# Theory of Sampling: Simple, Double and Multiple Sampling, Examples and Importance

In statistics, the sampling theory is the selection of a subset of units in a certain group (known as the statistical population). The purpose is to determine general characteristics of all individuals, but guided by the attributes of those selected in the chosen subset, without studying the entire population.

The observation that is carried out seeks to determine one or more observable characteristics in the objects or people to study, who are represented statistically as independent units. In conjunction with the sample, theories of statistics and probability are applied to carry out the investigations. Sampling is widely used in several scientific branches and in particular in medicine, to determine the behavior of diseases and medicines in the population without having to resort to the individual study of each person.

Index

• 1 Simple sampling
• 1.1 Example
• 2 Double sampling
• 2.1 Example
• 3 Multiple sampling
• 3.1 Example
• 4 Importance of sampling
• 5 References

## Simple sampling

Simple probabilistic sampling consists in choosing a sample among the statistical population in which each element has the same possibility of being selected randomly. In this method, the sample of the population is not subdivided into more parts or separated by sections.

Therefore, any pair of elements can be chosen with equal probability. That is, if a unit of the sample is selected, the next one to be selected has the same probability of being chosen as any other option.

This random selection of values ​​minimizes the preference for any unit or individual of the given sample, creating a random environment to perform the analysis that is needed. In addition, its use simplifies the analysis of the results.

The variation of the results obtained between individuals is usually a good indicator of the overall result: if a variance is obtained in a sample of 10 people drawn from a population of 100, it is highly probable that this number is the same or similar in the population of 100 individuals.

### Example

If a sample of 10 people is obtained from the population of any country, it is likely that a total of 5 men and 5 women will be obtained. However, in this type of random sample, 6 people are usually extracted from one sex and 4 from another, given the number of people in the population.

Another way to see simple sampling is by taking a classroom of 25 people, putting their names on papers and placing them in a bag. If 5 papers are selected from this bag without seeing and at random, the people who come out would represent a simple sample of the total population of the classroom.

## Double sampling

The double statistical sampling was created to give a greater level of depth to the results obtained from a simple sampling. This method is usually used for large statistical populations, and its use represents the study of additional variables to those obtained in simple sampling.

This method is also usually called two-phase sampling. Its main benefit is to obtain more specific results and with less probability of errors.

Usually, double sampling is used when the results obtained on the basis of simple sampling are not presented as decisive, or when they leave doubts to the statisticians.

In this case, an additional sample is obtained from the same statistical population from which the first one was obtained, and the results are compared between them to analyze them and reduce the margin of error.

Double sampling is widely used in the evaluation of the characteristics of certain mass-produced material goods (such as toys) and in the quality control of companies dedicated to products susceptible to manufacturing errors.

### Example

A sample with a size of 100 units is obtained based on a batch of 1000 toys. The characteristics of the 100 units extracted are evaluated and it is determined that the results do not have sufficient strength to decide if the toy lot should be discarded or taken to stores.

As a result of this, an additional sample of 100 more toys is taken from the same batch of 1000 toys. It is evaluated again and the results are compared with the previous ones. In this way, it is determined if the batch is defective or not and we proceed to pack or dispose of it, depending on the analysis of results.

## Multiple sampling

Multiple sampling is considered an additional extension of double sampling; however, it is not part of the same process. It is used to extensively evaluate the results obtained from the sample before reaching a final decision.

In this sampling, also known as sampling in multiple stages, it is customary to start with a large sample and with a low cost of study. In this type of practice the sample is usually acquired by obtaining strata and not individual units; that is, a pair of objects or people is selected, instead of just one.

After selecting each stratum, the results obtained are studied and one or two more strata are selected to study the results again and then compare them with each other.

### Example

The Australian Statistics Institute conducted an investigation in which the population was divided by collection areas and selected some of these areas at random (first stage of sampling). Then, each zone was divided into blocks, which are chosen at random within each zone (second stage of sampling).

Finally, within each block, the area of ​​residence of each household is selected and households are chosen at random (third stage of sampling). This avoids having to list the area of ​​residence of all households in the region, and only focus on the residences located within each block.

## Importance of sampling

Sampling is one of the essential tools of statistical research. This technique serves to save costs and a large amount of time, allowing the budget to be distributed in other areas.

In addition, the different sampling techniques help statisticians obtain more accurate results depending on the type of population with which they work, how specific are the attributes that are sought to study and how much depth you want to analyze the sample.

In addition, sampling is a technique so simple to use that it even facilitates access to statistics to people with little knowledge of this area.

## References

1. Double Sampling for Ratio Estimation, PennState College, (n.d.). Taken from psu.edu
2. Double, Multiple and Sequential Sampling, NC State University, (n.d.). Taken from ncsu.edu
3. Simple Random Sampling, (n.d.). Taken from investopedia.com
4. What is double sampling? - (n.d.). Taken from nist.gov
5. What is multiple sampling? - (n.d.). Taken from nist.gov
6. Sampling, (n.d.), January 19, 2018. Taken from wikipedia.org
7. Multistage Sampling, (n.d.), February 2, 2018. Taken from wikipedia.org