There is no national market data bank in Russia yet, so the necessary information has to be collected “bit by bit,” creating a more or less objective picture.

There are two methods of collecting such information - continuous observation, when all units of the general population are examined, and selectively, in which information is obtained only from a part of the units of this population. More common in marketing research is a selective method of collecting information that has the following advantages:

1 – information can be obtained much faster, which ensures timeliness of information;

2 – data obtained selectively is much more complete, because it is possible to characterize each unit of observation much more fully;

3 – information is more complete, because less information is collected, which means less possible errors.

However, the advantages of the sampling method can only be realized if certain rules are strictly observed when organizing and conducting sampling observations. These primarily include ensuring the quantitative and qualitative representativeness of the sample.

Quantitative representativeness means ensuring in the sample such a number of units that one can reasonably judge the magnitude of the characteristics being studied.

If nothing is known about the general population, then the required sample size is calculated using the formula:

where n is the required sample size;

D p is the sampling error we allow for the share (specified accuracy);

t – coefficient depending on the probability with which the specified sampling accuracy is guaranteed;

p, q – shares of opposite events (p + q = 1).

If nothing is known about the population, then take

p = 0.5 and q = 0.5, and the sample size calculated for these values ​​will be sufficient for any other "p" and "q" ratios.

In marketing research, a probability of an event equal to 0.954 is usually considered quite acceptable, at which t = 2 (from the table with p = 0.997, t = 3, etc.).

Example . Traders who sell agricultural machinery need to know how many farms use mowers. It is hardly possible to survey all households, so it is better to conduct a sample survey. But how many farms should we survey?

For the example in question:

p – share of farms using haymowers;

q – share of farms that do not use mowing machines;

If we can tolerate a sampling error of ±5% then D p = 0.05 and thus have a sample size

farms.

If something is known about the population (for example, from past studies it is known that there were 800 farms in the area of ​​which 80% used mowers), then the sample size is calculated using the formula:

,

Where N – volume of the general population.

For this example

farms.

If it is necessary to determine the average value of the population (for example, the average service life of an electric mower), then the sample size is calculated using the formula:

,

where s 2 – dispersion characterizing variations of the studied trait;

Dx – maximum permissible sampling error for the average.

For example, past research shows thats 2 amounts to±2.25 of the year. Then, with acceptable accuracy, we have±0.3 of the year.

farms.

The sample must be representative (Figure 1.4), i.e. should be represented by the maximum possible number of groups in the population.

Figure 1.4 - Qualitatively representative sample

Figure 1.5 - Qualitatively unrepresentative sample

To avoid unrepresentativeness (Figure 1.5), random mechanical selection is used in market research. Its essence is that random objects are examined at a certain interval.

After calculating the sample results, the effectiveness is assessed by calculating the actual error

a) for average b) for share

; .

Example. As a result of a sample survey of farms, it was found that47 % some of them use haymowers. A total of 194 farms were surveyed.

.

Therefore, the confidence interval for farms purchasing mowing machines ranges from 0.47-0.06 to 0.47+0.06 i.e. from 41% to 53%.

Based on this data, you can build your commercial policy.

The most common method of collecting market information is the questionnaire method.

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RUSSIAN INTERNATIONAL ACADEMY OF TOURISM

VOLGA-KAMA BRANCH

Faculty of Management

COURSE PROJECT

In the discipline "Statistics"

Sampling method

Completed:

Khaliullina Asiya

Naberezhnye Chelny

• Introduction
• I. Theoretical part. Sampling method
• 2. Sampling error
• 3. Small sample
• Average error of small samples
• The average serial sampling error is determined by the formulas
• II. Practical part
• 1. Problem
• 2. Solution
• 3. Conclusion
• Conclusion.
• Application

Introduction

The concept of “statistics” comes from the Latin word “status”, which in translation means position, condition, order of phenomena.

The term “statistics” was introduced into scientific circulation by Gottfried Achenwal (1719-1772), a professor at the University of Göttingen.

Statistics is an independent social science with its own subject and research method. It arose from the practical needs of social life. Already in the ancient world, there was a need to count the number of inhabitants of a state, take into account people suitable for military service, determine the number of livestock, the size of land and other property. Information of this kind was necessary for collecting taxes, waging wars, etc. Subsequently, as social life develops, the range of phenomena taken into account gradually expands.

On modern stage interest in statistical analysis is caused by the development of the economy in the country, the formation market relations. This requires deep economic knowledge in the field of collection, processing and analysis of economic information.

The general methodology for studying statistical populations is to use the basic principles that guide any science. These principles, as a kind of principles, include the following:

1. objectivity of the phenomena and processes being studied;

2. identifying the relationship and consistency in which the content of the factors being studied is manifested;

3. goal setting, i.e. achievement of set goals on the part of the researcher studying the relevant statistical data.

This is expressed in obtaining information about trends, patterns and possible consequences development of the processes being studied. Knowledge of the patterns of development of socio-economic processes that interest society is of great practical importance.

The features of statistical data analysis include the method of mass observation, the scientific validity of the qualitative content of groupings and its results, the calculation and analysis of generalized and generalizing indicators of the objects being studied.

As for specific methods of economic, industrial or statistics of culture, population, national wealth, etc., there may be specific methods for collecting, grouping and analyzing the corresponding aggregates (the sum of facts).

In economic statistics, for example, the balance method is widely used as the most common method of mutually linking individual indicators in a unified system of economic relations in social production. Methods used in economic statistics also include the compilation of groupings, the calculation of relative indicators (percentages), comparisons, the calculation of various types of averages, indices, etc.

To conduct this study, I chose a method in which a general indicator of the population under study is established for some part of it based on random selection, that is, the sampling method.

Target course work- study the sampling method of statistics.

I took the entire team as the object of study for statistical analysis. kindergarten No. 17 “Forest Fairy Tale”, located at st. Sh. Usmanova, 51/08. My main task is to determine average age people working in this kindergarten.

I. Theoretical part. Sampling method.

1. The essence of the sampling method and its practical significance

The sampling method is the main method of collecting information in a developed market economy.

Sampling is a type of non-continuous observation that allows one to determine the indicators of the entire population (general population) based on the study of part of it. In this case, the selected part is formed taking into account the provisions of probability theory and mathematical statistics.

Sampling has a long history, but its mathematical component was developed in the 2nd half of the 19th-20th century. Russian statisticians made a significant contribution to the formation of sampling theory. In the USSR, continuous statistical observation in the form of reporting dominated. The sample only covered:

§ Product quality assessment;

§ Observation of prices on urban collective farm markets;

§ Monitoring family budgets;

§ Study of demand.

Abroad at that time, sample surveys predominated. Continuous observation covered only customs statistics, taxation and periodically conducted population censuses, and industrial qualifications.

Advantages of sampling.

With a properly organized sample survey, no more than 20-25% of the population is studied, usually 10% is a lot. There is a huge saving of time and money. At the same time, thanks to the work of professional statisticians, the accuracy of observations significantly increases (it is often higher than with continuous observation). However, the sample parameters, due to objective reasons, may differ from the corresponding parameters of the general population, therefore the results of the sample study apply to general population with a certain probability.

Not every non-continuous observation is a scientifically based sample.

To obtain reliable results, the sample must be carefully prepared. Preparation includes the following steps:

1. Justification of the feasibility of sampling;

2. Preparation of a sampling program;

3. Solving organizational issues of sampling;

4. Determination of the selection method and sample size to ensure the representativeness of its results.

5. Selection of units of the general population.

6. Summary of the results obtained and calculation of sample parameters.

7. Determination of sampling errors.

8. Extension of sampling parameters to the general population.

The main task of sampling:

§ Calculation of the expected sampling error, that is, the difference between the same characteristics of the sample and the general population;

§ Determining the confidence probability that the representativeness error will not exceed a certain predetermined value;

§ Calculation of the sample size that ensures the required accuracy of research with a given probability.

2. Sampling error

It arises due to differences in the variation of the values ​​of the characteristic being studied between units of the sample and the general population. Since, subject to random sampling, all units in the population have an equal chance of being included in the sample, the composition of the sample can change significantly as tests are repeated. Accordingly, the sampling parameters will change and sampling errors will occur. Sampling errors are inevitable; they arise from the essence of the method. Sampling errors may not be constant when sampling is repeated.

Sampling error in statistics is a certain average value or general characteristic of errors obtained by repeating tests multiple times.

W-P

- sampling error;

- sample average;

- general average;

W is the proportion of units possessing the studied characteristic in the sample population (sample proportion);

P is the proportion of units possessing the studied characteristic in the general population.

The magnitude of errors depends on the selection method. In mathematical statistics, it has been proven that the average sampling error (the mathematical expectation of the average sampling error) is the standard deviation of the distribution of the sample mean.

The sampling error is determined by:

In mathematical statistics it has been proven that the average error of the actual random repeated selection is calculated:

Where

- average sampling error;

- dispersion of the general population;

- sample size.

If the sample fraction under repeated selection is examined, where is the variance of the binomial distribution.

The results of repeated selection obey the law of binomial distribution.

With non-repetitive sampling, the results of multiple sampling and the distribution of errors obey the hypergeometric distribution, and the formula for the average error has the form:

respectively for the sample fraction

When sampling large numbers, when from mass populations () a resampling formula can be used to calculate sampling errors.

General variance is present in the average sampling error formulas. However, it is usually unknown. If we sample to study only part of the population, we cannot know the population variance. The only exceptions are samples carried out to control the results of continuous observation.

However, mathematical statistics have proven that if the sample is taken from the normal distribution of the population, the general and sample variances are related to each other as follows:

2 - general variance;

S 2 - sample variance;

n - sample size.

From the formula it is clear that a sufficiently large sample is (n-1)n, and, hence 2 S 2. Therefore, sample variances are used in practice to calculate average sampling errors.

If samples are taken repeatedly from the same population, then the specific size of the sampling error will correspond to one or another statistical probability her appearance.

It is impossible to calculate the probabilities of a specific size of errors (inappropriate); it is much more important to know that the observational error will not go beyond certain limits.

The essence of the limit theorem: Chebyshev proved that the arithmetic mean is sufficiently large number independent random variables whose variances are limited by some constant becomes virtually independent of the game of chance.

According to Chebyshev’s formula, if

This formula is for re-selection conditions.

Academician Markov proved that the limit theorem is also valid for non-repetitive selection.

Academician Lyapunov proved that the probabilities of marginal errors of numerous samples obey the law of normal distribution, therefore, to determine the probabilities of finding a sampling error within given limits, one can use Laplace’s integral formula.

Curve area

Hence, if the confidence coefficient is t=1, then the probability that the marginal sampling error will not be greater than the average error, which is 0.683.

The probable interval of change in the general average or share in statistics is usually called a confidence interval.

3. Small sample

In the process of statistical research, it is often necessary to limit the sample size, especially in cases where the study of population units leads to their destruction.

Statistics have proven that even in a very small sample size (20-30, and sometimes 4-5 units) they can obtain results acceptable for analysis. The problem of small samples was solved in 1908. English statistician W. Gasset (pseudonym Student). He was able to determine the relationship between the value of the confidence coefficient t, as well as the size of the small sample n, on the one hand, and the probability of finding the sampling error within specified limits, on the other hand. This dependence is called the Student distribution. To simplify calculations, there are special tables of Student’s t-test values ​​(p. 372 of the “Workshop on the Theory of Statistics”).

N-1 - number of degrees of freedom.

The small sample is determined by the formula

t - Student's test;

Average Small Sample Error

Average Small Sample Error

Small sample variance

number of degrees of freedom.

4. Determining the optimal sample size

Labor and material costs for conducting a sample directly depend on its size, therefore it is extremely important to maintain the sample size to the optimum, so as not to lose its accuracy.

It is convenient to search for the optimal sample size based on the formulas for the average and maximum errors. From the formula for the average error of random repeated selection it is clear that the average error is inversely proportional to the square root of the sample size

To reduce the average error by 2 times, you need to increase the sample size by 4 times. Using the formula for the maximum sampling error, you can find the number

This is the optimal sample size for random resampling

The presence of general variance in the formula for the optimal number leads, at first glance, to a paradox: why do we need to sample if the general variance (and, consequently, the general average) is known? However, in practice, the general variance is usually not known; instead, the sample variance of the previous survey is used, since the variance as an indicator is more stable than the variants on the basis of which it is calculated.

If the selection is carried out repeatedly, then the sample size for such selection is calculated using the formula:

If in the conditions of the problem there is a marginal error in the sample fraction, then the formula:

For re-selection;

For non-repetitive selection.

5. Extension of the results of the sampling distribution to the general population

For these purposes, two methods are used:

§ Direct conversion method;

§ Method of correction factors.

The direct recalculation method is used to determine, from data on the sample share, the value of the interval within which in the general population, with a given probability, there is the number of units possessing the characteristic being studied.

The main purpose of the method of correction factors is to clarify data from continuous mass observation through random checks. Typically, such checks are carried out by instructor-controllers based on the results of censuses.

6. Classification of selection methods

The methodology and results of calculating the main parameters of the sample directly depend on the method of selecting units from the general population.

The selection method is a specific system for organizing a sample study. The use of one method or another depends on the purpose of the study, sampling conditions, the specifics of the research object, the required accuracy and efficiency of the results, and the funds allocated for research.

All selection methods are divided into 3 types:

Individual;

Group;

Combined.

In the individual form, individual units of the population are selected.

In the group view, groups and series of units of the totality are selected (for example: several boxes were selected from a container and all of them were checked).

The combined method combines individual and group.

If the sample population is obtained immediately, the selection is called single-stage.

If there are several successive stages of selection, the sample is considered multi-stage.

The selection unit changes at each stage. Unlike multi-stage sampling, multi-phase sampling retains the same unit at all stages of selection. However, the surveillance program is gradually expanding.

Depending on the selection scheme used, there are:

Repeated;

Repeatless.

Each type of selection can be carried out in the following ways:

1 Actually random;

2 Mechanical;

3 Typical (stratified);

4 Serial (nested);

5 Combined.

7. Organization of selection in various ways and assessment of the reliability of the results obtained

Different selection methods are distinguished by different sampling techniques and different algorithms for calculating representativeness errors.

Actually random selection organized in such a way that all units in the population have an equal opportunity to be included in the sample. This is ensured by selection by lot, according to tables random numbers or using random number generators. Regardless of how the units are selected, they must be numbered. When selecting by lot, these numbers are written on cards, balls, etc., which are then thoroughly mixed and a number of cards equal to the number of selections are selected at random.

A random number table is a matrix of 4 or 5 numbers, each digit of which is independent of the other digits of the given number and other numbers. Depending on the size of the sample, one, two, three or four-digit numbers are selected from the table. Numbers can be selected by columns or rows of the table (starting from any row or column) using a predefined selection algorithm.

Computers and some calculators have a random number generator that displays random numbers on the screen.

The average error of a purely random repeated or non-repetitive selection is determined by the formula: see point (2).

Mechanical selection This is a directed sample from a population previously ordered by an existing or non-existent characteristic.

At the first stage, the general population is ordered according to some characteristic. Regardless of the trait, during mechanical selection the proportion of selection is established according to the formula: N/n.

If the population is grouped according to an unimportant characteristic, then it does not matter from which unit the selection begins.

If the population is grouped or ordered according to an essential characteristic, then the selection should begin from the middle of the first group.

The average error of mechanical selection is calculated using formulas for random selection. This is true when the selection was made from a population ordered by an unimportant characteristic.

If the population was ordered according to an essential characteristic, then this method of calculation slightly overestimates the average sampling error.

In this case, the average of the within-group variances could have been used rather than the total variance.

Typical sample(stratified). With this sampling, the population is first divided into typical groups (strata), from which units are randomly selected. This type of sampling ensures that all typical groups in the sample population are represented, thereby reducing sampling error. There are proportional and disproportionate methods of typical selection.

With the proportional method, a number of units is selected from each group that is proportional to either the size of the group or the intragroup variation of the trait being studied.

With typical resampling proportional to size, the group average sampling error is determined by the formula:

Average sampling error for resampling;

average sampling error for non-repetitive sampling;

Average of within-group variances;

Within-group variance;

n j is the number of corresponding typical groups.

If the proportion of population units that have the characteristic being studied is studied, then the average errors and variance

For re-selection;

For non-repetitive selection.

The optimal size of a typical sample is proportional to the size of the groups, determined by the formulas:

For re-selection;

For non-repetitive selection.

The most accurate proportional methods of typical selection is selection of the proportional variation of trait values ​​in groups. This selection is appropriate in the presence of general within-group variances. This is possible when sampling is carried out to control data from a continuous observation or when data from a previous continuous observation are available.

The number of sample groups is determined by the formula:

Sample size from j-th typical groups;

General within-group variance;

The number of constituent typical groups in the general population.

The average sampling error of repetition-free typical selection is proportional to the variation of the trait in groups. Determined by the formula:

This selection method produces an error smaller than selection proportional to the size of the groups.

Most general case is disproportionate type selection. With arbitrary proportions of the formation of typical sample groups, the average sampling error is calculated using the formula:

Mean sampling errors in each typical group;

The number of corresponding typical groups.

In this case, the errors of the average sample for groups are determined by the formulas:

Within-group variance.

For re-selection;

For non-repetitive selection.

Serial or nest selection is a random selection of groups of units followed by continuous observation within the selected series. This sampling is used primarily for quality control of goods, when it is advisable to open and examine individual packages. This is a type of directional selection that helps reduce sampling error. Thanks to the continuous study of nests, partial variances do not affect the representativeness error, which depends only on the variation of serial means, that is, on intergroup variance, determined by the formula:

Partial sampling variance;

Overall average of the serial sample;

Number of selected episodes.

The average serial sampling error is determined by the formulas:

- for re-selection;

- for non-repetitive selection.

Combined sample is a combination of group and individual selection of observation units. Most often, serial and actual random selection are combined.

The sampling error of a combined selection is the sum of the sampling errors expected for each selection method included in the combination. Typically, non-repetitive combined sampling is used, although repeated combined sampling is theoretically possible. Composite sampling is multistage in nature. Despite the simplicity of the multi-stage selection methodology, the calculation of its error is quite complex and is determined by the formula:

for equal selection at each stage.

- average sampling errors at each selection stage;

- number of selection stages.

8. Momentary sampling observation

The method of momentary (instantaneous) observations was developed in 1938 by the English statistician Tiplett for selective study production process. The method is used for group photographs of working time costs and equipment operating time, when an observer periodically bypassing workplaces along a predetermined route records on a special form what the worker is doing at a particular moment in time, whether he is currently working or resting.

The method of momentary observations is a sample over time, where the general population is the working time fund of the object of observation, that is, a group of workers or a group of pieces of equipment. The sample population consists of time periods for recording the state of the research object.

Group photographs provide a significant reduction in costs compared to individual photographs, since they do not require the constant presence of an observer at each workplace throughout the entire working day. The method is effective for assessing the work of a group of workers performing similar operations.

The first stage of organizing instant observations is determining the sample size, that is, the required number of registration moments.

Confidence factor;

Selective proportion of units possessing the studied trait;

The maximum sampling error expressed as a percentage.

II. Practical part

1. Problem

A 20% random non-repetitive sample was taken from the entire staff of kindergarten No. 17 “Forest Fairy Tale” to determine the average age of people working in this institution.

The sample results were as follows:

My task is to determine, with a probability of 0.987, the confidence intervals in which the average age of people lies for the entire kindergarten staff.

Solution

The average age of workers (denoted by a letter) lies in a certain interval (-; +), where is the average age in the sample population and is the sampling error. Let's represent this as a formula

- ? ? +

To calculate the sample variance of a characteristic in a sample, we group the data in the form of an interval distribution series.

Using the presented data, we calculate the average age in the sample using the formula

To calculate the maximum error, I proceed from the following considerations

Р(| - | ?) = 2Ф(/) = ,

The standard deviation of a characteristic in the population. Since = t *

Р(| - | ?) = 2Ф((t *)/) = 2Ф(t) =

But since we do not know, we can find the maximum error using the average sampling error per 1 unit of this sample -

Since in our case the sample is non-repetitive, the average error is calculated in the following way, where

sample variance of a characteristic, n is the size of a given sample, and N is the size of the general population.

The t coefficient is determined based on the fact that the distribution random variable is considered normal, and that the probability of fulfilling the inequality for should be equal to = 0.987.

According to the table of values ​​of Laplace functions Ф(t) (see Appendix), the most approximate value is 0.9869. Select it:

t = 2.48, then it turns out that

2,48 * 1,312 = 3,25

Thus we find the confidence intervals

37,38 - 3,25 ? ? 37,38 + 3,25

3. Conclusion

Having examined the data presented to me by kindergarten No. 17 “Forest Fairy Tale” using the sampling method, I can conclude that with a probability of 0.987 (that is, 98.7%), the average age of workers in this institution will approximately lie in the range from 34 to 41 years .

Conclusion

The transition to a market economy fills the work of businessmen, economists and managers with new content. This places increased demands on the level of their statistical training. Mastery of statistical methodology is one of the indispensable conditions for understanding market conditions, studying trends and forecasting supply and demand, making optimal decisions at all levels of management, commercial activities in the market of goods and services.

Sample observation is one of the most modern species statistical observation. This is an observation in which a portion of the units of the population being studied are examined, selected on the basis of scientifically developed principles that provide sufficient reliable data to characterize the entire population as a whole.

Having studied this method and applied the knowledge gained to the study of the composition of personnel in the Lesnaya Skazka children's institution, we can conclude: the age of the majority of workers in the kindergarten is from 34 to 41 years.

Bibliography

With statistics sample error selection

1. Eleseeva M.A.<<General theory statistics >> M:<<Статистика>> 1988

2. Kharchenko L.P.<<Статистика>> M: INFRA - M 1997

3. Boyarsky A.Ya., Gromyko G.L. General theory of statistics, M.: "Moscow Universities", 1985.

4. Theory of Statistics: Textbook/Ed. prof. G.L. Gromyko. - M.: INFRA-M, 2002. - 414 p. - (Series “Higher Education”).

5. Workshop on the theory of statistics: textbook. allowance/Ed. R.A. Shmoilova. - M.: Finance and Statistics, 2003. - 416.: ill.

6. Personal details of employees of kindergarten No. 17 “Forest Fairy Tale”

7. http://www.referatw.ru.

8. http://www.referatus.ru.

9. http://www.bankreferatov.ru

Application

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The selective method of collecting information is a method in which a part of the whole is selected, and the characteristics obtained regarding this part are applied to the entire population.

The unit of observation is a direct, primary source of information, which can be an individual buyer, family, enterprise, social groups, etc. The unit of observation is determined depending on the goals and objectives of the study.

The entire set of observation units that has the properties of interest to the researcher is called the general population.

A sample population, or sample, is a portion of the population that is selected for research and analysis.

The main goal of any sampling study is to obtain, as a result of studying the sample population, statistical characteristics that fairly well reflect the properties of the general population. If a sample reflects the properties of the population quite well, it is called representative.

During selective observation, data recording errors may occur. These errors are not unique to the sampling method. They also arise during continuous accounting. However, during a sample study, errors arise that are not inherent in continuous observation - errors of representativeness.

Errors of representativeness are the discrepancies between the general indicators of the sample and the general population in the conditions of correctly conducted primary data registration. Representativeness errors can be systematic or random.

Systematic errors of representativeness arise due to violation of the requirements of sampling theory. In particular, such errors arise due to a violation of the sample structure, when the sample is formed from observation units with some values ​​of the characteristics being studied to the detriment of observation units with other values ​​of the characteristics. Sampling error is also called sampling bias. For example, if only large stores are selected from the entire population of trading enterprises to study the structure of sales of goods, then such a sample will not reflect the complete sales structure characteristic of the entire retail network.

In research practice, in order to eliminate sample bias, it is formed in two ways.

The first way is to build a miniature model of the general population through conscious selection. For example, if a sample is formed from residents of a certain settlement(district), then a part is taken that has a structure identical to the structure of the entire population (based on the main characteristics - gender, age, occupation, etc.). This type of sampling is called quota sampling.

The second method is to form a random sample. Random selection is not a random selection, but a specifically organized selection, in which each unit has equal chance get into the sample.

Both of these methods are most often used not independently, but in combination with each other. The design and specific methods of selection are determined by the characteristics of the observation units and the objectives of the study.

In theory, random selection has significant advantages. However, it is not always possible to practically apply it for marketing research. For random selection, you need to have a sampling frame, i.e. full list units of observation. Obtaining such lists in some cases is difficult or even impossible. For example, if it is necessary to identify the degree to which families are provided with technically complex goods, there must be a list of all families in the area under study (city, region, etc.). Compiling such lists is a difficult task. Therefore, the sampling is carried out through multi-stage selection. Sampling methods will be discussed in more detail below.

At correct formation There will be no sampling bias for representativeness. However, in this case, the characteristics of the sample and the general population will not necessarily coincide.

The discrepancy between the indicators of the sample and general populations in the conditions correct implementation selection and accurate recording are called random errors of representativeness or sampling errors. Random errors are due to the nature of the sampling method, i.e. they are a consequence of the sample size being smaller than the population size.

When conducting marketing research, there is a need to obtain information about both qualitative and quantitative characteristics. If qualitative characteristics are studied, their shares are calculated, and when quantitative characteristics are studied, the average values ​​are determined.

Sample surveys allow solving various problems: studying the structure of realized demand, the structure inventory, characteristics and extent of unmet demand, socio-economic composition of buyers, purchasing intentions, etc.

Questionnaire forms:

• - full-time;
• - correspondence.

Requirements for drawing up the questionnaire:

• Questions should be simple and understandable
• Questions must be clear
• Questions must be neutral
• * questions should go from simple to complex
• * questions should go from general to specific
• * questions must inspire confidence among respondents
• o issues that establish trust come first
• o in second place is the block of basic questions
• o in third place are control questions
• o at the end there are passport questions (about the individual) or company

The questionnaire is based on statistical methods of sampling observation. A necessary condition survey organizations are:

• · preliminary study of the general population;
• · assessment of its homogeneity (homogeneity)
• · sorting by main characteristics;
• · determination of the required number of respondents (sample)

A mechanical selection method in which the sample size is determined by the formula:

where n is the sample, t is the confidence coefficient, depending on the probability with which it can be guaranteed that the marginal error does not exceed the average error (with a probability of 0.99 it is equal to 3, more often e = 2), - the variance of the characteristic being studied, usually determined on the basis of experiment or by analogy, - the maximum (ordinary) sampling error, N - the number of units of the population being studied.

Processing the results. When processing the results, various mathematical methods are used. The results are presented in the form of tables and graphs. During the analysis of the results, the probability of error and the corresponding confidence interval are determined. Finally, a report is written that sets out the facts with scrupulous accuracy and minimal influence from the analyst's own beliefs.

Analysis of results. Each answer is carefully analyzed. If the answer is obviously incorrect, it is impossible to understand anything from it, or the answer is definable, or the respondent answered for show or without knowing the subject, his answer is excluded.

Marketing research is a very expensive undertaking and is not always within the means of enterprises. In this case, they turn to specialized organizations engaged in performing this type of work. Large companies often collect information themselves and employ special staff.

Depending on the nature of the use of information, methods of obtaining it, research techniques and its final results, different kinds and methods of conducting marketing research. The choice of a particular method should be determined, on the one hand, by the required accuracy and reliability of the results, and on the other hand, by the costs of its implementation.

Desk research are carried out on the basis of official printed sources of information and provide a general idea of ​​the state of general economic conditions and development trends of individual markets. In this case, methods are used economic analysis combined with elements of econometrics and mathematical statistics.

Observation Typically used in search engine marketing research. It allows you to maintain stable observation conditions and use technical means. Observation can be hidden (using television cameras, for example) and open (with the direct participation of the researcher). Depending on the goals pursued, observation can be free and standardized (certain criteria for the study are set).

Experiment As a method of marketing research, it is assumed that the analysis should exclude the influence of all factors except the one being studied. Therefore, the experiment assumes the presence of at least two comparable study groups, one of which is experimental and the other control. For example, this could be two products or two consumer groups.

Experiments taking place in an artificial setting (for example, tests of products, prices, advertising) are called laboratory, and those carried out in real conditions - in the field. The first ones allow you to control extraneous factors, the second ones do not exclude the influence of extraneous factors.

Field research, although the most complex and expensive, is also the most effective method market research. It is used only by large companies. It allows you to quickly and comprehensively become familiar with market requirements, trade practices, sales methods, prices and many other conditions. Quite a lot important also has the opportunity to establish personal contacts with potential buyers, purchase samples of goods that are in greatest demand in a given market, etc.

This method allows you to obtain and process primary information, which, although more expensive, does not provide a real picture of market demand and customer requirements for the company's products and take these results into account when developing market tactics, including pricing policy and sales organization issues.

Test sales method is used in the absence of the necessary information about the market and time for its comprehensive study, as well as when introducing new and rare goods for the market being studied. Despite a certain risk of incurring losses, it provides an opportunity to establish direct business relationships with possible buyers.

The market in which the test takes place must be representative of the target market in terms of: population structure and its needs, characteristics of trading enterprises, state of competition, influence of means mass media. It should be long enough to take into account repeat purchases, and optimally until they stabilize, which will allow predicting market share.

However, the trial sales method is associated with high costs, difficulties in selecting suitable markets, determining the duration of the study, reducing the effect of surprise for competitors, and additional workload for sales staff.

Personal business contacts with representatives of other firms is important for studying markets. These contacts are established and maintained through mutual visits to companies, during meetings business people at fairs, exhibitions, auctions, presentations, commodity exchanges, etc.

Personal contacts between company representatives and the buyer have great importance when studying the market for technically complex products, for example, machinery and equipment. In this case, the seller’s representative simultaneously acts as a technical consultant to the buyer. Such contacts can become a source of proposals for improving products and increasing their competitiveness.

Simulation modeling represents a mathematical, graphical or other model of controlled and uncontrollable factors that determine the strategy and tactics of the company and in subsequent experiments on the model in order to study the impact of changes in these factors on the object of study. Simulation modeling makes it possible to comprehensively study the many factors that determine marketing strategy.

Modeling is most widely used to study consumer behavior. The most well-known models of consumer behavior are probabilistic (stochastic), linear-experimental, and information processing models.

Probabilistic models are based on the assumption that previous, and especially recent, purchases determine future consumer behavior in the market. These models are used to predict demand for new products, to determine loyalty to product brands;

Linear experimental models are usually descriptive in nature and are used to model potential demand for goods, identify trends in consumer behavior in relation to specific goods, etc., such as the share of a particular brand in the total volume of consumer demand.

Models of information processing are based on the premise of multiple sources of information for the consumer to make a decision on the choice and purchase of a particular product.

Survey represents an oral or written appeal to certain respondents with questions containing the research problem.

This is the most common data collection method in marketing. It is used in about 90% of studies. The classification of surveys is shown in Fig. 1.

Rice. 1. Classification of surveys

The source of information when conducting mass surveys is the population that is not related by the nature of its activity to the subject of analysis. In specialized surveys, it is specialists (experts) - persons whose professional activities are closely related to the subject of research - who act as the main sources of information. Therefore, specialized surveys are often called expert surveys. They are used either at the beginning of market research to identify a problem, or at the final stage when a decision needs to be made.

One-time surveys show only the current reaction of market participants to the activities of the enterprise and its products, while repeated surveys reveal the life cycle of a product, consumer demands and purchasing preferences.

Complete surveys are usually used when studying the opinions of users of industrial goods, since their circle is relatively limited. In the consumer market, the number of potential buyers is so large that it makes it virtually impossible to use this method. In such cases, sample surveys are conducted on a sample of the population, which fairly fully reflects the properties of the general population. Such a sample is called representative.

The main survey forms are questionnaires and interviews. In the first case, the interviewee himself answers the questions in writing; in the second, during personal communication with the interviewee, the interviewer asks questions and records the answers.

Personal interview- a universal method of conducting a survey. The interviewer can not only ask more questions than provided by the questionnaire, but also supplement the interviewee’s answers with his own personal observations. This is the most expensive way to obtain information, both in terms of money and time spent. It requires the training of a qualified staff of interviewers.

It is somewhat cheaper and faster to collect information during a telephone interview. And in this case, the interviewer can clarify questions that are not entirely clear to the interviewee. However, the potential circle of respondents is limited to phone owners, firstly; the issues being addressed cannot be too personal; third, the interview should be relatively short.

Personal interviews can be individual or group (for example, conducted simultaneously with members of the same family, neighbors, team members, etc.).

In the practice of conducting marketing research, postal surveys, especially panel surveys, have become widespread. They provide information on a wide range of issues from large groups of consumers by repeatedly surveying them at regular intervals. Panel surveys make it possible to keep a constant record of ongoing changes in external environment, receiving information about the quantity of goods purchased by the family; financial expenses; preferred prices, types of packaging; differences in the behavior of consumers of different social groups and regions; brand loyalty, etc.

A consumer panel, as a research method, along with significant costs, is also associated with the problem of ensuring representativeness. The problem is not only in choosing objects and obtaining consent to cooperate, but also lies in the possible refusal of participants to cooperate, in their changing their place of residence, in moving to another consumer category, in a conscious or unconscious change in behavior (consumers begin to “prepare” for purchases, the share of spontaneous purchases decreases), in negligence in responses during long-term cooperation, in physical death, finally.

The accuracy of the results of a survey conducted in any form largely depends on the instrument used - a questionnaire or an interview form.

Questionnaire (questionnaire) is a system of questions aimed at identifying the characteristics of an object or subject of research.

It can be divided into four parts:

• introductory, where a respectful attitude towards the respondents is expressed and it is indicated who is conducting the survey; for what purpose; instructions for filling out the questionnaire.
• contact, where the questions are located that aim to interest the respondent and introduce them to the range of problems being studied;
• control- with questions to ensure the reliability of the data (for example, if in the contact part the main question was: “Are you familiar with the basic methods of caring for the skin of the eyelids?”), then the control part could be of the following type: “What are the methods of caring for the skin of the eyelids?” Do you think the most important?").
• final- with questions that relieve respondents’ psychological stress, allowing them to identify their socio-demographic characteristics (gender, age, location, social status, education, income level, etc.), and end with words of gratitude to the respondent for participating in the survey.

Particular attention should be paid to ensuring that the main and control questions do not follow each other, since most people answer the next question, being impressed by the content and answer to the previous one. The most difficult questions questions requiring reflection should be located in the middle of the questionnaire.

The questions themselves should be simple, understandable, unambiguous and neutral, and they should move from simple to complex, from general to special, from neutral to subtle (delicate).

The time required to fill out the questionnaire during a postal survey should not exceed 20 - 30 minutes.

The questions included in the questionnaires are open and closed. Open questions provide the right to formulate answers independently table. 3.3. This circumstance, although it makes processing the survey results more difficult, in some cases can offer an unexpected solution to the problem being studied and thus compensate for the costs.

Table 1

Types of open questions

Closed questions offer the respondent a set of possible answers to the question. The classification of types and examples of asking closed questions are given in Table. 2

Sampling method - statistical research method general properties a collection of any objects based on the study of the properties of only a part of these objects taken as a sample.

A well-studied example of the use of dependent observations is the estimation of an empirical distribution or its parameters in "general population" from N objects according to the derivative from it "sample", containing n< N объектов.

An example of the application of the sampling method is the following. Let a batch of N products have L defective ones. n are selected randomly from the batch< N изделий. Вероятность того, что число l дефектных изделий в выборке будет равно m, равна
.

Sampling method(method of sampling) - a statistical method for studying the general properties of a set of objects based on studying the properties of only a part of these objects. The set of studied objects of interest to the researcher is called the general population. And part of the objects to be studied is called a sample population or sample.

The need for a sampling method may be caused by objective reasons:

The object of research is very extensive, for example, research into consumer preferences in the product market, forecasting election results, etc.

Need to collect primary information in pilot studies.

Key sample survey questions:

Quantitative characteristics of the sample or determination of the minimum number of observations (sample size) to conduct the study;

Qualitative characteristics of the sample or ways and methods of forming a sample population.

The main task of a sample survey is to obtain as much as possible with a minimum sample size. exact description population of interest based on sample data. This can only be achieved on the basis of a representative sample, i.e. a sample that objectively reflects the properties of the general population.

The accuracy of the results of sample surveys is achieved through the use of complex sampling methods (cluster selection, assignment of stratification, use of probabilistic proportional sampling, simple random or random sampling, repeated or non-repetitive sampling).

The minimum sample size depends on many research parameters (the assessed indicator or system of indicators, the method and methods of sampling, the variation of the data being studied, the specified reliability of the results obtained, the maximum permissible error in the assessment of indicators) and is determined on the basis of mathematical statistics formulas or by expert opinion.

The sampling method is used primarily in sociology, marketing, and clinical research. But in fact, when statistically analyzing data in any field, the researcher usually works not with the general population, but with a sample. The mistake of many researchers is that they do not attach importance to this, they do not think about what methods were used to obtain the analyzed information and how well the sampling survey methodology was followed. Because of this, the results obtained do not correspond to really objectively existing patterns, because a non-representative sample is analyzed.

In the theory of the sampling method, various selection methods and types of sampling have been developed to ensure representativeness. Under selection method understand the procedure for selecting units from the population. There are two selection methods: repeated and non-repetitive. At repeated selection each selected in random order The unit, after being surveyed, is returned to the population and may be included in the sample again during subsequent selection.

This selection method is based on the “returned ball” scheme: the probability of being included in the sample for each unit of the population does not change regardless of the number of units selected. At repeatable In sampling, each unit selected at random is not returned to the general population after its examination. This selection method is based on the “non-returned ball” scheme: the probability of being included in the sample for each unit of the general population increases as selection proceeds.

Selective observation applies when the use of continuous surveillance physically impossible due to a large amount of data or not economically feasible. Physical impossibility occurs, for example, when studying passenger flows, market prices, and family budgets. Economic inexpediency occurs when assessing the quality of goods associated with their destruction, for example, tasting, testing bricks for strength, etc.

The statistical units selected for observation constitute the sampling frame or sample, and their entire array constitutes the general population (GS). In this case, the number of units in the sample is denoted by n, and in the entire HS - N. Attitude n/N called the relative size or proportion of the sample.

The quality of sample observation results depends on sample representativeness, that is, on how representative it is in the GS. To ensure representativeness of the sample, it is necessary to comply principle of random selection of units, which assumes that the inclusion of a HS unit in the sample cannot be influenced by any factor other than chance.

There are 4 ways to randomly select a sample:

1. Actually random selection or the “lotto method”, when statistical quantities are assigned serial numbers, recorded on certain objects (for example, barrels), which are then mixed in some container (for example, in a bag) and selected at random. In practice, this method is carried out using a random number generator or mathematical tables of random numbers.

2. Mechanical selection according to which each ( N/n)-th value of the general population. For example, if it contains 100,000 values, and you need to select 1,000, then every 100,000 / 1000 = 100th value will be included in the sample. Moreover, if they are not ranked, then the first one is selected at random from the first hundred, and the numbers of the others will be one hundred higher. For example, if the first unit was No. 19, then the next should be No. 119, then No. 219, then No. 319, etc. If the population units are ranked, then No. 50 is selected first, then No. 150, then No. 250, and so on.

3. The selection of quantities from a heterogeneous data array is carried out stratified(stratified) method, when the population is first divided into homogeneous groups to which random or mechanical selection is applied.

4. A special method of sampling is serial selection, in which they randomly or mechanically select not individual values, but their series (sequences from some number to some number in a row), within which continuous observation is carried out.

The quality of sample observations also depends on sample type: repeated or unrepeatable.

At re-selection Statistical values ​​or their series included in the sample are returned to the general population after use, having a chance to be included in a new sample. Moreover, all values ​​in the population have the same probability of inclusion in the sample.

Non-repetitive selection means that the statistical values ​​or their series included in the sample do not return to the general population after use, and therefore for the remaining values ​​of the latter the probability of being included in the next sample increases.

Non-repetitive sampling gives more accurate results, so it is used more often. But there are situations when it cannot be applied (studying passenger flows, consumer demand, etc.) and then a repeated selection is carried out.

Index methods in statistical research

Index- this is a generalizing relative indicator that characterizes the change in the level of a social phenomenon over time, in comparison with the development program, plan, forecast, or its relationship in space.

The most common comparative characteristic is over time. In this case, the indices act as relative values ​​of dynamics.

Index method is also the most important analytical tool for identifying connections between phenomena. In this case, it is no longer individual indexes that are used, but their systems.

In statistical practice, indices are used to analyze the development of all sectors of the economy, at all stages economic work. In a market economy, the role of price indices, household incomes, the stock market and territorial indices has especially increased.

Statistics classifies indices according to the following criteria:

1. Depending on the object of study:

Indices of volumetric (quantitative) indicators (indices of physical volume: turnover, products, consumption)

Indices of quality indicators (price indices, costs, wages)

Indices of volume indicators include indices of physical volume: trade turnover, products, consumption material goods and services; as well as other indicators of a quantitative nature: the number of employees, acreage, etc. Indices of quality indicators include indices: prices, production costs, wages, labor productivity, productivity, etc.;

2. According to the degree of coverage of the elements of the population:

Individual indices (give a comparative description of individual elements of the phenomenon)

General indices (characterize changes in a set of elements or the entire phenomenon as a whole)

3. Depending on the calculation methodology, general indices are divided into:

Aggregate (aggregate indices are the main form of indices and are constructed as aggregates by weighing the indexed indicator using a constant value of another indicator interrelated with it).

Average (derived from aggregate)

4. Depending on the basis of comparison, there are:

Basic (if, when calculating indices for several periods of time, the comparison base remains constant)

Chain (if the comparison base is constantly changing)