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In-Depth Guide of Simple Random Sampling: Definition, Pros, Cons, and Examples

Learn about the essence of simple random sampling and its wide-ranging applications across numerous fields in this comprehensive guide.

In-Depth Guide of Simple Random Sampling

Simple random sampling is a widely used technique in sampling methods, aiming to minimize bias by randomly selecting participants, ensuring each individual has an equal chance of being chosen. Its methodological rigor reduces systematic biases, enhancing the sample's representativeness and credibility.

This guide will unpack simple random sampling's essence, applications, and role in facilitating reliable, data-driven insights and decisions in today's data-centric landscape.

Understanding Simple Random Sampling

What Is The Simple Random Sampling?

Simple random sampling is a basic probability method where researchers randomly choose a subset of participants from a population. Each member has an equal chance of being selected. Researchers assign a unique number to each person and use a random method, such as a lottery or number generator, to pick participants. This method requires minimal prior knowledge about the group and helps ensure accuracy and reduce bias in the research.

An example of Simple random sampling is when a market research firm is hired by a car manufacturer to gauge public opinion on their new electric vehicle model. The firm uses a list of 500,000 registered drivers, each with a unique number, and randomly selects 2,000 to survey using statistical software. This approach helps obtain an unbiased view of driver preferences and purchase likelihood.
Simple random sampling - Probability sampling method

Simple Random Sampling Formulas And Examples

A Simple Random Sample calculator employs 2 distinct approaches: SRSWOR and SRSWR.

1. Simple random sample without replacement (SRSWOR)

Simple Random Sampling Without Replacement (SRSWOR) is a probability sampling method where a sample of size n is randomly selected from a population of size N, with each unit having an equal chance of being selected. Once a unit is selected, it is removed from the population and cannot be selected again.
The Formula of SRSWOR (1)
The probability associated with each sample in case of the SRSWOR scheme is: P(s) = 1 / C(N, n)

Where:
  • P(s) is the probability of selecting a specific sample s of size n from the population
  • C(N, n) represents the combination formula, which calculates the number of ways to choose n items from a set of N items
  • N is the total population size
  • n is the sample size
The combination formula is calculated as: C(N, n) = N! / (n! * (N-n)!)
Example: Suppose you have a population of 10 students, and you want to select a sample of 4 students using SRSWOR. What is the probability of selecting a specific sample, say, students {2, 4, 7, 9}?
Given:
  • N = 10 (total population size)
  • n = 4 (sample size)
Therefore, the probability of selecting the specific sample {2, 4, 7, 9} using SRSWOR is approximately 0.0048 or 0.48%. This also means that every possible sample of size 4 from this population of 10 students has a 0.48% chance of being selected.
Example of Simple Random Sampling Without Replacement
Note that the probability of selecting any specific sample is always the same in SRSWOR, as long as the sample size and population size remain constant. This is because each possible sample has an equal chance of being selected.

2. Simple random sample with replacement (SRSWR):

In SRSWR, after a unit is selected, it is put back into the population before the next selection, allowing for the possibility of the same unit being selected multiple times in the sample.
The Formula of SRSWR (1):
The probability associated with each sample in case of the SRSWR scheme is 1 / Nⁿ.

Where:
  • N is the total population size
  • n is the sample size
Example: A small school has 30 students (N = 30), and the principal wants to select a sample of 2 students (n = 2) for a special project using the SRSWR scheme. The probability associated with each sample in case of SRSWR scheme is 1 / 30²

Probability ≈ 0.0011 or 0.11%

In this example, the probability associated with each sample when using the SRSWR scheme is approximately 0.0011 or 0.11%. This means that every possible sample of size 2 from this population of 30 students has a 0.11% chance of being selected when using the SRSWR scheme.
Simple Random Sampling With Replacement Example
Using smaller population and sample sizes can avoid extremely small probabilities while illustrating the concept of SRSWR. Note that the probability of each sample in SRSWR is generally smaller than in SRSWOR, as the number of possible samples is larger due to the ability to select the same unit multiple times and the importance of the order of selection.

So, which is better, SRSWOR or SRSWR? In practical application, Sampling without replacement (SRSWOR) generates more efficient samples by ensuring each unit is represented only once.

Why Do Researchers Usually Use Simple Random Sampling?

Researchers often choose simple random sampling for 5 benefits:

Advantages

  • Simplify understanding and implementation, making it a popular choice.
  • Equalize selection and sampling bias, providing each individual an equal chance of selection.
  • Generate a representative population sample, facilitating generalizations.
  • Utilize statistical methods for data analysis and inference.
  • Capture attributes of homogeneous populations effectively.
Despite these advantages, simple random sampling has 5 main drawbacks:

Drawbacks

  • Demands a complete and up-to-date list of the population, which is not always possible.
  • Consumes time and resources, especially with sizable populations.
  • Might overlook distinct population subsets.
  • Risks sampling error, leading to chance deviations from population traits.
  • Impractical and expensive for dispersed populations.

When To Use Simple Random Sampling?

This method is particularly useful in the following 7 scenarios:
  • Homogeneous population: Simple random sampling can effectively represent the entire population, in case the population is relatively uniform.
  • Equal chance of selection: Simple random sampling ensures that every individual or item in the population has an equal probability of being selected, minimizing bias.
  • Smaller populations: This approach is more feasible and cost-effective compared to other sampling methods when dealing with smaller populations.
  • Preliminary research: We can use this method in pilot studies to gain initial insights into a population before conducting more extensive research.
  • Establishing a benchmark: Simple random sampling can provide a representative sample to serve as a reference point for future studies or to track changes over time.
  • Validating results: This method can be used to validate results obtained from other sampling methods or to cross-check findings from previous research.
  • Limited resources: This technique can efficiently obtain a representative sample even when resources such as time, money, or personnel are limited.
However, it is not the most appropriate method for large, diverse, or geographically dispersed populations, where other probability sampling techniques like stratified sampling or cluster sampling are more suitable.

How To Do Simple Random Sampling?

To do simple random sampling, you can follow 5 steps with examples below:
5 steps to do simple random sampling with examples

Step 1: Define the Population

Identify the population from which you want to draw your sample. This could be a group of people, objects, or events that share a common characteristic.

Example: A social media platform wants to conduct a survey to understand user preferences for new features. The population would be all active users of the platform.

Step 2: Create a Sampling Frame

Develop a complete list of all individuals or items in the population. This list is called a sampling frame and should be comprehensive and up-to-date.

Example: The social media platform generates a list of all active users from their database, including their user ID numbers and email addresses.

Step 3: Assign Numbers

Assign a unique number to each individual or item in the sampling frame. This step helps in the random selection process.

Example: The platform assigns a unique number to each user on the list, starting from 1 and ending with the total number of users.

Step 4: Select the Sample

Use a random method to select the desired number of individuals or items from the sampling frame. You can use a random number generator, a random number table, or draw numbers out of a hat.

Example:The platform decides to select a sample of 1,000 users. Using a random number generator, they select 1,000 unique numbers between 1 and the total number of users. The users corresponding to these numbers are included in the sample.

Step 5: Collect Data

Once you have selected the sample, collect the necessary data from the individuals or items using appropriate data collection methods, such as surveys, interviews, or observations.

Example: The social media platform sends out an online survey to the 1,000 users selected in the sample, asking them to rate their interest in potential new features and provide feedback. The platform then collects and analyzes the responses to inform their product development decisions.

By following these steps, you can effectively use simple random sampling to obtain a representative sample from a population, allowing you to draw conclusions that can be generalized to the entire population.

Simple Random Sampling in Action

Simple random sampling is a versatile tool used across various fields and industries such as market research, public health studies, education assessments, and opinion polling. To ensure the success of your research project, follow 6 tips and learn from real-world examples.

6 Best Practices for Simple Random Sampling

  • Define your population clearly: Have a clear and precise definition of the population you want to study. This helps create an accurate sampling frame.
  • Use a reliable source for your sampling frame: Get a complete and up-to-date list of all individuals or items from a trusted source, such as databases, customer lists, or census data.
  • Assign unique identifiers: Give each individual or item a unique number or identifier to make the random selection process easier.
  • Choose the right sample size: Determine the best sample size based on your research objectives, population size, and desired precision. Use statistical formulas or consult a statistician to ensure your sample size is sufficient.
  • Use a reliable random selection method: Choose individuals or items from the sampling frame using a trusted random number generator, random number table, or other unbiased method.
  • Document your sampling process: Keep detailed records of your sampling methodology, including the population definition, sampling frame source, sample size determination, and random selection method. Transparency enhances the credibility of your research.

Case Studies of Simple Random Sampling in Various Fields

Case Study 1: Online Learning Effectiveness During COVID-19 (2020) (2)

Researchers from the Faculty of Economics at Universitas Sulawesi Barat used simple random sampling to collect data from 115 students via online questionnaires. The study concluded the online learning system during the pandemic was effective for remote learning but inefficient due to increased costs compared to offline lectures.

Case Study 2: Credit Card Practices Among Working Adults (2019) (3)

To investigate financial knowledge and credit card practices among 100 working adults in Ipoh, Malaysia, researchers used simple random sampling. All participants had at least one credit card. Simple random sampling ensured each adult had an equal chance of selection, reducing bias and providing a representative sample. Data was analyzed to conclude about credit card practices and influencing factors.

Case Study 3: Cattle Parasite Infection Assessment (2012) (4)

Torgerson et al. used simple random sampling to estimate the average parasite eggs per gram in cattle feces. Each cow was assigned a number, and a random sample was selected for fecal testing. Equal chance of selection ensured the sample accurately represented the entire herd.

Key Takeaways

  • Simple Random Sampling (SRS): A statistical method ensuring each population member has an equal chance of selection, minimizing bias.
  • Versatility: Widely applicable in various fields including market research, opinion polling, and medical studies, enhancing the credibility of findings.
  • Method Schemes: Utilizes two main approaches—without replacement (SRSWOR) and with replacement (SRSWR)—to cater to different research needs.
  • Ideal Conditions: Most effective for homogeneous, smaller populations and situations where resources are limited.
  • Bias Reduction: Helps in reducing both selection and sampling biases, thereby facilitating more accurate and generalizable research outcomes.

Conclusion

While simple random sampling offers a straightforward and effective way to reduce bias and enhance the credibility of research findings, it also comes with limitations such as the need for a comprehensive sampling frame and potential impracticality for large or geographically dispersed populations. Researchers must weigh these pros and cons against their specific study requirements and consider alternative sampling methods if necessary. By adhering to best practices in defining populations, choosing appropriate sample sizes, and using reliable random selection methods, researchers can leverage simple random sampling to obtain high-quality data that is both representative and insightful.

FAQs

1. What is the best random sampling method?
Simple random sampling stands out as one of the most efficient probability sampling methods, optimizing time and resources. It ensures each member of the population is chosen solely by chance, making it a reliable approach for data collection.
2. Is simple random sampling qualitative or quantitative?
Simple random sampling is quantitative, commonly employed in quantitative studies utilizing survey instruments. Qualitative sampling methods include non-probability techniques such as convenience sampling, snowball sampling, purposive sampling, and quota sampling.
3. What Is The Difference Between Simple Random Sampling And Other Probability Sampling Methods?
Simple Random Sampling randomly selects individuals from the population, ensuring high representativeness for homogeneous populations. Other probability sampling methods like Cluster, Stratified, and Systematic Sampling employ different sample selection techniques for diverse target populations. Each method has specific advantages and limitations based on population characteristics and research goals. Learn more about other probability sampling methods and their distinctions.
4. Is simple random sampling the easiest?
Simple random sampling is straightforward and accessible, requiring minimal prior knowledge or planning. Its ease of implementation makes it a popular choice for researchers of varying expertise levels. However, its suitability depends on the characteristics of the population being studied, and more complex sampling methods may be necessary in certain cases.
5. How accurate is simple random sampling?
Considered by many as the most precise method for sampling a population, simple random sampling prevents research bias, ensuring an impartial representation of the population.
6. Is simple random sampling better than stratified?
The choice between simple random and stratified sampling hinges on factors such as population diversity and research goals. While simple random sampling is straightforward, stratified sampling may offer increased precision, especially with heterogeneous populations.

References

  • Tiwari, A. (2023). A Study on Some Design Based and Model Based Estimation Procedures in Sample Surveys.
  • Bahasoan, A. N., Ayuandiani, W., Mukhram, M., & Rahmat, A. (2020). Effectiveness of online learning in pandemic COVID-19. International journal of science, technology & management, 1(2), 100-106.
  • Jusoh, Z., & Lin, L. Y. (2012). Personal financial knowledge and attitude towards credit card practices among working adults in Malaysia. International Journal of Business and Social Science, 3(7).
  • Torgerson, P. R., Paul, M., & Lewis, F. I. (2012). The contribution of simple random sampling to observed variations in faecal egg counts. Veterinary parasitology, 188(3-4), 397-401.
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