Random Sampling is a method of probability sampling where a researcher randomly chooses a subset of individuals from a larger population. In this method, every individual has the same probability of being selected. The researcher aims to collect data from as large a portion as possible of this randomly chosen subset.

In the field of statistics, sampling serves as the technique for selecting a portion of the population to draw statistical inferences. This subset’s characteristics allow us to estimate the attributes of the entire population. In the realm of market research, sampling methods fall into two primary categories: Random or probability sampling and non-probability sampling.

This article discusses the specific category of probability sampling known as random sampling and its types, formulas, advantages, examples, etc.

What is Random Sampling?

Random sampling is a method used in statistics to select a subset of individuals or items from a larger population in such a way that each member of the population has an equal and independent chance of being included in the sample. It is a fundamental technique for conducting surveys and experiments.

Random Sampling Definition

Random sampling is a method employed for selecting observations from a population, facilitating generalization about the entire population.

Random Sampling is sometimes referred to as probability sampling, distinguishing it from non-probability sampling. This method encompasses various techniques, including simple random sampling, stratified sampling, cluster sampling, and multistage sampling. However, it should be noted that convenience samples, which are non-arbitrary, fall outside the realm of probability sampling.

Types of Random Sampling

Random sampling relies on a method that involves a degree of random selection. It allows all eligible individuals an equal opportunity to be part of the sample drawn from the entire sample space. While it can be laborious and costly, probability sampling is a powerful tool for creating a representative sample of the population. There are four main categories of this sampling technique, which include:

• Simple Sampling
• Systematic Sampling
• Stratified Sampling
• Cluster Sampling

Let’s discuss the these types in detail.

Simple Random Sampling

Simple random sampling involves randomly selecting items without any specific pattern or criteria. For example simple random sampling involves the unbiased, purely random selection of individuals from the population, where each member has an equal chance of being included. Each member of the population has an equal chance of being chosen, like drawing names from a hat.

Systematic Random Sampling

Selects individuals at regular intervals, offering an organized yet random way to choose a sample. For example in systematic random sampling, you select a starting point at random and then choose every ‘k’-th element from the population. It’s like selecting every n person from a list.

Stratified Random Sampling

Divides the population into distinct strata or subgroups and then randomly samples from each stratum, enhancing representation. For example, stratified random sampling involves dividing the population into subgroups or strata based on certain characteristics. Samples are then randomly chosen from each stratum in proportion to their size.

Cluster Random Sampling

Organises the population into clusters, randomly selects some of these clusters, and samples all individuals within the chosen clusters. For example, clustered sampling divides the population into clusters or groups, and then a random sample of clusters is chosen. All individuals within the selected clusters are included in the sample.

By utilising these techniques, probability sampling aims to provide reliable insights into the broader population while maintaining the essence of randomness.

How to Perform Simple Random Sampling

Define the Population: Clearly identify the entire group from which you want to draw a sample.

Assign Numbers: Assign a unique number to each member of the population.

Use a Random Method: Select members using a random method, such as:

Random Number Generator: Use software or a calculator to generate random numbers corresponding to the assigned numbers.

Lottery Method: Write numbers on slips of paper, mix them, and draw the required number of slips.

Select Sample Size: Determine the sample size you need and select that number of individuals based on the random method used.

Collect Data: Gather data from the selected individuals to conduct your study.

When to Use Random Sampling

1. When the population is relatively homogenous: Simple random sampling works well when the population shares similar characteristics, as each individual has an equal chance of being selected.
2. When the population size is known: If the total population size is known, simple random sampling ensures that every individual has a known and non-zero chance of being included in the sample.
3. When there is no need for specialized knowledge: Simple random sampling is straightforward to implement and does not require extensive prior information about the population.
4. When statistical inference is the primary goal: Simple random sampling is often used when researchers need to make generalizations about the population based on the sample data, as it provides an unbiased estimate of population parameters.
5. When resources are limited: Simple random sampling can be more cost-effective and less time-consuming compared to other sampling methods, making it suitable when resources are limited.

Random Sampling Formula

Formula of random sampling is mentioned as below:

P = 1 –[(N-1)/N] × [(N-2)/(N-1)] × . . . × [(N-n)/(N-(n-1))]

Where,

• P represents probability,
• n represents sample size, and
• N represents population.

In above formula cancelling 1-(N-n/n), it will yield a value of P = n/N.

So, sample getting selected for a chance of more than once

P = 1 – (1 – (1/N))ⁿ

Where,

• P represents probability,
• n represents sample size, and
• N represents population.

Advantages of Simple Random Sampling

Below are the advantages of Simple Random Sampling:

• Simple random sampling is unbiased form of sample classification.
• Simple random sampling is easy to implement and cost-effective.
• Simple random sampling ensures that each element in the population has an equal probability of being included in the sample.
• Simple random sampling is a reliable way to estimate population characteristics.

Disadvantage of Simple Random Sampling

Not Always Feasible: It can be impractical for very large populations due to time and resource constraints in listing and accessing every member.

Population List Required: A complete and accurate list of the population is needed, which can be difficult to obtain.

Potential for Sampling Error: Random selection might still result in an unrepresentative sample, especially with small sample sizes.

Resource Intensive: It may require significant resources and effort to ensure true randomness and to contact selected individuals.

Difficulty in Subgroup Analysis: It may not adequately capture smaller subgroups within the population, making it challenging to analyze these subgroups separately.

Random Sampling vs Non-Probability Sampling

Below are the differences between Probability Sampling vs Non-Probability Sampling: