Sampling schemes

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The sampling scheme is a detailed description of what data and in what way will be obtained. There are many schemes for sampling , so you need to choose for research one that will give the most representative results. The representativeness of the sample is the correspondence of the characteristics of the sample to the characteristics of the population.

Ideally, it’s best to work with the entire population, but it takes a lot of time and resources. Therefore, only part of it can be investigated, which is called the sample. Then the elements that fell into the sample are examined. Based on the values ​​obtained, unknown sampling elements are estimated.

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Basic principles of sampling


The idea is to transfer the results to the entire population. Therefore, the sample should be representative. In other words, it is proportional to both subgroups and the entire population, and does not exclude any particular groups.

The sample should be as large as possible to avoid erroneous judgment. In fact, the sample can be any subset of the population.

If the sample is not representative enough, the study will be considered biased. If it is not big enough - inaccurate.

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If you choose the right relationship between the sample and the population, then you can make the right conclusions about the nature of the entire population. Better to be perhaps right than definitely not right.

Sampling schemes for probability samples


Probabilistic samplings imply that the researcher is absolutely confident in the relationship of the sampling with the general population. If the links are not traced, or not all elements of the population are available, an improbable sample is used.

Draw based

The selection scheme is to conduct a series of tests without returning the element to the population. Each element of the population has the same chance of being selected.

One element is randomly selected from the N population; the probability of the element getting into the sample is 1 / N. Then, from the sample N-1, the second element with probability 1 / (N-1) is selected, and so on up to the nth element with probability 1 / (Nn).

Bernoulli selection

Selection comes from an ordered list of N elements. Let a certain number ε (1 <ε <0) and a set of N independent realizations of the random variable ε1 ... εN uniformly distributed on [0,1] be given in advance. Each element k is assigned a value. If εк <π, then this element is selected, otherwise it is not. The possibility that an element will be selected is π for each of the N elements. Thus, each element that fell into the sample is a binomially distributed quantity.

Systematic selection

Let N be the size of the population. and - some fixed number. a ∈ N. The first sample element is randomly selected among the first a elements of the population. The selected number r 1≤ r ≤a is called a random start (start), and the number a is called the sampling interval. Each element [1,2 ... a] has the same probability of being selected, equal to 1 / a. Then the elements with step a fall into the selection.

You can get a different samples, each of which has the same probability of being selected.

Simple random selection with return

In all of the above schemes, the element did not have the opportunity to get into the sample more than 1 time.
This is logical, because when you re-enable the item, new information is not added. But in this case, some estimates have very simple statistical properties, which makes it possible to investigate rather complicated selection procedures.

For example, m independent selections of elements from a population of size N with equal probabilities of 1 / N are performed. The selected item is returned to the collection. Thus, all N elements participate in the selection continuously.

Proportional selection: with and without return

Assumes that all numbers in the population should be well mixed. Then the researcher takes every ith element from the list.

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Stratified selection

In this selection, the general population is divided into groups that do not overlap. These groups are called strata. Elements in each stratum are homogeneous in certain respects. Each stratum selects elements. The selection method can be any, but not necessarily the same in each stratum. Selection from one stratum does not depend on other strata.

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The selection strategy in this case becomes more effective. The more the investigated characteristic changes, the larger the sample will be for a more accurate estimate. And if you divide the population into strata, in which the characteristics differ little, then a small sample from each stratum will be enough to assess the entire population.

Example:world income survey. Initially, the whole world is divided into strata, namely countries. These are areas that do not overlap, then the study is conducted for each country separately.

Selection Schemes for Incredible Samples


In this case, it is difficult to assess the probability of each element of the population falling into the sample. Researchers using these methods cannot draw accurate conclusions about the general population.

Cluster selection

If direct selection from the population is not possible, elements of the population are combined into clusters.

Cluster selection can take place in one stage, then the clusters are first selected, and then all the elements of the selected clusters are examined. For example, when exploring a city, the cluster may be a family or residents of the same house.

If the selection is carried out in two stages, then the totality is divided into clusters, which consist of other, smaller clusters. At the first stage, a probabilistic sample of primary clusters is obtained. At the second stage, elements are selected from the primary clusters.

The procedure may consist of three or more stages, then such a scheme is called multi-stage.

Type selection

Elements are selected based on whether they are in easy access. Such samples are very easy to compile, but there is no guarantee that they will be representative.

Snowball

It is usually used in the selection of candidates in a specific small group of experts. One person is selected to be interviewed, then he should advise several other people and so on.

Abstract


  1. Samples are probabilistic and improbability.
  2. If the selection method is not correctly selected. research may become biased or inaccurate.
  3. Better to be perhaps right than definitely not right.

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