SAMPLING THEORY: SIMPLE, DOUBLE AND MULTIPLE, EXAMPLES - SCIENCE - 2024

The theory of sampling, statistical, is the selection of a subset of units in a given group (known as statistical population). The purpose is to determine general characteristics of all individuals, but being 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 be studied, who are statistically represented as independent units. In conjunction with sampling, theories of statistics and probability are applied to carry out investigations.

Simple sampling

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

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

This random selection of values ​​minimizes the preference for some unit or individual in 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 in 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 will be 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 most likely that a total of 5 men and 5 women will be obtained.

However, in this type of random sample, 6 people of one sex and 4 of the other are usually drawn, given the number of people in the population.

Another way to look at simple sampling is by taking a classroom of 25 people, putting their names on paper, and placing these 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 often called two-stage sampling. Its use has the main benefit of obtaining more specific results with less probability of errors.

Usually, double sampling is used when the results obtained based on the 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 the two 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 factory errors.

Example

A sample with a size of 100 units is obtained based on a lot of 1000 toys. The characteristics of the 100 units extracted are evaluated and it is determined that the results are not conclusive enough to decide whether the lot of toys should be discarded or taken to stores.

As a consequence of this, an additional sample of 100 more toys is drawn 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 it is packed or discarded, depending on the analysis of the 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 multistage sampling, it is customary to start with a large sample and with a low study cost. 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 re-study the results and then compare them with each other.

Example

The Australian Institute of Statistics conducted an investigation in which it divided the population 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 the sampling). This avoids having to list the residence zone of all the homes in the region, and only focus on the residences located within each block.

Importance of sampling

Sampling is one of the essential tools of a statistical investigation. This technique serves to save costs and a great amount of time, allowing to distribute the budget in other areas.

In addition, the different sampling techniques help statisticians to obtain more accurate results depending on the type of population with which they are working, how specific the attributes to be studied are and how deeply they wish to analyze the sample.

Furthermore, sampling is such a simple technique to use that it even makes statistics easier for people with little knowledge of this area.

References

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