Random Sampling Method

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 organised 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.

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.

Random Sampling vs Non-Probability Sampling

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

Aspect	Probability Sampling (Random Sampling)	Non-Probability Sampling
Method of Selection	Random or systematic selection based on a known probability distribution.	Non-random or subjective selection without a known probability distribution.
Representativeness	Likely to yield a representative sample of the population, reducing bias.	May result in a non-representative sample, potentially introducing bias.
Generalizability	Results are more easily generalized to the entire population.	Generalizability may be limited due to the potential for bias in the sample.
Sample Size Determination	Easier to calculate sample size requirements based on probability theory.	Sample size determination may be more arbitrary and less statistically rigorous.
Types of Probability Sampling Methods	Simple Random Sampling, Systematic Sampling, Stratified Sampling, Cluster Sampling.	Convenience Sampling, Judgmental Sampling, Snowball Sampling, Quota Sampling.
Statistical Inference	Suitable for making statistical inferences and drawing conclusions about the population.	Limited suitability for making statistical inferences about the entire population.
Precision and Accuracy	Generally provides more precise and accurate estimates when properly conducted.	May result in less precise and accurate estimates, depending on the sampling method used.
Random Error	Random errors can be quantified and controlled, making it more reliable.	More susceptible to random errors due to non-random selection methods.
Bias Control	Better control over selection bias and the potential for under representation or over representation.	May introduce selection bias and potential for under representation or over representation.
Examples	Drawing a random sample of registered voters using a random number generator.	Surveying people who are conveniently available in a shopping mall for an opinion poll.

People Also Read:

• Quartile Formula
• Probability Distribution
• Normal Distribution

Random Sampling Examples

Example 1: A company has 500 products, and they want to randomly select 20 of them for quality testing. What is the probability of any single product getting selected?

Solution:

The chance of one-time selection is:

P = n/N

⇒ P = 20/500

⇒ P = 4%

Example 2: In a conference with 200 attendees, 50 will be randomly chosen for a survey. What is the probability that one attendee gets selected more than once?

Solution:

The probability of getting selected more than once is:

P = 1 – (1 – (1/N))ⁿ

⇒ P = 1 – (1 – (1/200))⁵⁰

⇒ P ≈ 9.56%

Example 3: A university has 1,200 students, and they want to select 100 students for a survey using simple random sampling. What is the probability of any single student being chosen?

Solution:

The chance of one-time selection is:

P = n/N

⇒ P = 100/1200

⇒ P = 8.33%.

Example 4: In a raffle, 50 tickets are drawn from a pool of 1,000 tickets. What is the probability that a specific ticket does not get selected?

Solution:

The chance of a specific ticket not being selected is:

P = 1 – (n/N)

⇒ P = 1 – (50/1000)

⇒ P = 95%.

Example 5: A deck of 52 playing cards is shuffled, and 5 cards are drawn with replacement. What is the probability of drawing a specific card (e.g., the Ace of Spades) at least once?

Solution:

The probability of drawing a specific card at least once when drawing 5 cards with replacement is:

P = 1 – (1 – (1/N))ⁿ

⇒ P = 1 – (1 – (1/52))⁵

⇒ P ≈ 9.36%.

Practice Questions on Random Sampling

Question 1: You’re conducting a survey about favourite ice cream flavours in a town with 5,000 residents. How can you perform simple random sampling for your study?

Question 2: What is the key distinction between stratified and cluster sampling methods, and in what situations would each be more suitable?

Question 3: A company needs to test a random sample of 50 smartphones from a production batch of 2,000. Explain the steps they should take for a systematic sampling procedure.

Question 4: In a school of 500 students, you want to ensure your random sample includes both juniors and seniors. How can you use stratified sampling to accomplish this?

Question 5: Discuss the importance of non-response and how it can impact the validity of research using random sampling techniques.

FAQs on Random Sampling

What is Random Sampling Method?

Random sampling is a method used in research to select a sample from a larger population in an unbiased way.

What is Simple Random Sampling?

Simple random sampling is a statistical method used to select a sample from a larger population in such a way that every possible subset of the population has an equal chance of being selected.

Why Random Sampling is Important?

Random Sampling is vital because it helps ensure the sample represents the population, making the research findings more reliable and generalisable.

What Are Some Common Methods for Random Sampling?

Common random sampling methods include:

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

How Does Simple Random Sampling Work?

Simple Random Sampling works by randomly selecting individuals or items from a population so that each has an equal chance of being chosen, ensuring a representative sample.

What Is Stratified Random Sampling?

Stratified Random Sampling divides the population into distinct subgroups (strata) based on certain characteristics, then randomly samples from each stratum to ensure representation of various groups within the population.

When Is Systematic Sampling Used?

Systematic Sampling is used when there’s a need for simplicity and efficiency. It involves selecting every kth item from a list, starting with a random item. It’s useful for large populations and can provide a representative sample.

What Is Cluster Sampling?

Cluster Sampling involves dividing the population into clusters, randomly selecting some clusters, and then sampling all individuals within the chosen clusters. It’s useful for geographically dispersed or large populations.

Are There Any Drawbacks to Random Sampling?

Yes, there are drawbacks to random sampling, including the potential for bias due to chance, non-response, and under representation of certain groups. Large populations can be costly and time-consuming to sample completely.

How Do You Calculate Sample Size for Random Sampling?

To calculate the sample size for random sampling, consider factors like population size, desired confidence level, margin of error, and population variability. Formulas such as the one for simple random sampling help determine the required sample size.