Random Sampling

Introduction

Sampling techniques refer to the different sampling techniques used to collect different types of samples in statistics. If you need to make statistical inferences about a population, it is almost impossible to collect data from all the units that belong to that group. In these situations, various sampling methods can help you select the correct sample from this population for analysis. In this tutorial, we will discuss random sampling, its type, formulas, and examples.

Random sampling Definition

Random sampling can be considered as a case of probability sampling. where each and every unit from the population into the sample is selected randomly according to some probability associated with it. As a result, the observations are not significantly different from the unsampled observations. We assume that the statistical experiment contains the data collected by sampling.

Types of Random Sampling

With this sampling method, any entity is randomly selected. In other words, each entity in such a population is equally likely to be selected as part of the sample. Probability sampling methods are used in quantitative studies. The purpose of this sampling procedure is to test the hypothesis. The sampling methods that fall into this category are −

• Simple random sample

• Systematic sample

• Stratified sample

• Cluster sample

Simple Random Sampling

With this sampling method, each member of the population is equally likely and likely to be included in the sample. Therefore, this is called "typical sampling".

Systematic Sampling

In stratified random sampling, researchers divide the population into non- overlapping subgroups based on specific characteristics. Researchers calculate the number of entities to sample from each subgroup based on the population ratio. Then use simple or systematic random sampling to select samples individually from each subgroup. These sampling procedures ensure an accurate representation of each subgroup.

Stratified Sampling

This sampling technique divides the population into subgroups and takes an easy random sample from each group to complete the sampling process (for example, the number of girls in class 50). These small groups are called layers. Small groups are formed supported some characteristics of the population. After dividing the population into smaller groups, researchers randomly selected samples.

Clustered Sampling

In this sampling method, researchers divide the entire population into subgroups called clusters. Each subgroup needs the same attributes as the entire sample.Researchers then select arbitrary clusters to form samples, rather than randomly selecting individuals. Although such sampling techniques are used for large populations, they are error prone because each cluster can be significantly different from the other clusters.

Non-Probability Sampling

This sampling technique includes a non-random sampling technique in which samples are selected based on specific criteria. This shows that not all companies are selected as part of the sample. The non-probability sampling method is used in qualitative research. However, this sampling method is prone to sampling bias and weakens the conclusions about the population.

Convenient Sampling

In convenient method the collection of data from a subject depends on the accessibility of the subject. In other words, the entities that researchers can easily access make up the sample. This sampling method is used when initial data needs to be collected at low cost. However, the information collected using this sampling technique may not be representative of the entire population. An example of this sampling method is people standing in a mall handing out leaflets on specific occasions.

Discretionary or purposeful sampling

This sampling is used when a researcher needs to collect data for a very specific purpose. The target group from which the sample is selected is at the discretion of the researcher. This sampling method is used when you need to gather detailed knowledge about a particular phenomenon. A researcher wants to understand the experience of a student with a disability. To collect this data, she asks only students with disabilities about their experiences

Important Sampling Precautions

• The sampling technique is used to select the correct sample from the population and characterize it.

• There are two types of sampling methods: probabilistic sampling and non- probability sampling.

• The probability sample is used to test the hypothesis in a quantitative study.

• The non-probability sample is used to first understand the population for qualitative research.

Random Sampling Formula

The random sample formula is when this sample is selected only once.

$$\mathrm{p\:=\:1\:-\:\frac{N\:-\:1}{N}\:.\:\frac{N*\:-\:2}{N\:-\:1}\:....................\:\frac{N\:-\:n}{N\:-\:(n\:-\:1)}}$$

Where P is the probability, n is the sample size, and N is the population.

$\mathrm{Cancel\:=\:1\:-\:\frac{(N\:-\:n)}{n}}$

$\mathrm{P\:=\:\frac{n}{N}}$

In addition, the sample should be able to be selected multiple times.

$\mathrm{P\:=\:1\:-\:(1\:-\:\frac{1}{N})^{n}}$

Advantages

Some of the benefits of random sampling are −

• Compared to other sampling methods, it helps reduce sampling-related bias and is considered a fair sampling method.

• This method is a basic method for collecting data and does not require any technical knowledge.

• The data collected in this way is well informed.

• The large population size of simple random samples allows researchers to create the desired sample size.

• It's easy to choose a smaller sample size from the available population.

Examples

Example 1 − What is the sampling method used to extract a random sample of 455 employees in a company?

Solution − This is an example of probability sampling because each employee is equally likely to be selected. Also, the sampling method used is simple random sampling because the selection is based on chance.

Example 2 − A researcher wants to analyse the characteristics of people who belong to three different income groups. Less than 899000, 698,000, or more than 568,000. What sampling method do researchers use?

Solution − A stratified random sample is used because people need to be divided into different layers (or groups).

Example 3 − A company has 245 offices around the world, with the same number of employees playing similar roles. A researcher wants to determine employee satisfaction in a company, but what is the most effective sampling method

Solution − Researchers can consider each office as a cluster because they cannot go to all offices of the company to collect data. You can collect data from several random clusters (here offices) to create samples and perform analysis. Therefore, cluster sampling is the most efficient sampling method in this situation.

Conclusion

Sampling techniques are used to select the exact sample, that represents the population to be analysed. If the sample selected for analysis is inaccurate, this results is an incorrect estimation of the population parameters. Random sampling can be considered as a case of probability sampling where each and every unit from the population into the sample is selected randomly according to some probability associated with it.

FAQs

1. What do you mean by random sampling?

Random sampling can be considered as a case of probability sampling where each and every unit from the population into the sample is selected randomly according to some probability associated with it.

2. What is simple random sampling?

With this sampling method, each member of the population is equally likely and likely to be included in the sample. Therefore, this is called "typical sampling".

3. What is systematic sampling?

This method selects items from the target population by selecting a random selection point and then selecting another method after a specific sampling period.

4. What is stratified sampling?

This sampling technique divides the population into subgroups and takes an easy random sample from each group to complete the sampling process.

5. What is clustered sampling?

In this sampling method, researchers divide the entire population into subgroups called clusters. Each subgroup needs the same attributes as the entire sample.