What is a sample population sample. General population and sampling method. Research Window: Brilliant! But who will read this

Sampling any subgroup of elements (subjects, respondents) isolated from the general population for the experiment is called. In this case, a separate individual from the sample with whom the psychologist works is called the subject (respondent).

A complete or continuous study of the entire general population is an unrealistic task. Therefore, research is carried out on representative samples.

Option (x) - it is a sample unit, each individual x is the result of a separate measurement.

Sample size (n)- total number of variants in the sample . The sample size can be any, but not less than two respondents. In statistics, a small ( n< 30), medium (30 < n < 100) and a large sample n>100

Frequency (f) -a number showing how many times each option x occurs in the sample.

Frequency (ω) -this is the share of each frequency in the total sample size, i.e. ω \u003d f / n.

Samples can be independent (disconnected) and dependent (connected).

Samples are called independent (disconnected) if the experimental procedure and the results of measuring a certain property in the subjects of one sample do not affect the peculiarities of the course of the same experiment and the results of measuring the same property in the subjects (respondents) of the other sample.

Samples are called dependent (connected) if the experimental procedure and the obtained results of measuring a certain property in subjects of one sample affect the characteristics of the course of the same experiment and the results of measuring the same property in subjects (respondents) of another sample.

A number of mandatory requirements are applied to the sample, determined primarily by the goals and objectives of the study. One of the important requirements is the requirement of sample uniformity. It means that a psychologist, studying, for example, adolescents, cannot include adults in the same sample.

All the requirements for any sample are reduced to the fact that on its basis the psychologist should obtain the most complete, undistorted information about the characteristics of the general population from which this sample is taken. In other words, the sample must be representative. A representative sample, or representative sample, is a sample in which all the main features of the general population are presented in approximately the same proportion and the same frequency with which a given feature appears in a given general population. A representative sample is a smaller but accurate model of the population it should represent. The representativeness of the sample allows us to extend the conclusions drawn from it to the entire general population.

The representativeness of the sample is very important, however, for objective reasons, it is extremely difficult to keep it. So, it is a well-known fact that 70 - 90% of all psychological research human were conducted in the United States with psychology students. In laboratory studies performed on animals, rats are the most common objects of study. Therefore, it is no coincidence that psychology used to be called "the science of sophomore students and white rats." The sample of students is not representative as a model that claims to represent the entire population of the country.

A natural question arises, how to form a representative sample? Consider two methods to ensure that the sample is representative.

First formation method simple randomsampling. You can get a simple random sample by drawing lots (by analogy with the lottery) or using special tables of random numbers. In the latter case, the elements of the general population are renumbered and the numbers of elements to be taken into the sample are written out from the table of random numbers. This procedure is difficult to implement, since for its implementation it is necessary to take into account each representative of the general population.

The second method is based on the concept stratified random sample... To do this, it is necessary to divide the elements of the general population into strata (groups) in accordance with some characteristics (age, gender, social belonging, nationality, place of residence (city, village)). A random sample is made separately from each group (stratum).

The sample size depends on the research objectives and on the statistical methods that are supposed to be used. Some nonparametric methods can be used when comparing groups of 5-7 people, and factor analysis is most adequate if the sample size is about 100 people.

Sampling concept.

Lecture 4

1. The concept of sampling. 2. Types of samples and methods of constructing samples. 3. Determination of the sample size.

General population- the set of all elements with some common properties that are essential for their characteristics. The formation of the sample is based on knowledge of the outline of the general population, which is understood as a list of all consumers of interest to the researcher. For example, a list of all homeowners in a particular region or city, or a list of all retail outlets selling products.

Depending on the size of the general population and the objectives of the study, methods can be used continuous or selective survey. When conducting continuous surveys study all units of the population. This method can be used if the number of elements in the general population is small (vip clients in consumer research, organizations in business-to-business research).

The most common way to get data in marketing research is selective observation. Fulfillment of certain rules for the selection of units in the sample population and the observance of the representativeness of the sample allows you to extend the sample data to the general population.

When forming the sample, probabilistic and improbable (deterministic) methods.

Probability sampling - a sample into which each element of the research object can fall with a given degree probabilities. In probability samples, each element of the population is known and has a certain probability of being included in the survey. It should be noted that it is not possible to accurately calculate the probabilities due to the lack of information on the size of the general population. Therefore, the term “definite probability” has more to do with sampling rules than with knowledge of the exact size of the population.

Non-probability sampling - a sample into which items fall based on predetermined preferences or judgments. IN improbability samples the condition of equal probability of each object in the general population being included in the sample is not met. For this type The sampling error (margin of error) cannot be calculated. But this does not mean that the study will receive inaccurate results. Improbability sampling requires less time and money. Often, improbability samples are used for relatively small general populations (thousands, tens of thousands of consumers).

The following types of deterministic samples are distinguished:

· Unrepresentative;

· Intentional;

· Quota;

· main array.

Convenience sampling is based on a selection of the most affordable items (shoppers in stores, passers-by, etc.). The researcher relies on the principle of the respondent's belonging to the projected general population.

Judgmental sampling is based on manual selection of those elements that, in the opinion of the researcher, meet the objectives of the study. A type of deliberate sampling is snowball sampling. It consists in identifying the original elements, each of which points to several new ones, and so on. Such a sample is used when examining objects with specific features that occupy a small share in the total set of similar objects and closely interact with each other. Intentional sampling has the same main disadvantage as non-representative sampling - the impossibility of assessing its error and a low degree of representativeness.

Quota sampling - Quota sampling - deterministic samples formed by including elements in the sample in the same proportion according to the main characteristics in which they are present in the general surveyed population

one of the most popular sampling methods. When using the quota method, one or several characteristics are selected by which the sample will be controlled. The number of units in the sample with certain characteristics should be proportional to the number of such units in the general population. It is believed that when using the quota method, it is possible to make a sample of a smaller size than with random sampling, since quota sampling gives an almost complete coincidence of the sample and the general population for the given parameters, i.e. the property of representativeness (representativeness) of the sample is observed. However, this statement cannot be confirmed using mathematical methods. Most often, social and demographic characteristics (gender, age, education, income level, etc.) are used as quota parameters.

Method main array assumes the inclusion in the sample of more than 50% of the objects of the general population. The advantage of polling by main array method lies in the fact that the sample has a high specific weight in the general population. This eliminates possible errors. In principle, it is sufficient to interview a large proportion of respondents in the general population, which minimizes the difference between the sample average and the general average.

Probabilistic methods.If the sample units have a known chance (probability) of being included in the sample, then the sample is called probabilistic. Probabilistic methods include:

· Simple random selection;

· Systematic selection;

· Cluster selection;

· Stratified selection.

Simple random sampling (SRS) - a sample in which each element of the research object with equal probability can be included in the sample population The simplest method of forming a probability sample. Such a sample is formed by a random, equiprobable selection of elements from their complete list. The main disadvantage of such a sample is the need to have a complete list of elements of the studied population. , which is provided in the practice of marketing research quite rarely. With a simple random sampling, selection is made from the entire mass of units of the general population without first dividing it into any groups, and each element has the same probability of being included in the sample (P), which can be calculated as the ratio of the sample size to the size of the general population. For example, if the population size is 10,000 thousand people, and the sample size is 600 people, then the probability of a particular person being included in the sample is 6% (400/10000 * 100). The simplest way to organize a random sample is to draw lots or use a table of random numbers. During a telephone interview, the computer can randomly generate phone numbers, as it has a random number generator.

Elements that are covered by the experiment (observation, survey).

Sample characteristics:

Qualitative characteristics of the sample - what exactly we choose and what methods of constructing the sample we use for this.
Quantitative characteristics of the sample - how many cases we select, in other words, the sample size.

Sampling requirement:

The research object is very extensive. For example, consumers of the products of a global company are a huge number of geographically dispersed markets.
There is a need to collect secondary information.

Sample size

Sample size - the number of cases included in the sample.

The samples can be conditionally divided into large and small, since in mathematical statistics different approaches are used depending on the sample size. It is believed that samples larger than 30 can be classified as large.

Dependent and independent samples

When comparing two (or more) samples, an important parameter is their dependence. 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 the relationship is important for the characteristic measured on the samples), such samples are called dependent... Examples of dependent selections:

pairs of twins,
two measurements of any sign before and after the experimental exposure,
husbands and wives
etc.

If there is no such relationship between the samples, then these samples are considered independent, eg:

men and women ,
psychologists and mathematicians.

Accordingly, dependent samples always have the same size, and the volume of independent samples may differ.

Comparison of samples is performed using various statistical criteria:

Pearson criterion (χ 2)
Student's criterion ( t )
Wilcoxon test ( T )
Mann - Whitney criterion ( U )
Sign criterion ( G )
and etc.

Representativeness

The sample can be considered representative or unrepresentative. The sample will be representative when examining a large group of people, if within this group there are representatives of different subgroups, this is the only way to draw correct conclusions.

An example of a non-representative sample

Research with experimental and control groups, which are placed in different conditions.
- Study with experimental and control groups using a pairwise selection strategy
A study using only one group - experimental.
Research using a mixed (factorial) design - all groups are placed in different conditions.

Sample types

Samples are divided into two types:

probabilistic
improbable

Probability samples

Simple probabilistic 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. On the basis of the list of the general population, cards with the numbers of the respondents are drawn up. They are placed in a deck, shuffled and a card is taken out of them at random, a number is recorded, then returned back. Then the procedure is repeated as many times as we need the sample size. Minus: repetition of selection units.

The procedure for constructing a simple random sample includes the following steps:

1) you need to get full list members of the general population and number this list. Recall that such a list is called the sampling frame;

2) determine the estimated sample size, that is, the expected number of respondents;

3) extract from the table of random numbers as many numbers as we need sample units. If there should be 100 people in the sample, 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 out random numbers

Simple random sampling has obvious advantages. This method is extremely easy to understand. The research results can be extended to the target population. Most approaches to obtaining statistical inference involve collecting information using simple random sampling. 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 simple random sampling.

2) a simple random sample may result in a large population, or a population spread over a large geographic area, which significantly increases the time and cost of data collection.

3) the results of using a simple random sample are often characterized by low accuracy and a larger standard error than the results of using other probabilistic methods.

4) as a result of using the SRS, an unrepresentative sample may be formed. Although samples obtained by simple random selection, on average, adequately represent the general population, some of them are extremely inaccurately representative of the studied population. This is especially likely with a small sample size.

Simple non-repeating sampling. The sampling procedure is the same, except that the cards with the respondent's numbers are not returned to the deck.

Systematic probability sampling. It is a simplified version of simple probability sampling. Based on the list of the general population, respondents are selected at a certain interval (K). The K value is determined by chance. The most reliable result is achieved with a homogeneous general population, otherwise the step size and some internal cyclical patterns of the sample may coincide (mixing of the sample). Cons: Same as for simple probability sampling.
Serial (nested) sampling. 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.
Regional sample. In the case of a heterogeneous population, before using probabilistic sampling with any selection technique, it is recommended to divide the population into homogeneous parts, such a sample is called zoned. Zoning groups can be both natural formations (for example, city districts), and any feature underlying the study. The characteristic on the basis of which the division is carried out is called the characteristic of stratification and regionalization.
"Convenient" selection. The “convenience” sampling procedure consists of establishing contacts with “comfortable” sampling units - a group of students, a sports team, friends and neighbors. If it is necessary to obtain information about the reaction of people to a new concept, such a sample is quite reasonable. A “convenient” sample is often used for preliminary testing of questionnaires.

Group building strategies

Selection of groups for their participation in psychological experiment is carried out using various strategies that are needed in order to ensure the maximum 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 can be included in the sample with equal probability. For example, to make a random sample of 100 university students, you can put pieces of paper with the names of all university students in a hat, and then get 100 pieces of paper out of it - this will be a random selection (Goodwin J., p. 147) ......

Pairwise selection

Pairwise selection - a strategy for constructing sample groups, in which groups of subjects are composed of subjects 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).

Most sociological research is not continuous, but selective: according to strict rules, a certain number of people are selected, reflecting the structure of the object under study by socio-demographic characteristics. Such a study is called selective.

A sample survey is a way of systematically collecting data on the behavior and attitudes of people by interviewing a specially selected group of respondents who provide information about themselves and their opinions. It is a more economical and no less reliable method than a continuous study, although it requires a more sophisticated methodology and technique.

Correct sampling is the key to success and a prerequisite for any survey if it is not a national census. If the sociologist made the wrong sample, i.e. the group of people that is going to interview, the results of the study will turn out to be incorrect, and therefore not useful to anyone.

Why is it irrational and practically impossible to interview all the people who make up the research object? It is possible to roughly calculate the cost of a continuous survey of adult residents of at least one urban area with a population of, say, 200 thousand people. Considering that one questionnaire (interviewer) is able to interview no more than three people per hour, with a seven-hour working day, his development will be 20 questionnaires. This means that for the complete collection of information, we will need 85 thousand man-days. We want to complete the survey in 10 days and pay 20 rubles for each interview. thus, we need to attract 8.5 thousand assistants and pay 340 thousand rubles. As important as the information is, it is not worth the cost, which is why sociologists resort to selective survey methods.

The essence of the sampling method lies in the fact that according to certain, rather strict, rules from the total number of people, called the general population(the population of the entire country, the entire urban population, residents of one district, only young people, etc.) a limited number of people are selected, which is intended as a kind of model to reproduce the structure of the object. In the language of sociologists, this group of people, as well as the procedure for its definition, is called sampling.Correct construction sample population- the basis and guarantee of high accuracy of sociological research.

The program includes the definition of the target population, since the vast majority of studies are not continuous, but selective. It is very important to correctly, according to certain rules, select the required number of people for the survey.

General population -the whole set of studied elements that have the same social characteristics, which testify to belonging to one object, i.e. it is the entire subject to which the conclusions of the study apply. It is usually localized in time, geographically, etc. The size of the general population in formulas and tables is usually indicated by the symbol N, and the part of its members selected from the general population is called the sample, or the sample population will be denoted by a small n.

Sample population -it is a part, a scaled-down model of the general population. The basic rule for its preparation is: Each element of the population should have the same chance of being included in the sample.But how can this be achieved? First of all, you need to find out as many properties or parameters of a gene as possible. aggregates, for example, the variation in age, income, nationality, place of residence of the respondents. The spread in the age of the respondents is called variation, specific values \u200b\u200bof age - values, and the totality of all values \u200b\u200bforms variable.Thus, the variable “age” ranges from 0 to 70 (average life expectancy) and more years. Values \u200b\u200bcan be grouped into intervals: 0 - 5, 6 - 10, 11 - 15 years, etc. it all depends on the objectives of the study.

Units of analysis or selection -

Experience has shown that a correctly sampled sample represents or represents well (from lat. Represento- I represent) the structure and state of the general population. She must be representative - i.e. reproduce proportionally all the basic characteristics of the general population, and must guarantee for each element of the general population an equal probability of being included in the sample. The sampling process is based on the interrelation and interdependence of the qualitative characteristics and features of a social object, and is also based on the legitimacy of conclusions about the whole based on the study of its part, provided that in its structure this part is a micro-model of the whole. In other words, a representative sample in sociology is considered to be such a sample population, the main characteristics of which fully coincide (presented in the same proportion or with the same frequency) with the same characteristics of the general population.

A representative study is one in which the deviation in the sample population for control characteristics does not exceed 5%.

As soon as the sociologist has decided who he wants to interview, he determined the sampling frame, after which the question of the type of sampling, the sampling method, and the sampling structure is decided.

Sample types the main types of statistical sampling are called: random -probabilistic (if the general population is homogeneous elements) and not accidental -improbable (purposeful, quota).

Sampling methodIs a method of constructing the type of sample, the name of which this method bears, for example, the method of probability sampling.

To ensure representativeness, a complete and accurate list of sampling units is required, this list forms sampling frame.Elements for selection are called sampling units, gene element. the aggregate from which information is directly collected is called unit of observation, -it is a separate person.

Analysis units areelements of the elective, or surveyed population (individuals, groups).

If the sampling frame includes a list of sampling units, then the sampling design implies their grouping, reflecting the percentage distribution of the genes. the aggregate for some important characteristics, for example, the distribution of individuals by profession, qualifications, gender or age. Sample structure -these are the percentage proportions of the characteristics of the object, on the basis of which the sample is compiled. So if the gene. population, for example, 30% of young people, 50% of middle-aged people and 20% of elderly people, then in the sample population the same percentages of the three ages should be observed.

TYPES AND METHODS OF SAMPLING

In statistical science, depending on the selection method, the following types of samples are distinguished:

1) Random sampling with return, or another name accidentally repeated.

2) Random sampling with no return, or accidentally nonrepeatable.

3) Mechanical.

4) Typical.

5) Serial.

When forming the sample, probabilistic (random) and improbable (non-random) methods are used. If all sample units have a known chance (probability) of being included in the sample, then the sample is called probabilistic, in other words, it is a sample for which each element of the population has a certain, predetermined probability of being sampled. This allows the researcher to calculate how correctly the sample reflects the general population from which it is selected (designed). This sample is sometimes also called random.

If this probability is unknown, then the sample is called improbable.(non-random, targeted, purposeful).

Probability sampling -her model is related to the concept of statistical probability. The probability of some expected event is the ratio of the number of expected events to the number of all possible ones. Moreover, the total number of events should be large enough (statistically significant).

P \u003d 100/600 \u003d 1/6where R -the probability of the expected event.

The probability that any of the events will necessarily occur is always equal to one, i.e. is an reliableapproval.

Probabilistic methods include:

Simple random selection,

Systematic selection,

Cluster selection,

Stratified selection.

Simple random selection can be carried out using blind sampling (lottery method) and using a table of random numbers. In one case, you make your choice without looking, in the other - realizing everything, but in order not to interfere and not spoil anything, we turn to special tables. Simple random selection is subdivided into two varieties already according to a different criterion, namely, on the return or non-return of the lottery ball (instead of it there may be the respondent's surname) back into the basket. In this case, there are:

Random re-sampling (with return),

Random irreversible (no return) selection.

Sampling methods probabilistic (random) (the first two are given above)

1) Mechanical sampling method(for large general populations, implies the homogeneity of the elements of the gene. aggregate, selection from gene. aggregates at regular intervals of the required number of elements). All elements of the general population are brought together into a single list, and from it, at regular intervals, the corresponding number of respondents is selected.

K - Selection stepcalculated:

K \u003d N / n Where N -size (or number) of gen. aggregate, and n -the size of the sample.

2) Serial sampling method(convenient and accurate), splitting gen. aggregates into homogeneous parts, followed by selection within the series.

If it is possible to split the gene. aggregate into homogeneous parts (series) for a given criterion, then the selection of respondents can be carried out from each series separately. Moreover, the number of respondents selected from the series is proportional to the total number of elements in it. Allocation of respondents into homogeneous groups.

From each series, it is possible to select units of analysis using proper random or mechanical sampling. The number of respondents to be selected from each series separately.

3) Nested sampling method(small groups) - selection as research units, not individual respondents, but groups. With the subsequent continuous survey in the selected groups. A nested sample is representative if the composition of the groups is maximally similar in terms of the main demographic characteristics of the respondents. Lists or cards are compiled only for groups (brigades, sections, students, class, etc.) that represent an object from the point of view of the sociological study of the problem.

A sample is a group of statistical

units selected from a larger group, general

the aggregate. Studying

sample, we hope to make reasonable conclusions about the population.

Excellent definition

Incomplete definition ↓

Sample

the process of forming a sample. This process, regardless of whether a single-stage or multi-stage selection scheme is used (see. Single-stage sampling and Multi-stage sampling), is characterized by the following features: 1) the number of stages of selection; 2) the type of selected objects of representation at intermediate stages of selection; 3) the method of regionalization of objects of representation identified at intermediate stages of selection; 4) the method of selection of objects of representation and units of observation at each stage; 5) the volume of the sample (the number of observation units). The first four features describe the type of sample, that is, the features of the process of selecting units of observation, the fifth (the size of the sample population) makes it possible to distinguish the sample within the type itself by the number of units of observation. Two samples are considered similar only if all the characteristics describing the structure of the formation of the sample population and the sets of features on the basis of which the objects of representation are zoned at intermediate stages of selection are identical. The sample population is a part of the general population, the objects of which act as the main objects of observation. This part of the general population is selected according to special rules so that its characteristics reflect the properties of the general population. Thus, by examining a part of the general population, you can get the most complete picture of the entire population as a whole, which in turn gives savings in time, human resources and material costs. V. s. should reflect the main (from the point of view of research objectives) properties (signs) of the general population. Taking into account the distributions of these features, the sample is designed and its quality is assessed; they are used in contingency tables when analyzing results in combination with features of primary interest to researchers. It is implied that the reproduction of the general distributions of the controlled features in the sample ensures its representativeness in terms of features not used in the calculations. How much this assumption corresponds to reality largely depends on the specifics of the research subject, on the correct solution to the problem of the relationship between the characteristics of the description of the research object and the empirical object of the survey.