The concept of sampling. Sample types
Parameter name | Meaning |
Article subject: | Sample |
Rubric (thematic category) | Connection |
inferential analysis
It includes:
1. Estimation of the parameters of the general population
2. Hypothesis testing
Statistical observations or the collection of statistical data on a continuous or non-continuous basis is the first stage of statistical research.
Continuous surveys of all respondents, that is, a survey of 100%, can be carried out only in cases where the number of respondents does not exceed 300-500 people. Only the state can poll a larger number (population census).
If the survey population is more than 500 people, then it is enough to interview only the sample and distribute the result of the survey of the sample population to the general population. But this is possible only if the sample is representative, that is, reliable and reflects the structure of the general population.
It is customary to call a selective observation such a non-continuous observation, in which signs are recorded in individual units of the studied statistical population, selected using special methods, and the results obtained during the study are distributed with a certain level of probability to the entire initial (general) population.
To ensure representativeness, 2 methods are used:
- The collection (selection) in the sample is carried out by the method of random numbers (random sampling). Allocate:
a) random sampling
b) randomly-unrepeated
c) mechanical step-by-step sampling
In a random re-sampling, the unit that is in the sample is subjected to examination, the values of its characteristics are recorded, and then it is returned back to the general population and, along with others, can again be included in the sample and be examined.
In case of non-repetitive selection, the unit that is included in the sample is subjected to examination, but no longer participates in the further selection procedure.
If the selection is non-repetitive, then the sample size is determined by the formula:
where N is the number of units in the studied general population
t is a confidence factor that depends on the probability with which it can be guaranteed that the marginal sampling error will not exceed t times the average error.
For example, with a probability of 0.990 t = 3
Most often, in marketing research, they rely on a probability of 0.954, at which t = 2.
The mathematician Lyapunov derived a formula for calculating t, on the basis of which the following table is formed:
The problem is that the measures of variance and error are calculated from the results of the survey, and it is extremely important to calculate the sample size before conducting the survey. For this reason, the value of the dispersion σ 2 and Δ is determined on the basis of the pilot survey experiment or from the results of similar studies that were carried out earlier.
σ is usually taken equal to 50%, therefore the dispersion σ 2 will be equal to 0.25
Δ - the limiting specified sampling error is taken equal to 0.05, therefore its square will be equal to 0.0025.
To transfer the results of a sample study to the general population, the sampling error is calculated using the following formula:
where n is the sample size
N - the size of the general population
σ 2 - dispersion
Let P be the general share, w be the sample share, - general average, - sample average, then the result will be written as follows:
for the general share:
for the general average:
These two types of samples are used when it is extremely important to evaluate a material object (packaging, etc.). But in social research they are not used, since it is difficult to ensure randomness. For this reason, in social research, the element of randomness must be provided by mechanical sampling.
Mechanical sampling consists in the selection of units from the general population at regular intervals from a certain location in the general population (alphabetically, geographically, in time).
There are 2 tasks here:
1. definition of the reference step - the distance between units
2. select the unit to start counting from
1) The reference step is determined by dividing the size of the general population by the size of the sample population. This method is used when N is small.
In marketing research, non-random types of samples are most often used, that is, elements of non-randomness are introduced. First, the characteristics of the general population are known, and then, based on these parameters, samples are built. Samples are spontaneous (arbitrary), quota (typical), concentrated, serial (formed by the method of flower beds).
Spontaneous (random) sampling– sampling elements are selected without a plan. This sample has the lowest representativeness.
Quota sampling- a sample in which the structure of the general population is preserved according to a small number of features. This sample is also called zoned.
Example: it is extremely important to interview 10 thousand students, the sample is 100 people. Of these, in the Oktyabrsky district - 20%, in the Industrial - 10%, Pervomaisky - 10%, Ustinovsky - 10%, Leninsky - 20%. Including in the Oktyabrsky district of gymnasiums 10%, lyceums 20%, secondary schools - 70%. Therefore, it is necessary to interview 2 people from the gymnasiums of the Oktyabrsky district, 4 people from the lyceums of the Oktyabrsky district, 14 people from the general education schools of the Oktyabrsky district, and so on.
serial sampling- is used in cases where the units of the population under study are combined into small groups or series (families, classes, groups, etc.) The series are selected using mechanical or random sampling, and within the selected series they can be studied as everything without exception units, and selectively. This sampling is also called the flower bed sampling.
Concentrated sampling- is formed in the event that the important, most significant properties of the general population are investigated, and the non-essential properties are discarded. For example, when it is extremely important to study the balance of personnel in enterprises, only large enterprises are taken, and small ones are discarded.
Samples are formed multistage and multiphase ways.
Multistage the method involves extracting from the general population first enlarged groups of units, then groups smaller in volume, and so on until those groups or units that will be subjected to observation are selected. That is, the sample is taken several times. Moreover, it should be so that the sample unit of the previous stage will be the general population for the subsequent sample. For example, people around the world are selected: first a country is selected, then a city, then an enterprise, and finally a group of people or a specific person who will be subjected to research.
Multivariate sampling- ϶ᴛᴏ such a sample, when sample populations are processed in such a way that some information is collected for all sampling units, and others (deeper) only for some units. For example, a consumer survey to identify the image of an ideal car: first, the question is asked whether the respondent has a car, then only those who have are selected from all, and they are interviewed according to a more in-depth program.
Selective observation with strict observance of the conditions of randomness and a reliably large number of selected units is representative. Based on the results of studying a certain part of the units, with a degree of accuracy sufficient for practice, one can judge the entire population.
Primary information can also be obtained as a result of a survey of experts. Often, expert assessments do not have sufficient stability, that is, an expert can evaluate the same events differently during several repeated examinations. The more stable the expert's assessments, the more trustworthy he is.
Repeated examinations are, as a rule, very expensive, therefore, the reliability of estimates can be improved as follows: it is extremely important to analyze the data on the discrepancy between expert estimates and their actual values found in the process of implementing events, and make appropriate reassessments of the experts' competence. For this, apply:
The concordance coefficient lies in the interval (can take values) from -1 to +1
Sampling - concept and types. Classification and features of the category "Sampling" 2017, 2018.
Sample
Sample or sampling frame- a set of cases (subjects, objects, events, samples), using a certain procedure, selected from the general population for participation in the study.
Sample characteristics:
- Qualitative characteristics of the sample - who exactly we choose and what methods of sample construction we use for this.
- The quantitative characteristic of the sample is how many cases we select, in other words, the sample size.
Need for sampling
- The object of study is very broad. For example, consumers of the products of a global company are a huge number of geographically dispersed markets.
- There is a need to collect primary information.
Sample size
Sample size- the number of cases included in the sample. For statistical reasons, it is recommended that the number of cases be at least 30-35.
Dependent and independent samples
When comparing two (or more) samples, their dependence is an important parameter. If it is possible to establish a homomorphic pair (that is, when one case from sample X corresponds to one and only one case from sample Y and vice versa) for each case in two samples (and this basis of relationship is important for the trait measured in the samples), such samples are called dependent. Examples of dependent selections:
- pair of twins
- two measurements of any feature before and after experimental exposure,
- husbands and wives
- etc.
If there is no such relationship between the samples, then these samples are considered independent, for example:
Accordingly, dependent samples always have the same size, while the size of independent samples may differ.
Samples are compared using various statistical criteria:
- and etc.
Representativeness
The sample may be considered representative or non-representative.
An example of a non-representative sample
- Study with experimental and control groups, which are placed in different conditions.
- Study with experimental and control groups using a paired selection strategy
- Study using only one group - experimental.
- A study using a mixed (factorial) plan - all groups are placed in different conditions.
Sample types
Samples are divided into two types:
- probabilistic
- improbability
Probability samples
- Simple probability sampling:
- Simple resampling. The use of such a sample is based on the assumption that each respondent is equally likely to be included in the sample. Based on the list of the general population, cards with the numbers of respondents are compiled. They are placed in a deck, shuffled, and a card is taken out of them at random, a number is written down, then returned back. Further, the procedure is repeated as many times as the sample size we need. Minus: repetition of selection units.
The procedure for constructing a simple random sample includes the following steps:
1. you need to get a complete list of members of the general population and number this list. Such a list, recall, is called the sampling frame;
2. determine the expected sample size, that is, the expected number of respondents;
3. extract as many numbers from the table of random numbers as we need sample units. If the sample should include 100 people, 100 random numbers are taken from the table. These random numbers can be generated by a computer program.
4. select from the base list those observations whose numbers correspond to the written random numbers
- A simple random sample has obvious advantages. This method is extremely easy to understand. The results of the study can be extended to the study population. Most approaches to statistical inference involve collecting information using a simple random sample. However, the simple random sampling method has at least four significant limitations:
1. It is often difficult to create a sampling frame that would allow for a simple random sample.
2. A simple random sample can result in a large population, or a population distributed over a large geographic area, which significantly increases the time and cost of data collection.
3. The results of applying a simple random sample are often characterized by low accuracy and a larger standard error than the results of applying other probabilistic methods.
4. As a result of the application of the SRS, an unrepresentative sample may be formed. Although the samples obtained by simple random selection, on average, adequately represent the general population, some of them extremely incorrectly represent the population under study. The probability of this is especially high with a small sample size.
- Simple non-repetitive sampling. The procedure for constructing the sample is the same, only the cards with the numbers of the respondents are not returned back to the deck.
- Systematic probability sampling. It is a simplified version of a simple probability sample. Based on the list of the general population, respondents are selected at a certain interval (K). The value of K is determined randomly. The most reliable result is achieved with a homogeneous general population, otherwise the step size and some internal cyclic patterns of the sample may coincide (sample mixing). Cons: the same as in a simple probability sample.
- Serial (nested) sampling. The sampling units are statistical series (family, school, team, etc.). The selected elements are subjected to continuous examination. The selection of statistical units can be organized according to the type of random or systematic sampling. Cons: Possibility of greater homogeneity than in the general population.
- Zoned sample. In the case of a heterogeneous population, before using probability sampling with any selection technique, it is recommended to divide the population into homogeneous parts, such a sample is called a zoned sample. The zoning groups can be both natural formations (for example, city districts) and any feature underlying the study. The sign on the basis of which the division is carried out is called the sign of stratification and zoning.
- "Convenient" selection. The "convenience" sampling procedure consists in establishing contacts with "convenient" sampling units - with a group of students, a sports team, with friends and neighbors. If it is necessary to obtain information about people's reactions to a new concept, such a sample is quite reasonable. "Convenience" sampling is often used for preliminary testing of questionnaires.
Incredible Samples
The selection in such a sample is carried out not according to the principles of chance, but according to subjective criteria - accessibility, typicality, equal representation, etc.
- Quota sampling - the sampling is built as a model that reproduces the structure of the general population in the form of quotas (proportions) of the studied characteristics. The number of sample elements with a different combination of the characteristics under study is determined in such a way that it corresponds to their share (proportion) in the general population. So, for example, if we have a general population of 5,000 people, of which 2,000 women and 3,000 men, then in the quota sample we will have 20 women and 30 men, or 200 women and 300 men. Quota samples are most often based on demographic criteria: gender, age, region, income, education, and others. Cons: usually such samples are not representative, because it is impossible to take into account several social parameters at once. Pros: easily accessible material.
- Snowball method. The sample is constructed as follows. Each respondent, starting with the first, is asked to contact his friends, colleagues, acquaintances who would fit the selection conditions and could take part in the study. Thus, with the exception of the first step, the sample is formed with the participation of the objects of study themselves. The method is often used when it is necessary to find and interview hard-to-reach groups of respondents (for example, respondents with a high income, respondents belonging to the same professional group, respondents who have some similar hobbies / passions, etc.)
- Spontaneous sampling - sampling of the so-called "first comer". Often used in television and radio polls. The size and composition of spontaneous samples is not known in advance, and is determined by only one parameter - the activity of the respondents. Disadvantages: it is impossible to establish what kind of general population the respondents represent, and as a result, it is impossible to determine representativeness.
- Route survey - often used if the unit of study is the family. On the map of the settlement in which the survey will be carried out, all streets are numbered. Using a table (generator) of random numbers, large numbers are selected. Each large number is considered as consisting of 3 components: street number (2-3 first numbers), house number, apartment number. For example, the number 14832: 14 is the street number on the map, 8 is the house number, 32 is the apartment number.
- Zoned sampling with selection of typical objects. If, after zoning, a typical object is selected from each group, i.e. an object that approaches the average in terms of most of the characteristics studied in the study, such a sample is called zoned with the selection of typical objects.
6.Modal selection. 7. expert sample. 8. Heterogeneous sample.
Group Building Strategies
The selection of groups for their participation in a psychological experiment is carried out using various strategies, which are necessary in order to ensure the greatest possible compliance with internal and external validity.
Randomization
Randomization, or random selection, is used to create simple random samples. The use of such a sample is based on the assumption that each member of the population is equally likely to be included in the sample. For example, to make a random sample of 100 university students, you can put papers with the names of all university students in a hat, and then get 100 pieces of paper out of it - this will be random selection (Goodwin J., p. 147).
Pairwise selection
Pairwise selection- a strategy for constructing sample groups, in which groups of subjects are made up of subjects that are equivalent in terms of side parameters that are significant for the experiment. This strategy is effective for experiments using experimental and control groups with the best option - attracting twin pairs (mono- and dizygotic), as it allows you to create ...
Stratometric selection
Stratometric selection- randomization with the allocation of strata (or clusters). With this method of sampling, the general population is divided into groups (strata) with certain characteristics (gender, age, political preferences, education, income level, etc.), and subjects with the corresponding characteristics are selected.
Approximate modeling
Approximate modeling- drawing up limited samples and generalizing the conclusions about this sample to a wider population. For example, when participating in a study of students in the 2nd year of university, the data of this study are extended to "people aged 17 to 21 years." The admissibility of such generalizations is extremely limited.
Approximate modeling is the formation of a model that, for a clearly defined class of systems (processes), describes its behavior (or desired phenomena) with acceptable accuracy.
Notes
Literature
Nasledov A. D. Mathematical methods of psychological research. - St. Petersburg: Speech, 2004.
- Ilyasov F. N. Representativeness of survey results in marketing research. Sotsiologicheskie issledovaniya. 2011. No. 3. P. 112-116.
see also
- In some types of studies, the sample is divided into groups:
- experimental
- control
- Cohort
Links
- The concept of sampling. The main characteristics of the sample. Sample types
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Synonyms:- Schepkin, Mikhail Semyonovich
- Population
See what "Selection" is in other dictionaries:
sample- a group of subjects representing a certain population and selected for an experiment or study. The opposite concept is the totality of the general. The sample is part of the general population. Dictionary of practical psychologist. M .: AST, ... ... Great Psychological Encyclopedia
sample- sampling The part of the general population of elements that is covered by the observation (often called the sampling population, and the sample is the method of sampling observation itself). In mathematical statistics, it is accepted ... ... Technical Translator's Handbook
Sample- (sample) 1. A small quantity of a commodity selected to represent its entire quantity. See: sale by sample. 2. A small amount of product given to potential buyers to give them the opportunity to spend it ... ... Glossary of business terms
Sample- part of the general population of elements that is covered by the observation (it is often called the sampling population, and the sampling is the method of sampling observation itself). In mathematical statistics, the principle of random selection is adopted; this is… … Economic and Mathematical Dictionary
SAMPLE- (sample) Random selection of a subgroup of elements from the main population, the characteristics of which are used to evaluate the entire population as a whole. Sampling is used when it is too long or too expensive to survey the entire population... Economic dictionary
It often happens that it is necessary to analyze a particular social phenomenon and obtain information about it. Jobs like this often come up...
Sampling is ... Definition, types, methods and results of sampling
By Masterweb
09.04.2018 16:00It often happens that it is necessary to analyze a particular social phenomenon and obtain information about it. Such tasks often arise in statistics and in statistical research. Verification of a fully defined social phenomenon is often impossible. For example, how to find out the opinion of the population or all residents of a certain city on any issue? Asking absolutely everyone is almost impossible and very laborious. In such cases, we need a sample. This is exactly the concept on which almost all research and analysis is based.
What is a sample
When analyzing a particular social phenomenon, it is necessary to obtain information about it. If we take any study, we can see that not every unit of the totality of the object of study is subject to research and analysis. Only a certain part of this totality is taken into account. This process is sampling: when only certain units from the set are examined.
Of course, much depends on the type of sample. But there are also basic rules. The main one says that the selection from the population must be absolutely random. The population units to be used should not be selected due to any criterion. Roughly speaking, if it is necessary to collect a population from the population of a certain city and select only men, then there will be an error in the study, because the selection was not carried out randomly, but was selected according to gender. Almost all sampling methods are based on this rule.
Sampling rules
In order for the selected set to reflect the main qualities of the entire phenomenon, it must be built according to specific laws, where the main attention should be paid to the following categories:
- sample (sample population);
- general population;
- representativeness;
- representativeness error;
- population unit;
- sampling methods.
Features of selective observation and sampling are as follows:
- All the results obtained are based on mathematical laws and rules, that is, with the correct conduct of the study and with the correct calculations, the results will not be distorted on a subjective basis
- It makes it possible to get a result much faster and with less time and resources, studying not the entire array of events, but only a part of them.
- It can be used to study various objects: from specific issues, for example, the age, gender of the group of interest to us, to the study of public opinion or the level of material support of the population.
Selective observation
Selective - this is such a statistical observation in which not the entire population of the studied is subjected to research, but only some part of it, selected in a certain way, and the results of the study of this part apply to the entire population. This part is called the sampling frame. This is the only way to study a large array of the object of study.
But selective observation can be used only in cases where it is necessary to study only a small group of units. For example, when studying the ratio of men to women in the world, selective observation will be used. For obvious reasons, it is impossible to take into account every inhabitant of our planet.
But with the same study, but not of all the inhabitants of the earth, but of a certain 2 "A" class in a particular school, a particular city, a particular country, selective observation can be dispensed with. After all, it is quite possible to analyze the entire array of the object of study. It is necessary to count the boys and girls of this class - that will be the ratio.
Sample and population
It's actually not as difficult as it sounds. In any object of study there are two systems: general and sample population. What is it? All units belong to the general. And to the sample - those units of the total population that were taken for the sample. If everything is done correctly, then the selected part will be a reduced layout of the entire (general) population.
If we talk about the general population, then we can distinguish only two of its varieties: definite and indefinite general population. Depends on whether the total number of units of a given system is known or not. If it is a certain population, then sampling will be easier due to the fact that it is known what percentage of the total number of units will be sampled.
This moment is very necessary in research. For example, if it is necessary to investigate the percentage of low-quality confectionery products at a particular plant. Assume that the population has already been defined. It is known for sure that this enterprise produces 1000 confectionery products per year. If we make a sample of 100 random confectionery products from this thousand and send them for examination, then the error will be minimal. Roughly speaking, 10% of all products were subject to research, and based on the results, taking into account the representativeness error, we can talk about poor quality of all products.
And if you take a sample of 100 confectionery products from an indefinite general population, where there were actually, say, 1 million units, then the result of the sample and the study itself will be critically implausible and inaccurate. Feel the difference? Therefore, the certainty of the general population in most cases is extremely important and greatly affects the result of the study.
Population representativeness
So, now one of the most important questions - what should be the sample? This is the most important point of the study. At this stage, it is necessary to calculate the sample and select units from the total number into it. The population was selected correctly if certain features and characteristics of the general population remain in the sample. This is called representativeness.
In other words, if, after selection, a part retains the same tendencies and characteristics as the entire quantity of the examined, then such a population is called representative. But not every specific sample can be selected from a representative population. There are also such objects of research, the sample of which simply cannot be representative. This is where the concept of representativeness error comes from. But let's talk about this a little more.
How to make a sample
So, in order to maximize representativeness, there are three basic sampling rules:
- The most unique indicator of the sample number is considered to be 20%. A statistical sample of 20% will almost always give a result as close to reality as possible. At the same time, there is no need to transfer to the collected larger part of the general population. 20% of the sample is the figure that has been developed by many studies. Let's take a look at some more theory. The larger the sample, the smaller the error of representativeness and the more accurate the result of the study. The closer the sample population is to the general population in terms of the number of units, the more accurate and correct the results will be. After all, if you examine the entire system, then the result will be 100%. But there is no selection here. These are those studies in which the entire array is examined, all units, so this does not interest us.
- In case of inexpediency of processing 20% of the general population, it is allowed to study units of the population in an amount of at least 1001. This is also one of the indicators of the study of the array of the object of study, which has developed over time. Of course, it will not give accurate results with large arrays of research, but it will bring it as close as possible to the possible accuracy of the sample.
- There are many formulas and tabulations in statistics. Depending on the object of study and on the sampling criterion, it is expedient to choose one or another formula. But this item is used in complex and multi-stage studies.
Error (error) of representativeness
The main characteristic of the quality of the selected sample is the concept of "representativeness error". What is it? These are certain discrepancies between the indicators of selective and continuous observation. According to the error indicators, the representativeness is divided into reliable, ordinary and approximate. In other words, deviations of up to 3%, from 3 to 10% and from 10 to 20%, respectively, are acceptable. Although in statistics it is desirable that the error does not exceed 5-6%. Otherwise, there is reason to talk about the insufficient representativeness of the sample. To calculate representativeness error and how it affects a sample or population, many factors are taken into account:
- The probability with which an accurate result is to be obtained.
- Number of sampling units. As mentioned earlier, the smaller the number of units in the sample, the greater the representativeness error will be, and vice versa.
- Homogeneity of the study population. The more heterogeneous the population, the greater the representativeness error will be. The ability of a population to be representative depends on the homogeneity of all its constituent units.
- A method of selecting units in a sample population.
In specific studies, the percentage error of the mean is usually set by the investigator himself, based on the observation program and according to data from previous studies. As a rule, the maximum sampling error (error of representativeness) within 3-5% is considered acceptable.
More is not always better
It is also worth remembering that the main thing in organizing selective observation is to bring its volume to an acceptable minimum. At the same time, one should not strive to excessively reduce the sampling error limits, since this can lead to an unjustified increase in the amount of sample data and, consequently, to an increase in the cost of sampling.
At the same time, the size of the representativeness error should not be excessively increased. After all, in this case, although there will be a decrease in the sample size, this will lead to a deterioration in the reliability of the results obtained.
What questions are usually asked by the researcher?
Any research, if carried out, is for some purpose and to obtain some results. When conducting a sample survey, as a rule, the initial questions are:
- Determination of the required number of sampling units, that is, how many units will be examined. In addition, for an accurate study, the population must be representative.
- Calculation of the error of representativeness with the established level of probability. It should be noted right away that selective studies do not happen with a 100% probability level. If the authority that conducted the study of a particular segment claims that their results are accurate with a probability of 100%, then this is a lie. Many years of practice has already established the percentage of probability of a correctly conducted sample study. This figure is 95.4%.
Methods for selecting research units in the sample
Not every sample is representative. Sometimes one and the same sign is differently expressed in the whole and in its part. To achieve the requirements of representativeness, it is advisable to use various sampling methods. Moreover, the use of one method or another depends on the specific circumstances. Some of these sampling methods include:
- random selection;
- mechanical selection;
- typical selection;
- serial (nested) selection.
Random selection is a system of activities aimed at random selection of population units, when the probability of being included in the sample is equal for all units of the general population. This technique is advisable to apply only in the case of homogeneity and a small number of its inherent features. Otherwise, some characteristic features run the risk of not being reflected in the sample. Features of random selection underlie all other methods of sampling.
With mechanical selection of units is carried out at a certain interval. If it is necessary to form a sample of specific crimes, it is possible to remove every 5th, 10th or 15th card from all the statistical records of recorded crimes, depending on their total number and available sample sizes. The disadvantage of this method is that before the selection it is necessary to have a complete account of the units of the population, then it is necessary to conduct a ranking, and only after that it is possible to sample at a certain interval. This method takes a lot of time, so it is not often used.
Typical (regional) selection is a type of sample in which the general population is divided into homogeneous groups according to a certain attribute. Sometimes researchers use other terms instead of "groups": "districts" and "zones". Then, from each group, a certain number of units is randomly selected in proportion to the share of the group in the total population. A typical selection is often carried out in several stages.
Serial sampling is a method in which the selection of units is carried out in groups (series) and all units of the selected group (series) are subject to examination. The advantage of this method is that sometimes it is more difficult to select individual units than series, for example, when studying a person who is serving a sentence. Within the selected areas, zones, the study of all units without exception is applied, for example, the study of all persons serving sentences in a particular institution.
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Section II. MATH STATISTICS
Topic 6. Selective method. Variation series
And its characteristics
Mathematical statistics is concerned with the study of the patterns that govern mass phenomena, based on the results of observations.
Purpose of MS: creation of methods for collecting and processing statistical data to obtain scientific and practical conclusions.
Methods of mathematical statistics are needed to solve two tasks:
1) an indication of the methods for collecting and grouping statistical information obtained as a result of experiments or observations;
2) development of statistical data analysis methods (evaluation of distribution functions and parameters; testing of statistical hypotheses; evaluation of dependencies between random variables).
The concept of selective observation and its theoretical properties.
In the practice of statistical observations, two types of observations are distinguished:
Continuous, when all objects of the population are studied (population census);
Selective, when a part of randomly selected objects is studied (sociological studies covering a part of the population).
The theory of selective observation is based on statistical regularities that are formed and found in mass phenomena and processes.
Patterns associated with chance and only in a variety of phenomena manifesting themselves as a law are called statistical. This property of patterns is connected with the law of large numbers. The mathematical basis of the law of large numbers, and of statistical science in general, is the theory of probability, which studies random phenomena (events) that have a stable particularity, and, consequently, probability, which helps to identify patterns in the mass repetition of phenomena.
General population and sample. Sample types.
General population is the set of all objects to be studied, from which a sample is made.
sampling set, or, sampling, is a set of objects randomly selected from the general population, subject to direct study.
Population size is the number of its objects. The general population can have both finite and infinite size (N), while the sample can only have a finite size (n).
Example. Of the 2000 products, 100 products were selected for the survey, then the volume of the general population is , and the sample size is .
Sampling method- This is a research method in which the properties of the general population are examined using a sample. At the same time, the conclusions obtained in the study of this part are distributed to the entire set of objects.
Sample types
Simple random sampling, formed by a random selection of elements without dividing the general population into parts.
Mechanical sampling, in which elements from the general population are selected at a certain interval. So, if the sample size should be 10% of the general, then every 10th element is selected.
Typical sample, into which elements are randomly selected from typical groups, into which the general population is divided according to some criterion. For example, the selection of parts from the production of each machine, and not from the total.
serial sampling, in which not individual elements are randomly selected, but entire groups of the population (series).
Repeated called a sample in which the selected object after the study is returned to the general population and it can be re-selected.
Non-repeating called a sample in which the selected object in the sample is not returned to the general population.
representative(representative) is a sample by which we can judge the trait of interest to us in the entire general population. Sample representativeness conditions:
1) parts of the sample should be proportional to parts of the general population;
2) the sample should clearly demonstrate all the features of the trait under study;
3) the sample must be large enough;
4) random sampling.