intermediate and general results, calculating interrelated quantities of an analytical nature.

The next stage of statistical research is the preparation of information obtained during observation for analysis. This stage is called summary.

Summary includes:

— systematization of information obtained during observations;

— their grouping;

— development of a system of indicators characterizing educated groups;

— creation of development tables for grouped data;

— calculation of derived quantities using development tables.

In the literature on the theory of statistics, one often encounters consideration of summary and grouping as independent stages of research. However, it should be noted that the concept of summary includes actions to group statistical data, so here the concept of “summary” is adopted as the name of the research stage.

Statistical analysis is a study of the characteristic features of the structure, relationships of phenomena, trends, patterns of development of socio-economic phenomena, for which specific economic-statistical and mathematical-statistical methods are used. Statistical analysis concludes with the interpretation of the results obtained.

Statistical forecast is a scientific identification of the state and probable paths of development of phenomena and processes, based on a system of established cause-and-effect relationships and patterns.

EXERCISE 1

As a result of a sample survey of wages of 60 employees of an industrial enterprise, the following data were obtained (Table 1).

Construct an interval distribution series based on the effective attribute, forming five groups with equal intervals.

Determine the main indicators of variation (variance, standard deviation, coefficient of variation), the average power value (the average value of the characteristic) and structural averages. Represent it graphically in the form of: a) a histogram; b) cumulates; c) ogives. Draw a conclusion.

SOLUTION

1. Let us determine the scope of variation according to the effective attribute - according to production experience using the formula:

R = Хmax – Хmin = 36 – 5 = 31

where Xmax is the maximum size of assets

Хmin – minimum asset size

2. Determine the size of the interval

i = R/n = 31/5 = 6.2

Taking into account the obtained intervals, we group the banks and get

3. Let's build an auxiliary table

Recognition group	Meaning of values in a group x i	Quantity of characteristic frequency (frequency) f i	in % of total ω	Cumulative frequency S i	Middle of the interval	*fi	ω
I 5 – 11,2	6,8,7,5,8,6,10,9,9,7, 6,6,9,10,7,9,10,10, 11,8,9,8, 7, 6, 9, 10		43,3	43,3		210,6	350,73		46,24	1202,24
II 11,2 – 17,4	16,15,13,12,14,14, 12,14,17,13,15,17, 14		21,7		14,3	185,9	310,31		0,36	4,68
III 17,4 – 23,6	18,21,20,20,21,18, 19,22,21,21,21,18, 19		21,7	86,7	20,5	266,5	444,85		31,36	407,68
IV 23,6 –29,8	28,29,25,28, 24				26,7	133,5	221,61	11,8	139,24	696,2
V 29,8 – 36	36,35,33,				32,9	98,7	164,5
TOTAL						895,2	1492		541,2	3282,8

4. The average value of a characteristic in the population under study is determined by the arithmetic weighted formula:

of the year

5. The variance and standard deviation of a characteristic are determined by the formula

Determination of variability

Thus, V>33.3%, therefore, the population is heterogeneous.

6. Definition of fashion

Mode is the value of a characteristic that occurs most frequently in the population being studied. In the interval variation series under study, the mode is calculated using the formula:

Where

x M0
– lower limit of the modal interval:

i M0– the value of the modal interval;

f M0-1 f M0 f M0+1– frequencies (frequencies) of modal, pre-modal and post-modal intervals, respectively.

A modal interval is the interval that has the greatest frequency (frequency). In our problem, this is the first interval.

7. Calculate the median.

Median is an option located in the middle of an ordered variation series, dividing it into two equal parts, such that half of the population units have attribute values less than the median, and half more than the median.

In an interval series, the median is determined by the formula:

where is the beginning of the median interval;

– value of the median interval

– frequency of the median interval;

– the sum of accumulated frequencies in the pre-median interval.

The median interval is the interval in which the serial number of the median is located. To determine it, it is necessary to calculate the sum of the accumulated frequencies to a number exceeding half of the totality.

According to gr. 5 of the auxiliary table we find the interval in which the amount of accumulated amounts often exceeds 50%. This is the second interval - from 11.6 to 18.4, and it is the median.

Then

Consequently, half of the workers with work experience are less than 13.25 years, and half have more than this value.

6. Let us depict the series in the form of a polygon, a histogram, a cumulative line, or an ogive.

Graphic representation plays an important role in the study of variation series, as it allows one to analyze statistical data in a simple and visual form.

There are several ways to graphically display series (histogram, polygon, cumulate, ogive), the choice of which depends on the purpose of the study and on the type of variation series.

A distribution polygon is mainly used to depict a discrete series, but you can also construct a polygon for an interval series if you first convert it to a discrete series. The distribution polygon is a closed broken line in a rectangular coordinate system with coordinates (x i, q i), where x i is the value of the i-th feature, q i is the frequency or frequency of the i-ro feature.

A distribution histogram is used to display an interval series. To construct a histogram, segments equal to the intervals of the characteristic are laid out sequentially on the horizontal axis, and on these segments, as on bases, rectangles are constructed, the heights of which are equal to the frequencies or particulars for a series with equal intervals, densities; for a series with unequal intervals.

Cumulates are a graphical representation of a variation series, when accumulated frequencies or particulars are plotted on the vertical axis, and characteristic values are plotted on the horizontal axis. The cumulate is used for graphical representation of both discrete and interval variation series.

Conclusion: Thus, the main indicators of variation in the series under study were calculated: the average value of the attribute - production experience is 14.9 years, the dispersion was calculated to be 54.713, in turn, the standard deviation of the attribute is 7.397. The mode has a value of 9.13, and the modal interval is the first interval of the series being studied. The median of the series, equal to 13.108, divides the series into two equal parts, indicating that in the organization under study, half of the employees have less than 13.108 years of work experience, and half have more.

TASK 2

The following initial data are available that characterize the dynamics for 1997 – 2001. (table 2).

Table 2 Initial data

Year	1997	1998	1999	2000	2001
Production of granulated sugar, thousand tons	1620	1660	1700	1680	1700

Determine the main indicators of the dynamics series. Present the calculation in the form of a table. Calculate the average annual values of the indicators. In the form of a graphic image - a polygon, indicate the dynamics of the analyzed indicator. Draw a conclusion.

SOLUTION

Given

Year	Years
Year	1997	1998	1999	2000	2001
	1620	1660	1700	1680	1700

1) The average level of dynamics is calculated using the formula

2) Chain and base growth rates are calculated as follows:

1. Absolute growth is determined by the formula:

Аib = yi – y0

Aic = yi – yi-1

2. The growth rate is determined by the formula: (%)

Trb = (yi / y0) *100

Trc = (yi / yi-1)*100

3. The growth rate is determined by the formula: (%)

Тnрb = Трb –100%:

Tnrts = Trts – 100%

4. Average absolute increase:

y n
– final level of the time series;

y 0
– initial level of the dynamic series;

n c
– number of chain absolute increases.

5. Average annual growth rate:

6. Average annual growth rate:

3) Absolute content of 1% increase:

A = Xi-1/100

We summarize all calculated indicators in a table.

Indicators	Years
Indicators	1997	1998	1999	2000	2001
Number of surgical operations during the period	1620	1660	1700	1680	1700
2. Absolute increase

Aic
3. Growth rate
Trib		102,5	104,9	103,7	104,9
Trits		102,5	102,4	98,8	101,2
4. Growth rate
Тпib
Tpitz
5. Value of 1% increase		16,2	16,6	17,0	16,8

5) Average annual value

7. Let's depict it graphically in the form of a polygon.

Thus, the following is obtained. The largest absolute and relative increase in surgical operations for the period was in 1999 and amounted to 1700, the absolute increase compared to the base year was 80 operations, the growth rate compared to the base year 1997 was 104.9%, and the base growth rate was 4.9 %. The largest chain absolute increases were in 1998 and 1999 – 40 operations each. The highest chain growth rate was observed in 1998 - 102.5%, and the lowest chain growth rate in the number of transactions was in 2000 - 98.8%.

TASK 3

There are data on sales of goods (see table 3)

Table 3 Initial data on sales of goods

Product	Base year		Reporting year
Product	quantity	price	quantity	price

	1100		1000

		1350		1300

	1650		1700

Determine: a) individual indices ( i p , i q); b) general indices (I p, I q, I pq); c) absolute change in trade turnover due to: 1) the number of goods; 2) prices.

Draw a conclusion based on the calculated indicators.

SOLUTION

Let's create an auxiliary table

View	Basic		Reporting		Work		Indexes
View	Quantity, q 0	Price, p 0	Quantity, q 1	Price, p 1	q 0 * p 0	q 1 * p 1	i q =q 1 /q 0	i p =p 1 /p 0	q 1 * p 0
					44000	35000	0,875	0,909	38500
	1100		1000		41800	40000	0,909	1,053	38000
					7500	8400	1,200	0,933	9000
		1350		1300	40500	26000	0,667	0,963	27000
					45000	44000	1,100	0,889	49500
	1650		1700		26400	25500	1,030	0,938	27200
TOTAL					205200	178900			189200

Conclusion: As we can see, the total increase in trade turnover for the year was (-26,300) conventional units, including the impact of a change in the quantity of goods sold by - 16,000 and due to changes in the price of goods - 10,300 conventional units. The overall increase in trade turnover was 87.2%. It should be noted that according to the calculated indices of the quantity of goods by assortment, there is a slight increase in turnover for product “P” by 120% and product “C” by 110%, a slight increase in sales of product “T” is only 103%. Sales of goods “P” decreased quite significantly - only 66.7% of sales in the base year, sales of goods “N” were slightly higher - 87.5% and goods “O” - 90.9% of the corresponding indicator for the base year. The individual price index shows that the price increased only for product “O” - by 105.3%, while at the same time for all other product names - “N”, “P”, “R”, “S”, “T” the individual price index indicates negative dynamics (decrease), respectively – 90.9%; 93.3%;, 96.3%, 88.9; 93.8.

The general index of physical sales volume indicates a slight decrease in total sales volume by 94.6%; the general price index indicates a general decrease in the price of goods sold by 92.2%, and the general trade turnover index indicates a general decrease in trade turnover by 87.2%.

TASK 4

From the initial data of table No. 1 (select rows from 14 to 23) based on two characteristics - length of service and wages - conduct a correlation-regression analysis, determine the parameters of correlation and determination. Construct a graph of the correlation between two characteristics (resultative and factorial). Draw a conclusion.

SOLUTION

Initial data

Production experience	Salary amount
	1800
	2500
	1750
	1580
	1750
	1560
	1210
	1860
	1355
	1480

Straight-line dependence

The parameters of the equation are determined using the least squares method, using the system of normal equations

To solve the system we use the method of determinants.

Parameters are calculated using formulas

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Ministry of Education and Science of the Russian Federation

"Law Institute"

Faculty of Jurisprudence

Essay

by discipline

"Legal Statistics"

Methods and main stages of statistical research.

The work was completed by a student

Gribanov A.S.

Moscow

Introduction

1. The concept of statistical research

2. Methods of statistical research

3. Organization and stages of statistical research

Conclusion

List of used literature

Introduction

Statistics know everything,” Ilf and Petrov asserted in their famous novel “The Twelve Chairs” and continued: “It is known how much food the average citizen of the republic eats per year... It is known how many hunters, ballerinas... machines, bicycles, monuments, lighthouses and sewing machines... How much life, full of ardor, passions and thoughts, looks at us from statistical tables!..” Why are these tables needed, how to compile and process them, what conclusions can be drawn based on them - statistics answers these questions (from the Italian stato - state, Latin status - state). Statistics is a science that studies, processes and analyzes quantitative data about a wide variety of mass phenomena in life.

Statistical research has become firmly established in our daily life. Government and business entities regularly collect extensive information about society and the environment. This data is published in the form of tables and charts. Every person must be well versed in the flow of information. This means he must extract, analyze and process information, make decisions in a variety of situations.

In my work I will consider statistical research, what they are, what the methods of statistical research are, how these studies are organized and what stages they consist of.

1. The concept of statistical research

Observation as the initial stage of research is associated with the collection of initial data about the issue being studied. It is characteristic of many sciences. However, each science has its own specifics, differing in its observations. Therefore, not every observation is statistical.

Statistical research is a scientifically organized collection, summary and analysis of data (facts) about socio-economic, demographic and other phenomena and processes of social life in the state, with registration of their most significant features in accounting documentation, organized according to a unified program.

The distinctive features (specificity) of statistical research are: purposefulness, organization, mass participation, systematicity (complexity), comparability, documentation, controllability, practicality.

In general, a statistical study should:

* have a socially beneficial purpose and universal (state) significance;

* relate to the subject of statistics in the specific conditions of its place and time;

* express a statistical type of accounting (and not accounting or operational);

* be carried out according to a pre-developed program with its scientifically based methodological and other support;

* collect mass data (facts), which reflects the entire set of cause-and-effect and other factors that characterize the phenomenon in many ways;

* register in the form of accounting documents of the established form;

* guarantee the absence of observation errors or reduce them to the possible minimum;

* provide certain quality criteria and methods of monitoring the collected data, ensuring their reliability, completeness and content;

* focus on cost-effective technology for collecting and processing data;

* be a reliable information base for all subsequent stages of statistical research and all users of statistical information.

Studies that do not meet these requirements are not statistical.

Non-statistical studies, for example,

observations and research: mothers watching their child play (personal question);

spectators at a theatrical production (there is no accounting documentation for the spectacle);

a scientist for physical and chemical experiments with their measurements, calculations and documentary registration (not mass public data);

doctor for patients with maintaining medical records (operational records);

accountant for the movement of funds in the company's bank account (accounting);

journalists on the public and personal activities of government officials or other celebrities (not the subject of statistics).

A statistical population is a set of units that have mass, typicality, qualitative homogeneity and the presence of variation.

The statistical population consists of materially existing objects (Employees, enterprises, countries, regions) and is the object of statistical research.

Statistical observation is the first stage of statistical research, which is a scientifically organized collection of data about the phenomena and processes of social life being studied.

2. Methods of statistical research

It should be emphasized that statistical materials will be those that are specially created according to predetermined principles and methods and are subject to further processing by mathematical methods, i.e. will study the quantitative characteristics of the object being studied. They are created in two stages:

1) primary documents (primary sources) - questionnaires, checklists, questionnaires, etc.;

2) summary statements, summary tables, which are processed by methods of mathematical statistics; these summary documents are usually called "statistics".

Any statistical study assumes the following:

1) serious preliminary work;

2) direct data collection;

3) work on analyzing the data obtained.

The research is carried out according to a specific algorithm, and the passage of each stage requires the use of special methods and is focused on the content of the work being performed.

The algorithm for conducting a statistical study can be presented as follows.

1. Development of a research program or observation program. At this stage, the goals and objectives of the survey are determined, the coverage of the objects being studied, the degree of coverage of the objects, chronological and geographical framework, units of observation, indicators to be recorded, the primary source form for filling in data, and mechanisms for collecting information, monitoring the quality of information collection, processing and analysis of the obtained data.

An observation program is a list of signs to be recorded. surveillance registration accounting documentation

Observation period is the time during which information is recorded.

The critical observation date is the date as of which information is reported.

2. Conducting statistical observation can be short-term or long-term (carried out over a period of time), continuous or selective. As a result, as a rule, a complex of mass documents appears.

3. Summary and grouping of statistical data - calculation and grouping of collected data, as a result of which the latter turns into a system of statistical tables and subtotals.

4. Data analysis, which involves preliminary formulation of problems, carried out by methods of statistical analysis.

5. Interpretation of data - explanation of the results obtained, comparing them with similar indicators.

The types of statistical documents and methods of their subsequent processing are determined in accordance with the methods of data collection; all this is reflected and determined by a pre-developed program and depends on the objectives of the study.

At the data collection stage, statistical observation has two main forms:

1) reporting based on current observation, current (continuous) registration of facts and events;

2) specially organized statistical observation.

Statistical observation can be carried out using the following methods.

1. By time:

1) current (continuous) observation, carried out systematically;

2) periodic observation, repeated after a certain period of time (livestock census);

3) one-time observation, carried out as necessary, without taking into account the time interval (document flow accounting).

2. By coverage of observation units:

1) continuous observation, as a result of which all units of the population being studied are examined (general population census);

2) not continuous observation, when a part of the units of the object being studied is examined, selected in a certain way; types of non-continuous observation are:

a) the main array method, when a part of the population units is examined that has the most clearly expressed characteristics being studied;

b) questionnaire observation, when using survey sheets a set of characteristics is studied, which is then extrapolated to the entire population;

c) monographic observation, i.e. identification of various trends in the development of phenomena and characteristics in one set;

d) sample observation - part of the studied units processed randomly (family budget);

e) direct observation, in which a fact to be recorded is established, and on this basis, entries are made in the registration log (form).

In statistics, there is the following classification of methods for collecting information:

Correspondent, carried out by a staff of volunteer correspondents;

Expeditionary, implemented orally by specially trained workers;

Questionnaire (in the form of questionnaires);

Self-registration (filling out forms by respondents themselves);

Private (marriages, children, divorces).

Processing information obtained from primary sources usually involves systematizing the information. Over time, information processing methods have changed significantly.

Appearing initially as a system of numerical description, which involved accounting for population and land, in the 18th century. Having been enshrined in legislative acts, domestic statistics underwent significant evolution in the 19th and 20th centuries and emerged as a complex, branched system based on scientific mathematical methods and computer technologies.

By the beginning of the 20th century. I had serious experience in the field of statistics, and the basic principles of collecting and analyzing information were formed. The main directions of statistics, its methods (reports, surveys, censuses; the structure of statistical material and the system of statistical research), laid down and tested in the 19th century, developed throughout the 20th century.

Statistical (quantitative) descriptions within the framework of regional studies, using simple arithmetic calculations, were gradually replaced by complex mathematical and computer methods that make it possible to obtain detailed statistics, as well as to predict and model the development of statistical indicators on its basis.

The first objects of research were population and land; taxation problems were solved, for which calculations of the total number of inhabitants were carried out, patterns in population development were identified, and land censuses were carried out. The main demographic characteristic was the total population. Data were provided on births, deaths, number of marriages, tables of mortality and survival to a certain age were compiled, and by calculating the difference between the number of births and deaths per year, the average population growth was determined.

Today, statistics uses mass statistical observations, the method of groupings, averages, indices, the balance method, the method of graphical images and other methods of analyzing statistical data.

The types of documents also gradually changed. Military-statistical descriptions and descriptions of the province "in historical, statistical and ethnographic terms", scribal books and audits were replaced by complex selective and general censuses ("The First General Census of Population Russian Empire 1897", agricultural census and industrial census), a system of multifactor reports and the development of an interindustry balance National economy on years.

3. Organization and stages of statistical research

To get an idea of a particular phenomenon and draw conclusions, it is necessary to conduct a statistical study. The subject of statistical research in health care and medicine can be the health of the population, the organization of medical care, various sections of the activities of medical institutions, and environmental factors that influence the state of health.

The methodological sequence of performing a statistical study consists of certain stages.

Stage 1. Drawing up a research plan and program.

Stage 2. Collection of material (statistical observation).

Stage 3. Material development, statistical grouping and summary

Stage 4. Statistical analysis of the phenomenon under study, formulation of conclusions.

Stage 5. Literary processing and presentation of the results obtained.

Upon completion of the statistical study, recommendations are developed and management decisions, the research results are being implemented into practice, and the effectiveness is being assessed.

In conducting statistical research the most important element is to adhere to a strict sequence in the implementation of these stages.

The first stage of statistical research - drawing up a plan and program - is preparatory, at which the purpose and objectives of the study are determined, a research plan and program is drawn up, a program for summarizing statistical material is developed, and organizational issues are resolved.

The goal determines the main direction of the research and, as a rule, is not only theoretical, but also practical in nature. The goal is formulated clearly, clearly, unambiguously.

To reveal the set goal, research objectives are determined.

An important point in the preparatory stage is the development of an organizational plan. The organizational plan of the study provides for the determination of the place (administrative and territorial boundaries of observation), time (specific terms of observation, development and analysis of material) and the subject of the study (organizers, performers, methodological and organizational management, sources of funding for the study).

The research plan includes:

Definition of the object of study (statistical population);

Scope of research (continuous, not continuous);

Types (current, one-time);

Methods of collecting statistical information. The research program includes:

Definition of the unit of observation;

List of questions (accounting characteristics) to be registered in relation to each observation unit*

Development of an individual accounting (registration) form with a list of questions and characteristics to be taken into account;

Development of table layouts, into which the research results are then entered.

A separate form is filled out for each observation unit; it contains the passport part, clearly formulated program questions posed in a certain sequence and the date of filling out the document.

To ensure the possibility of statistical development of data from these documents, information is copied onto specially designed accounting forms, the content of which is determined in each individual case in accordance with the objectives of the study.

Currently, in connection with the machine processing of observation results using a computer, program questions can be formalized when questions in an accounting document are posed as an alternative (yes, no), or ready-made answers are offered, from which a specific answer must be selected.

At the first stage of statistical research, along with the observation program, a program for summarizing the obtained data is drawn up, which includes establishing the principles of grouping, identifying grouping characteristics, determining combinations of these characteristics, and drawing up layouts of statistical tables.

The second stage - collection of statistical material (statistical observation) - consists of registering individual cases of the phenomenon being studied and the accounting characteristics characterizing them on registration forms. Before and during this work, the surveillance performers are instructed (oral or written) and provided with registration forms.

In terms of time, statistical observation can be current or one-time.

In ongoing surveillance, a phenomenon is studied over a specific period of time (week, quarter, year, etc.) by recording the phenomenon on a daily basis as each occurrence occurs.

With one-time observation, statistical data are collected at a certain (critical) point in time. A one-time registration reflects the state of the phenomenon at the time of study. This type of observation is used to study slowly changing phenomena.

The choice of the type of observation over time is determined by the purpose and objectives of the study.

Depending on the completeness of coverage of the phenomenon being studied, a distinction is made between continuous and non-continuous research.

In a continuous study, all units of observation included in the population are studied, i.e. general population. A comprehensive study is carried out to establish the absolute dimensions of the phenomenon. The continuous method is also used in cases where information is necessary for operational work.

In a non-continuous study, only part of the population is studied. It is divided into several types: questionnaire, monographic, main array, selective.

Monographic method - provides a detailed description of individual units of the population that are characteristic in some respect and a deep, comprehensive description of objects.

The main array method involves the study of those objects in which a significant majority of observation units are concentrated. The disadvantage of this method is that a part of the population remains uncovered by the study, although small in size, but which may differ significantly from the main array.

The questionnaire method is the collection of statistical data using specially designed questionnaires addressed to a specific circle of people. This study is based on the principle of voluntariness, therefore the return of questionnaires is often incomplete. Often the answers to the questions posed bear the imprint of subjectivity and randomness. This method is used to obtain an approximate characteristic of the phenomenon being studied.

Sampling method - comes down to the study of some specially selected part of observation units to characterize the entire population. The advantage of this method is that it produces results with a high degree of reliability, as well as a significantly lower cost. The study involves a smaller number of performers, and also requires less time.

According to the method of obtaining information during statistical observation and the nature of its implementation, several types are distinguished:

1) direct observation

2) sociological methods: interview method (face-to-face survey), questionnaire (correspondence survey - anonymous or non-anonymous), etc.;

3) documentary research.

The third stage - grouping and summarizing the material - begins with checking and clarifying the number of observations, the completeness and correctness of the information received, identifying and eliminating errors, duplicate records, etc.

For the correct development of the material, encryption of primary accounting documents is used, i.e. designation of each characteristic and its group with a symbol - alphabetic or digital. Encryption is a technical technique that facilitates and speeds up the development of material, increasing the quality and accuracy of development. Ciphers - symbols - are generated arbitrarily. When encoding diagnoses, it is recommended to use the international nomenclature and classification of diseases; when encrypting professions - with a dictionary of professions.

The advantage of encryption is that, if necessary, after completing the main development, you can return to the development material in order to clarify new connections and dependencies. Encrypted accounting material allows you to do this easier and faster than unencrypted accounting material. After verification, the characteristics are grouped.

Grouping is the division of the totality of data being studied into homogeneous, typical groups according to the most significant characteristics. Grouping can be carried out according to qualitative and quantitative criteria. The choice of grouping characteristic depends on the nature of the population being studied and the objectives of the study.

Typological grouping is made according to qualitative (descriptive, attributive) characteristics.

Grouping by quantitative (variational) characteristics is carried out on the basis of the numerical dimensions of the characteristic. Quantitative grouping requires solving the issue of the size of the grouping interval: the interval can be equal, but in some cases it can be unequal, and even include so-called open groups.

When determining the number of groups, they proceed from the purpose and objectives of the study. It is necessary that groups can reveal the patterns of the phenomenon being studied. A large number of groups can lead to excessive fragmentation of the material and unnecessary detailing. A small number of groups leads to a blurring of characteristic features.

Having finished grouping the material, proceed to the summary.

Summary - generalization of individual cases obtained as a result of statistical research into certain groups, counting them and entering them into table layouts.

A summary of statistical material is carried out using statistical tables. A table that is not filled with numbers is called a layout.

Statistical tables can be listed, chronological, or territorial.

The table has a subject and a predicate. The statistical subject is usually placed along horizontal lines on the left side of the table and reflects the main, main feature. The statistical predicate is placed from left to right along vertical columns and reflects additional accounting characteristics.

Statistical tables are divided into simple, group and combinational.

Simple tables present the numerical distribution of the material according to one characteristic and its constituent parts. A simple table usually contains a simple list or summary of the entire phenomenon being studied.

When compiling tables, certain requirements must be met:

Each table should have a title that reflects its contents;

Inside the table, all columns must also have clear short names;

When filling out a table, all cells of the table must contain the appropriate numeric data. Cells in the table that are left blank due to the absence of this combination are crossed out (“-”), and if there is no information in the cell, “n.s.” is entered. or "...";

After filling out the table, the vertical columns and horizontal rows are summed up in the bottom horizontal row and the last vertical column on the right.

Tables must have a single sequential numbering.

In studies with a small number of observations, summaries are performed manually. All accounting documents are divided into groups in accordance with the attribute code. Next, the data is calculated and recorded in the appropriate cell of the table.

The fourth stage - statistical analysis - is a critical stage of the study. At this stage, statistical indicators are calculated (frequency, structure, average size of the phenomenon being studied), their graphical representation is given, dynamics and trends are studied, and connections between phenomena are established. forecasts are given, etc. Analysis involves interpreting the data obtained and assessing the reliability of the research results. Finally, conclusions are drawn.

The fifth stage - literary processing is the final one. It involves the finalization of the results of a statistical study. The results can be presented in the form of an article, a report, a dissertation, etc. For each type of presentation, there are certain requirements that must be observed when processing the results of a statistical study in literature.

Conclusion

To study various social and socio-economic phenomena, as well as some processes occurring in nature, special statistical studies are carried out. Any statistical study begins with the targeted collection of information about the phenomenon or process being studied.

The purpose of statistical research, like any scientific research, is to reveal the essence of mass phenomena and processes, as well as their inherent patterns. The distinctive feature of these patterns is that they do not apply to each individual unit of the population, but to the entire mass of units as a whole. The general principle underlying the study of statistical patterns is the so-called law of large numbers.

To generalize and systematize the data obtained as a result of statistical observation, they are divided into groups according to some criterion and the grouping results are summarized in tables.

When conducting a statistical study, after collecting and grouping data, they proceed to their analysis, using various general indicators for this.

List of used literature

1. Eliseeva I.I. Social statistics Textbook 3rd ed., revised. and additional -M.: Finance and Statistics, 2003.

2. Methods of statistical research/Electronic source (http://studme.org/43731/istoriya/metody_statisticheskih_issledovaniy).

3. Legal statistics: textbook / Ed. B.C. Lyalina, A.V. Simonenko. -2nd ed., revised. and additional M.: UNITY-DANA, 2010.

4. Savyuk L.K. Legal statistics / Textbook, M.: Yurist, 2004.

5. Statistics: textbook for bachelors / ed. I. I. Eliseeva. -- 3rd ed., revised. and additional - M.: Yurayt Publishing House, 2014.

6. Encyclopedia of statistical terms. v.1. Methodological basis statistics. FSGS, 2012.

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The methodological sequence of performing a statistical study consists of certain stages.

Stage 1. Drawing up a research plan and program.

Stage 2. Collection of material (statistical observation).

Stage 3. Material development, statistical grouping and summary

Stage 4. Statistical analysis of the phenomenon under study, formulation of conclusions.

Stage 5. Literary processing and presentation of the results obtained.

Upon completion of the statistical study, recommendations and management decisions are developed, the research results are implemented into practice, and effectiveness is assessed.

In conducting a statistical study, the most important element is adherence to a strict sequence in the implementation of these stages.

First stage statistical research - drawing up a plan and program - is preparatory, at which the purpose and objectives of the study are determined, a research plan and program is drawn up, a program for summarizing statistical material is developed, and organizational issues are resolved.

When starting a statistical study, you should accurately and clearly formulate the purpose and objectives of the study and study the literature on this topic.

The goal determines the main direction of the research and, as a rule, is not only theoretical, but also practical in nature. The goal is formulated clearly, clearly, unambiguously.

To reveal the set goal, research objectives are determined.

Pl A n research d ov A nia includes:

Definition of the object of study (statistical population);

Scope of research (continuous, non-continuous);

Types (current, one-time);

Methods of collecting statistical information. Research program includes:

Definition of the unit of observation;

List of questions (accounting characteristics) to be registered in relation to each observation unit*

Development of an individual accounting (registration) form with a list of questions and characteristics to be taken into account;

Development of table layouts, into which the research results are then entered.

A separate form is filled out for each observation unit; it contains the passport part, clearly formulated program questions posed in a certain sequence and the date of filling out the document.

Medical registration forms used in the practice of medical treatment institutions can be used as registration forms.

Sources for obtaining information can be other medical documents (medical histories, and individual outpatient records, child development histories, birth histories), reporting forms from medical institutions, etc.

Currently, in connection with machine processing of observation results using a computer, program questions can be formalized , when questions in an accounting document are presented in the form of an alternative (yes, no) , or ready-made answers are offered, from which a specific answer must be selected.

At the first stage of statistical research, along with the observation program, a program* is compiled for summarizing the data obtained, which includes establishing the principles of grouping, identifying grouping characteristics , determination of combinations of these characteristics, drawing up layouts of statistical tables.

Second phase- collection of statistical material (statistical observation) - consists of registering individual cases of the phenomenon being studied and the accounting characteristics characterizing them on registration forms. Before and during this work, the surveillance performers are instructed (oral or written) and provided with registration forms.

In terms of time, statistical observation can be current or one-time.

At current observation Yu Denia the phenomenon is studied for a specific period of time (week, quarter , year, etc.) by daily recording the phenomenon as each case occurs. An example of current observation is the recording of the number of births , dead, sick , discharged from the hospital, etc. This takes into account rapidly changing phenomena.

At one-time observation Yu Denia statistical data is collected at a certain (critical) point in time. One-time observations include: population census, study of the physical development of children, accounting of hospital beds at the end of the year, certification of medical institutions, etc. This type also includes preventive examinations of the population. A one-time registration reflects the state of the phenomenon at the time of study. This type of observation is used to study slowly changing phenomena.

The choice of type of observation over time is determined by the purpose and objectives of the study. For example, characteristics of hospitalized patients can be obtained as a result of the ongoing registration of those leaving the hospital (ongoing surveillance) or from a one-day census of patients in the hospital (one-time observation).

Depending on the completeness of coverage of the phenomenon being studied, a distinction is made between continuous and non-continuous research.

At completely The study examines all units of observation included in the population, i.e. general population. A comprehensive study is carried out to establish the absolute dimensions of the phenomenon, for example, total number population, the total number of births or deaths, the total number of people sick with a particular disease, etc. The continuous method is also used in cases where information is necessary for operational work (accounting for infectious diseases, doctors’ workload, etc.)

At not continuous The study examines only a portion of the population. It is divided into several types: questionnaire, monographic, main array, selective. The most common method in medical research is the sampling method.

Monographic method- gives a detailed description of individual units of the population that are characteristic in some respect and a deep, comprehensive description of objects.

Main Array Method- involves the study of those objects in which a significant majority of observation units are concentrated. The disadvantage of this method is that a part of the population remains uncovered by the study, although small in size, but which may differ significantly from the main array.

Questionnaire method is the collection of statistical data using specially designed questionnaires addressed to a specific circle of people. This study is based on the principle of voluntariness, therefore the return of questionnaires is often incomplete. Often the answers to the questions posed bear the imprint of subjectivity and randomness. This method is used to obtain an approximate characteristic of the phenomenon being studied.

Sampling method- comes down to the study of some specially selected part of observation units to characterize the entire population. The advantage of this method is that it produces results with a high degree of reliability, as well as a significantly lower cost. The study involved fewer performers , In addition, it requires less time.

In medical statistics, the role and place of the sampling method is especially great, since medical workers usually deal only with part of the phenomenon being studied: they study a group of patients with a particular disease, analyze the work of individual departments and medical institutions , evaluate the quality of certain events, etc.

According to the method of obtaining information during statistical observation and the nature of its implementation, several types are distinguished:

1) direct observation(clinical examination of patients , conducting laboratory , instrumental studies , anthropometric measurements, etc.)

2) sociological methods: interview method (face-to-face survey), questionnaire (correspondence survey - anonymous or non-anonymous), etc.;

3) documentary research A tion(copying information from accounting records medical documents, information from official statistics of institutions and organizations.)

Third stage- grouping and summary of material - begins with checking and clarifying the number of observations , completeness and correctness of the information received , identifying and eliminating errors, duplicate records, etc.

For the correct development of the material, encryption of primary accounting documents is used , those. designation of each characteristic and its group with a symbol - alphabetic or digital. Encryption is a technique , facilitating and accelerating material development , increasing the quality and accuracy of development. Ciphers - symbols - are generated arbitrarily. When encoding diagnoses, it is recommended to use the international nomenclature and classification of diseases; when encrypting professions - with a dictionary of professions.

The advantage of encryption is that, if necessary, after completing the main development, you can return to the development material in order to clarify new connections and dependencies. Encrypted accounting material makes this easier and faster , than unencrypted. After verification, the characteristics are grouped.

Grouping- division of the totality of the studied data into homogeneous ones , typical groups according to the most essential characteristics. Grouping can be carried out according to qualitative and quantitative criteria. The choice of grouping characteristic depends on the nature of the population being studied and the objectives of the study.

Typological grouping is made according to qualitative (descriptive, attributive) characteristics, for example, by gender , profession, disease groups, severity of the disease, postoperative complications, etc.

Grouping by quantitative (variational) characteristics is carried out on the basis of the numerical dimensions of the characteristic , For example , by age , duration of the disease, duration of treatment, etc. Quantitative grouping requires solving the issue of the size of the grouping interval: the interval can be equal, but in some cases it can be unequal, and even include so-called open groups.

For example , When grouped by age, open groups can be defined: up to 1 year . 50 years and older.

Having finished grouping the material, proceed to the summary.

WITH vodka- generalization of individual cases , obtained as a result of statistical research, into certain groups, counting them and entering them into table layouts.

A summary of statistical material is carried out using statistical tables. Table , not filled with numbers , called a layout.

Statistical tables can be lists , chronological, territorial.

Statistical tables are divided into simple , group and combinational.

IN simple tables presents the numerical distribution of material according to one characteristic , its components (Table 1). A simple table usually contains a simple list or summary of the entire phenomenon being studied.

Table 1

Distribution of deaths in hospital N. by age

IN group tables a combination of two characteristics is presented in connection with each other (Table 2).

table 2

Distribution of deaths in hospital N. by gender and age

IN combine A qi O these tables the distribution of material according to three or more interrelated characteristics is given (Table 3).

Table 3

Distribution of deaths in hospital N. due to various diseases by age and gender

Diagnosis of the underlying disease	Age
0-14	15-19	20-39	40-59	60 and >	Total
m	and	m	and	m	and	m	and	m	and	m	and	m+f
Diseases of the circulatory system.	-	-	-	-
Injuries and poisoning		-		-					-
Malignancy neoplasms.	-	-	-	-	-	-
Others.	-	-	-	-
Everyone got sick.		-		-

When compiling tables, certain requirements must be met:

Each table should have a title that reflects its contents;

Inside the table, all columns should also have clear, short titles;

After filling out the table, the vertical columns and horizontal rows are summed up in the bottom horizontal row and the last vertical column on the right.

Tables must have a single sequential numbering.

Currently, computers are widely used in sorting and summarizing material. . which allow not only to sort the material according to the characteristics being studied , but perform calculations of indicators.

Fourth stage- statistical analysis is a critical stage of the study. At this stage, statistical indicators are calculated (frequency , structures , average size of the phenomenon being studied), their graphic representation is given , dynamics are being studied , trends, connections between phenomena are established . forecasts are given, etc. Analysis involves interpreting the data obtained and assessing the reliability of the research results. Finally, conclusions are drawn.

Fifth stage- literary treatment is final. It involves the finalization of the results of a statistical study. The results can be presented in the form of an article, report, report , dissertations, etc. For each type of design there are certain requirements , which must be observed when processing the results of statistical research in literature.

The results of medical and statistical research are introduced into healthcare practice. There are various options for using the research results: familiarization with the results to a wide audience of medical and scientific workers; preparation of instructional and methodological documents; preparation of rationalization proposals and others.

STATISTICAL VALUES

For comparative analysis of statistical data, statistical values are used: absolute , relative , average.

Absolute values

The absolute values obtained in the summary tables during the statistical study reflect the absolute size of the phenomenon (the number of medical institutions, the number of beds in the hospital, the population , number of deaths, births, illnesses, etc.). A number of statistical studies end with obtaining absolute values. In some cases they can be used to analyze the phenomenon being studied , For example , when studying rare phenomena , if necessary, know the exact absolute size of the phenomenon , if necessary, pay attention to individual cases of the phenomenon being studied, etc. With a small number of observations , in the case when it is not necessary to determine the pattern , Absolute numbers can also be used.

In many cases, absolute values cannot be used for comparison with data from other studies. Relative and average values are used for this.

Relative values

Relative values (indicators , coefficients) are obtained as a result of the ratio of one absolute value to another. The most commonly used indicators are: intensive , extensive, ratios , visibility.

Intensive- frequency indicators , intensity, prevalence of the phenomenon in the environment , producing this phenomenon. In healthcare, morbidity is studied , mortality , disability, fertility and other indicators of public health. Wednesday , in which the processes occur is the population as a whole or its individual groups (age, gender, social , professional, etc.). In medical and statistical research, a phenomenon is, as it were, a product of the environment. For example , population (environment) and sick people (phenomenon); sick (environment) and dead (phenomenon), etc.

The value of the base is selected in accordance with the value of the indicator - by 100, 1000, 10000, 100000, depending on this, the indicator is expressed as a percentage , ppm , prodecimille, prosantimelle.

The intensive indicator is calculated as follows: for example, in Iran in 1995. There were 67,283 thousand inhabitants, and 380,200 people died during the year.

Intensive indicators can be general and special.

General intensive indicators characterize the phenomenon as a whole . For example , general fertility rates , mortality, morbidity, calculated for the entire population of the administrative territory.

Special intensive indicators (by group) are used to characterize the frequency of the phenomenon in various groups (morbidity by gender, age , mortality among children under 1 year of age , mortality for individual nosological Forms, etc.).

Intensive indicators are used: to determine the level . frequencies , prevalence of the phenomenon; to compare the frequency of a phenomenon in two different populations; to teach changes in the frequency of a phenomenon in dynamics.

Extensive- indicators of specific gravity, structure, characterize the distribution of a phenomenon into its component parts, its internal structure. Extensive indicators are calculated by the ratio of a part of a phenomenon to the whole and are expressed as a percentage or fraction of a unit.

The extensive indicator is calculated as follows: for example, in Greece in 1997 there were 719 hospitals, including 214 general hospitals.

Extensive indicators are used to determine the structure of a phenomenon and comparatively assess the relationship of its constituent parts. Extensive indicators are always interconnected, since their sum is always equal to 100 percent: for example, when studying the structure of morbidity, the proportion of an individual disease may increase with its true growth; at the same level, if the number of other diseases has decreased; with a decrease in the incidence of this disease , if the number of other diseases decreases at a faster rate.

Ratios- represent the ratio of two independent, independent of each other , qualitatively different quantities. Ratio indicators include indicators of the population’s availability of doctors, paramedics, hospital beds, etc.

The ratio is calculated as follows: for example, in Lebanon, with a population of 3,789 thousand inhabitants, 3,941 doctors worked in medical institutions in 1996.

Visibility- are used for the purpose of a more visual and accessible comparison of statistical values. Visual indicators provide a convenient way to convert absolute, relative or average values into an easy to compare Form. When calculating these indicators, one of the compared values is equated to 100 (or 1), and the remaining values are recalculated according to this number.

The calculation of visibility indicators is carried out as follows: for example, the population of Jordan was: in 1994. - 4275 thousand people, in 1995 - 4440 thousand people , in 1996 - 5439 thousand people.

Visibility indicator: 1994 - 100%;

1995	=	4460 *100	=	103.9%;


1996	=	5439*100	=	127.2%

Visual indicators indicate by what percentage or how many times there was an increase or decrease in the compared values. Visual indicators are most often used to compare data over time. , to present the patterns of the phenomenon being studied in a more visual form.

When using relative values, some errors may be made. Here are the most common of them:

1. Sometimes a change in the frequency of a phenomenon is judged on the basis of extensive indicators that characterize the structure of the phenomenon, and not its intensity.

3. When calculating special indicators, you should choose the right denominator for calculating the indicator: for example , the postoperative mortality rate must be calculated in relation to those operated on , and not for all patients.

4. When analyzing indicators, the time factor should be taken into account:

It is impossible to compare indicators calculated for different periods of time: for example, the incidence rate for a year and for half a year , which can lead to erroneous judgments. 5. It is impossible to compare general intensive indicators calculated from populations with heterogeneous composition, since heterogeneity in the composition of the environment can affect the value of the indicator.

Average values

Average values provide a general characteristic of a statistical population according to a certain changing quantitative characteristic.

The average value characterizes the entire series of observations with one number, expressing the general measure of the characteristic being studied. It levels out random deviations of individual observations and gives a typical characteristic of a quantitative characteristic.

One of the requirements when working with average values is the qualitative homogeneity of the population for which the average is calculated. Only then will it objectively reflect the characteristic features of the phenomenon being studied. The second requirement is that the average value only expresses the typical dimensions of a trait when it is based on a mass generalization of the trait being studied, i.e. calculated on a sufficient number of observations.

Average values are obtained from distribution series (variation series).

Variation series- a number of homogeneous statistical quantities characterizing the same quantitative accounting characteristic, differing from each other in their magnitude and arranged in a certain order (decreasing or increasing).

The elements of the variation series are:

Option- v - numeric value the changing quantitative characteristic being studied.

Frequency- p (pars) or f (frequency) - repeatability of a variant in a variation series, showing how often a particular variant occurs in a given series.

Total number of observations- n (numerus) - the sum of all frequencies: n=ΣΡ. If total number There are more than 30 observations, the statistical sample is considered large, if n is less than or equal to 30 - small.

Variation series are discontinuous (discrete), consisting of integers, and continuous, when the values of the variant are expressed as a fraction. In discontinuous series, adjacent options differ from each other by an integer, for example: the number of pulse beats, the number of respirations per minute, the number of days of treatment, etc. In continuous series, options may differ by any fractional value of one. There are three types of variation series. Simple- a series in which each option occurs once, i.e. frequencies are equal to unity.

ABOUT bullish- a series in which options appear more than once.

Grouped A ny- row. in which options are combined into groups according to their magnitude within a certain interval, indicating the frequency of repetition of all options included in the group.

The grouped variation series is used when large number observations and the sick range of extreme values is an option.

Processing the variation series consists of obtaining the parameters of the variation series ( average size, standard deviation and mean error of the mean).

Types of averages.

In medical practice, the following average values are most often used: mode, median, arithmetic mean. Other average values are used less frequently: geometric average (when processing the results of titration of antibodies, toxins, vaccines); root mean square (when determining the average diameter of a cell cut, the results of skin immunological tests); average cubic (to determine the average volume of tumors) and others.

Fashion(Mo) is the value of a characteristic that occurs more often than others in the aggregate. The mode is taken to be the variant that corresponds to the largest number of frequencies in the variation series.

Median(Me) is the value of a characteristic that occupies the middle value in the variation series. It divides the variation series into two equal parts.

The magnitude of the mode and median are not affected by the numerical values of the extreme variants available in the variation series. They cannot always accurately characterize the variation series and are used relatively rarely in medical statistics. The arithmetic mean characterizes the variation series more accurately.

WITH arithmetic mean(M, or) - calculated based on all numerical values of the characteristic being studied.

In a simple variation series, where options occur only once, the simple arithmetic mean is calculated using the formula:

Where V is the numeric values of the option,

n - number of observations,

Σ - sum sign

In a regular variation series, the weighted arithmetic mean is calculated using the formula:

Where V is the numeric values of the option.

Ρ - frequency of occurrence of the variant.

n is the number of observations.

S - sum sign

An example of calculating the arithmetic weighted average is given in Table 4.

Table 4

Determination of the average duration of treatment for patients in a specialized department of a hospital

In the example given, the mode is the option equal to 20 days, since it is repeated more often than others - 29 times. Mo = 20. The ordinal number of the median is determined by the formula:

The place of the median falls on the 48th option, the numerical value of which is 20. The arithmetic mean, calculated using the formula, is also equal to 20.

Average values are important general characteristics of a population. However, individual values of the characteristic are hidden behind them. Average values do not show variability or variability of a trait.

If the variation series is more compact, less scattered and all individual values are located around the average, then the average value gives a more accurate description of the given population. If the variation series is stretched, individual values deviate significantly from the average, i.e. If there is a large variability of a quantitative characteristic, then the average is less typical and reflects the entire series less well.

Averages of equal magnitude can be obtained from series with different degrees of dispersion. So, for example, the average duration of treatment for patients in a specialized department of a hospital will also be 20 if all 95 patients were inpatient treatment for 20 days. Both calculated averages are equal to each other, but were obtained from series with different degrees of variability.

Consequently, to characterize the variation series, in addition to the average value, another characteristic is needed , allowing one to assess the degree of its variability.