Simple Random Sample: Definition & Examples

KEY TAKEAWAYS

• With simple random sampling (SRS), every element has the same probability of being selected and the sample is representative of the whole population. 
• SRS is useful for data analysis and can be applied in many situations, including surveys and experiments. 
• There are several types of sampling that can be used in conjunction with SRS to minimize bias and make data analysis more effective. These include stratified sampling, cluster sampling, and systematic sampling. 
• For data analysis, SRS is useful because it helps ensure the sample is representative of the whole population and minimizes bias.

What Is a Simple Random Sample?

A sample is a subset of data selected from an entire population. A simple random sample (SRS) is a statistical sampling technique that uses chance as a factor to decide which data points are included in the sample.

In SRS, every element has the same probability sampling. There are other types of sampling, such as stratified and cluster sampling, that are also useful. These types of sampling are often used in conjunction with SRS to minimize bias and make data analysis more effective.

Random sampling helps ensure that the sample is representative of the entire population, and it minimizes bias so that data analysis is more effective and reliable.

For example, if a survey company wants to survey all major cities in the United States, it would be nearly impossible to survey each city.

Instead, the survey company could choose a representative sample of cities, and the sample would likely reflect the sample population.

Simple Random Sampling Formula

There are a few ways to select a simple random sample. One method is to use a table of random numbers. This table can be found in most statistical textbooks, or you can generate your own using a random number generator.

To use a table of random numbers, first identify the population you want to select from and the number of individuals you want in your sample. Then, find a table that has at least as many rows as there are members in your population and at least as many columns as you need for your sample size.

Random Sampling with Replacement

Once you’ve selected your first individual from the population using the table of random numbers, you replace them back into the population before selecting the next individual. The random sampling process repeats until you have the desired number of individuals in your sample.

Simple random sampling with replacement is used when you want to:

Estimate a population mean

Calculate a population variance

The formula for this is:

Simple Random Sampling without Replacement

When you select an individual from the population and remove them from the pool of available individuals, this is called sampling without replacement. Once an individual has been selected, they cannot be selected again.

This method is used when you want to:

• Estimate a population proportion
• Calculate a population standard deviation

The formula for this is: 

Simple Random Sampling Methods

There are a few different methods that can be used to select a simple random sample:

• Random number table
• Random number generator
• Systematic sampling
• Stratified sampling

Random Number Table

The most common method of selecting a simple random sample is to use a table of random numbers. To do this, you first need to identify the population you want to select from and the number of individuals you want in your sample. 

Then, find a table that has at least as many rows as there are members in your population and at least as many columns as you need for your sample size.

Random Number Generator

Another option for selecting a simple random sample is to use a random number generator. This works by hand or with random number generator software.

To do this, you first need to identify the population you want to select from and the number of individuals you want in your sample.

Then, generate a random number for each member of the population. The numbers can be generated in any order, but they should be unique. Random number generator software will take care of this for you.

Systematic Sampling

Systematic sampling is a method of selecting a simple random sample in which the members of the population are listed in some order and every Nth participant gets selected, where N is the desired sample size.

This method is used when it is difficult to randomly select members of the population, such as when selecting people from a phone book.

Stratified Sampling

The stratified sampling strategy is a method of selecting a simple random sample in which the population is divided into subgroups, or strata, and a separate random sample is selected from each stratum.

This method is used when the population is homogeneous strata, or when you want to ensure that the stratified sample is representative of the different subset of participants

How to Perform Simple Random Sampling

When conducting simple random sampling, remember to get the total number of elements in the population, select the sample size, and then choose the elements from the population at random. 

To determine which elements are included in the sample, you can use a random number generator or a random selection method. The following example illustrates how to perform simple random sampling. 

A researcher wants to survey 10 people from a population of 100 respondents. The researcher gets the total number of elements in the population (100), selects the sample size (10), and draws numbers from 1 to 10. The first person to be surveyed is 1, the second person is 2, the third person is 3, and so on.

Advantages of Simple Random Samples

Some of the benefits of simple random samples include:

Representativeness

Because every element has an equal chance of being selected, simple random samples are likely to reflect the whole population.

Minimizing Sampling Bias

Since every element in the population has an equal chance of being selected, researchers are less likely to introduce bias as they would in other types of sampling.

Ease of Implementation

Because simple random sampling doesn’t involve too many calculations, researchers can easily understand and implement the technique. The process is even easier when using a sample size calculator.

Wide Applicability

Simple random sampling applies to a wide variety of situations, including random surveys and experiments. Your method of lottery determines your target sample size.

Disadvantages of Simple Random Samples

Some of the drawbacks of simple random samples include:

Smaller Sample Sizes

With SRS, the larger the population size, the smaller the random sampling size will be. Smaller sample sizes are often less representative of the population and are usually not as accurate for data analysis.

Difficulty in Obtaining Representative Samples

In order for a sample to be representative of the population, the researcher must be able to pick the correct sample size and must be able to select elements at random.

If the population of participants is limited or you have an incomplete list, you will get a sampling error.

Your sampling of people needs to be complete and balanced. The goal is to achieve an unbiased sample with a complete list of residents.

Example of Simple Random Sampling

Say you want to survey people about their eating habits. You could survey everyone in a particular city, but that sample may not be representative of all cities in the country. 

You could instead survey people from 10 different cities, but that sample may not be representative of the eating habits of the entire country. With simple random sampling, you could select a sample of people from each of the 10 cities at random.

That sample would likely be representative of eating habits across the country. Simple random sampling has many applications, including surveys, experiments, and data analysis. It’s often used in conjunction with other sampling methods to maximize its effectiveness and reduce bias.

Summary

Simple random sampling is a method of selecting a sample from a population in which each member of the population has an equal chance of being selected. 

This type of sampling is used when you want to estimate a population mean or proportion. 

When selecting a simple random sample, it is important to make sure that the sample is representative of the population. This works by stratifying the population if it is heterogeneous or by using a random number generator to select the members of the population.