Statistical Research (SI) allows you to get an idea of ​​a particular phenomenon, study its size, level, and identify patterns. The subject of SI can be population health, organization of medical care, factors external environment, affecting health, etc.

When conducting SI, they can be used 2 methodological approaches:

1) studying the intensity of the phenomenon in the environment, the prevalence of the phenomenon, identifying trends in the health of the population - are carried out on general populations or sample populations sufficiently large in number, making it possible to obtain intensive indicators and reasonably transfer the obtained data to the entire general population

2) conducting strictly planned studies to study individual factors without identifying the intensity of the phenomenon in the environment - are carried out, as a rule, on small populations in order to identify new factors, study unknown or little-known cause-and-effect relationships

Stages of statistical research:

Stage 1. Drawing up a research plan and program– is preparatory, during which the purpose and objectives of the research are determined, a research plan and program is drawn up, a program for summarizing statistical material is developed, and organizational issues are resolved.

A) the purpose and objectives of the study must be clearly formulated; the goal determines the main direction of the research and, as a rule, is not only theoretical, but also practical in nature, it is formulated clearly, clearly, unambiguously; To reveal the set goal, research objectives are determined.

B) it is necessary to study literature on this topic.

B) needs to be developed Organizational plan – provides for the determination of 1) place (administrative and territorial boundaries of observation), 2) time (specific terms of observation, development and analysis of material) and 3) subject of research (organizers, performers, methodological and organizational management, sources of research funding).

D) development Research plan – includes the definition:

– object of study (statistical population);

– volume of research (continuous, non-continuous);

– types (current, one-time);

– methods of collecting statistical information.

D) it is necessary to compile Research (observation) program – includes:

– definition of the observation unit;

– 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 treatment and preventive institutions can be used as registration forms.

Other medical documents (medical histories, etc.) can serve as sources of information. individual cards outpatient, child development history, birth history), reporting forms from medical institutions, etc.

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 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 you must choose a specific answer.

E) it is necessary to draw up a program for summarizing the obtained data, which includes establishing grouping principles and identifying grouping characteristics , Determining combinations of these characteristics, drawing up layouts of statistical tables.

Stage 2. Collection of material (statistical observation)– – consists of registering individual cases of the phenomenon being studied and the accounting features that characterize them on registration forms. Before and during this work, instructions (oral or written) are provided to surveillance performers and they are provided with registration forms.

Statistical observation can be:

A ) by time:

1) Current– the phenomenon is studied for a specific period of time (week, quarter , Year, etc.) by daily recording the phenomenon as each case occurs (counting the number of births , Dead, sick , Discharged from hospital). This takes into account rapidly changing phenomena.

2) One-time– statistical data are collected at a certain (critical) point in time (population census, study physical development children, preventive examinations of the population). A one-time registration reflects the state of the phenomenon at the time of study and 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 (characteristics of hospitalized patients can be obtained as a result of the current registration of those leaving the hospital - current observation or by a one-day census of patients in the hospital - one-time observation).

B) depending on the completeness of coverage of the phenomenon being studied:

1) Solid– all observation units included in the population are studied, i.e. the general population. They are carried out in order to establish the absolute size of the phenomenon (total population, total number of births or deaths). It is also used in cases where information is necessary for operational work (taking into account infectious diseases, doctors’ workload, etc.)

2) Not continuous– only part of the general population is studied, divided into several types:

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

2. 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.

3. 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.

4. Sampling method- the most common 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 high degree reliability, as well as significantly lower cost. The study involved fewer performers , In addition, it requires less time. Role and place in medical statistics sampling method are especially large, 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).

C) by the method of obtaining information during the process and the nature of its implementation

1. Direct observation(clinical examination of patients , Conducting laboratory , Instrumental Research , Anthropometric measurements, etc.)

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

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

Stage 3. Material development, statistical grouping and summary– begins with checking and clarifying the number of observations , Completeness and correctness of the information received , Identifying and eliminating errors, duplicate records, etc.

For proper development of the material, it is used Encryption of primary accounting documents, That is, the designation of each feature and its group with a sign - alphabetic or digital. Encryption is a technique , Facilitates and accelerates material development , Increasing quality and precision of development. Ciphers - symbols - are generated arbitrarily. When encoding diagnoses, it is recommended to use the international nomenclature and classification of diseases; when encoding 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 data being studied into homogeneous ones , Typical groups based on 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.

A) Typological grouping produced according to qualitative (descriptive, attributive) characteristics (gender , Profession, disease groups)

B) Variational grouping(by quantitative characteristics) is carried out on the basis of the numerical dimensions of the characteristic (age , Duration of the disease, duration of treatment, etc.). Quantitative grouping requires resolving the issue of the size of the grouping interval: the interval can be equal, but in some cases it can be unequal, even include the so-called open groups(when grouped by age, open groups can be defined: up to 1 year, 50 years and older).

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 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. Table , Not filled with numbers , Called Layout.

Statistical tables can be lists , Chronological, 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:

A) Simple– presents the numerical distribution of material according to one characteristic , Its components. A simple table usually contains a simple list or summary of the entire phenomenon being studied.

B) Group– a combination of two characteristics is presented in connection with each other

IN) Combination– the distribution of material is given according to three or more interrelated characteristics

When compiling tables, certain requirements must be met:

– each table must have a title reflecting its contents;

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

– when filling out the table, all cells of the table must contain the corresponding numerical 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.” or "…";

– after filling out the table, the vertical columns and horizontal rows are summed up in the bottom horizontal row and in 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. 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.

Stage 4. Statistical analysis of the phenomenon under study, formulation of conclusions– a critical stage of the study, at which the calculation of statistical indicators (frequency , Structures , Average sizes of the phenomenon being studied), their graphic representation is given , Dynamics is being studied , Trends, connections between phenomena are established . Forecasts are made, etc. Analysis involves interpreting the data obtained and assessing the reliability of the research results. Finally, conclusions are drawn.

Stage 5. Literary processing and presentation of the results obtained– is final and involves finalization of the results of the statistical study. The results can be presented in the form of an article, report, report , Dissertations, etc. For each type of registration there are certain requirements , Which must be observed during literary processing of the results of statistical research.

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

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

Main stages of statistical research

Let's consider the most important method statistics – statistical observation.

Usage in various ways and techniques of statistical methodology

presupposes the availability of comprehensive and reliable information about what is being studied

object. The study of mass social phenomena includes stages of collection

statistical information and its primary processing, information and grouping

observation results in certain populations, generalization and analysis

received materials.

At the first stage of statistical research, primary

statistical data, or raw statistical information that

is the foundation of the future statistical building. So that the building is

its foundation must be strong, sound and of high quality. If when collecting

there was an error in the primary statistical data or the material turned out to be

of poor quality, it will affect the correctness and reliability of both

theoretical and practical conclusions. Therefore, statistical

observation from the initial to the final stage - obtaining the final

materials - must be carefully thought out and clearly organized.

Statistical observation provides the source material for generalization, the beginning

which the summary serves. If during statistical observation about each of its

unit receives information characterizing it from many sides, then the data

reports characterize the entire statistical population and its individual parts.

At this stage, the totality is divided according to differences and united according to

signs of similarity, total indicators are calculated for groups and in

in general. Using the grouping method, the phenomena being studied are divided into the most important

types, characteristic groups and subgroups according to essential characteristics. By using

groupings are limited by qualitatively homogeneous in significant respects

totality, which is a prerequisite for the definition and application

generalizing indicators.

At the final stage of analysis using general indicators

relative and average values ​​are calculated and a summary assessment is given

variations of signs, the dynamics of phenomena are characterized, indices are used,

balance sheet constructions, indicators characterizing crowding are calculated

connections in changes in characteristics. For the purpose of the most rational and visual

Presentation of digital material is presented in the form of tables and graphs.

3.Statistical observation: concept, basic forms.

This is scientific and organizational work on data collection. Forms:stat. 1) reporting, cat. is based on documentary accounting. Since 1998, 4 unified forms of federal state supervision have been introduced: FP-1 (production of enterprises), FP-2 (investment), FP-3 (financial state of organizations), FP-4 (number - number of workers, labor), 2) specially organized observation (census), 3) register - this is a set of units, cat.har-t of each unit of observation: registers of us- research, production, construction and contracting organizations, retail and wholesale trade. Types of observation: 1) continuous, non-continuous (selective, qualified based on the main array method, monograph). The observation can be current, periodic, one-time. Methods of observation: direct, documentary, survey (expedition, questionnaire, personal appearance, correspondence). Statistical observations are carried out according to a plan, which includes: program and methodological issues (goals, objectives), organizational issues (time, place). As a result of the observations carried out, errors arise, which reduce the accuracy of the observations, so data control is carried out (logical and counting). As a result of checking the reliability of the data, the following observation errors are revealed: random. errors (registration errors), intentional errors, unintentional errors. (systemic and non-systemic), errors of representativeness (representativeness).

Program and methodological issues of statistical observation.

Program and methodological issues of statistical observation

Each observation is carried out for a specific purpose. When conducting it, it is necessary to establish what is subject to examination. The following issues need to be resolved:

Observation object – a set of objects and phenomena from which information must be collected. When defining an object, its main distinctive features(signs). Every object of mass observation consists of individual units, so it is necessary to resolve the question of what element of the aggregate that will serve as the unit of observation.

Unit of observation – this is a component element of an object, which is the carrier of characteristics subject to registration and the basis of the account.

Census – these are certain quantitative restrictions for the object of observation.

Sign - this is a property that characterizes certain features and characteristics inherent in the units of the population being studied.

Organizational issues of statistical observation.

The observation program is drawn up in the form of forms (questionnaires, forms) in which primary data is entered. A necessary addition to the forms is instructions that explain the meaning of the questions.

Organizational issues of the program include:

observation period;

critical moment of observation;

preparatory work;

The observation period to which the recorded information relates. Called objective observation time. This might be a certain period of time (day, decade, month) or a certain moment. The moment to which the recorded information relates is called the critical moment of observation.

For example, the critical moment of the micro-census of 94. was 0.00 o'clock on the night of February 13-14. By establishing the critical moment of observation, it is possible to determine the true state of affairs with photographic accuracy.

Preparatory work involves providing surveillance with documents, as well as compiling a list of reporting units, forms, and instructions.

Documents will be filled out during the observation or based on its results.

Important place in system preparatory work has the selection and training of personnel, as well as briefing of those who will participate in the observation.

Any statistical study of mass social phenomena includes 3 main stages:

Statistical observation - primary statistical data, or initial statistical information, which is the basis of statistical research, is generated. If an error is made during the collection of primary statistical data or the material turns out to be of poor quality, this will affect the correctness and reliability of both theoretical and practical conclusions;

Data summary and grouping - at this stage, the population is divided according to the signs of difference and united according to the signs of similarity, the total indicators are calculated for the groups and as a whole. Using the grouping method, the phenomena under study are divided into types, groups and subgroups, depending on their essential characteristics. The grouping method makes it possible to limit populations that are qualitatively homogeneous in significant respects, which serves as a prerequisite for the definition and application of generalizing indicators;

Processing and analysis of received data, identifying patterns. At this stage, with the help of generalizing indicators, relative and average values ​​are calculated, a summary assessment of the variation of characteristics is given, the dynamics of phenomena are characterized, indices and balance sheets are used, indicators are calculated that characterize the closeness of connections in changes in characteristics. For the purpose of the most rational and visual presentation of digital material, it is presented in the form of tables and graphs.

Lecture No. 2. Statistical observation

1. Concept and forms of statistical observation

Statistical observation is the first stage of any statistical research.

Statistical observation is a scientifically organized work to collect mass primary data on phenomena and processes public life.

However, not every collection of information is a statistical observation. We can talk about statistical observation only when statistical patterns are studied, i.e. those that appear only in the mass process, in large number units of some aggregate.

Therefore, the statistical observation should be:

systematic - to prepare and carry out according to a developed plan, which includes issues of methodology, organization, technology for collecting information, quality control of the collected material, its reliability, and presentation of the final results;

massive - to cover a large number of cases of manifestation of a given process, sufficient to obtain true statistical data characterizing not only individual units, but also the entire population as a whole;

systematic - the study of trends and patterns of socio-economic processes characterized by quantitative and qualitative changes is possible only on the basis of systematicity.

The following basic requirements apply to statistical observation:

completeness of statistical data (completeness of coverage of units of the population being studied, aspects of a particular phenomenon, as well as completeness of coverage over time);

reliability and accuracy of data;

uniformity and comparability of data.

In statistical practice there are two organizational forms observations:

1) reporting is an organizational form in which observation units present information about their activities in the form of forms of a regulated sample. The peculiarity of reporting is that it is mandatory, documented and legally confirmed by the signature of the manager;

2) special statistical surveys, examples of which are population censuses, sociological studies, censuses of residual material, and other observations that are carried out if problems arise for which there is not sufficient information. They give additional material to the reporting data or using them to check the reporting data.

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 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.

An important point 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).

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 for 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.

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 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, instructions (oral or written) are provided to surveillance performers and they are 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 continuous study is carried out in order to establish the absolute size of a phenomenon, for example, the total 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 medical records and reports, 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 sign - 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 data being studied 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.

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.

WITH vodka- generalization of individual cases , obtained as a result of statistical research, into certain groups, their calculation and inclusion in 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.

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.

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

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;

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 in 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.

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 statistical data uses statistical values: absolute , relative , average.

Absolute values

Absolute values ​​obtained in pivot tables during a statistical study, reflect the absolute size of the phenomenon (number of medical institutions, number of beds in a hospital, 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 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 interrelated, since their sum is always equal to 100 percent: for example, when studying the structure of morbidity specific gravity 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%;

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 is the numerical value of 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 values ​​option 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.

A grouped variation series is used when there is a large number of observations and a large range of extreme values.

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 median is located in the 48th option, the numerical value of which is 20. The arithmetic mean, calculated using the formula, is also 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 more exact description of this aggregate. 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.

Equally sized averages can be obtained from series with varying degrees scattering. 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.

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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 observation program of 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 wages The following data were obtained from 60 employees of an industrial enterprise (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 size assets

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 obtain

3. Let's build an auxiliary table

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 graphic image 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 rectangular system coordinates 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 build a histogram on horizontal axis lay down sequential segments equal to the intervals of the characteristic, and on these segments, as on bases, rectangles are built, 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

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

1) Average level dynamics is calculated by 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 dynamic series;

y 0
– First level 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.

5) Average annual value

7. Let's depict it graphically as 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 is data on sales of goods (see table 3)

Table 3 Initial data on sales of goods

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

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 the 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

Straight-line dependence

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

To solve the system we use the method of determinants.

Parameters are calculated using formulas