Your guide to simple random sampling

There are a few ways to find out what a population thinks about something. 

If the population is small, say a school class or department of a small company, it shouldn’t be too much trouble to ask everyone their thoughts on the matter. With a simple questionnaire and a few hours to analyze the answers from everyone, you will have a definitive answer. 

But what if you want to know what the population of a town thinks? Or a country? In this case, you can’t ask everyone, so it’s time to reduce the numbers. It’s time to think about sampling—selecting a few people to speak to and represent the group as a whole. 

How can you make sure their answers reflect the wider population? Random selection. Congratulations, you’ve just found one of the most statistically valid study methods: simple random sampling.

What is simple random sampling?

Simple random sampling is a way of selecting a representative subset, or sample, from a larger population. 

The key word here is random. To be valid and worthy of the term, when you’re carrying out simple random sampling, every member of the population needs to have an equal chance of being chosen. This randomness helps make sure that the sample accurately reflects the bigger picture, making it a valuable tool for researchers, analysts, and anyone who wants to understand a group without surveying everyone.

 When to use simple random sampling

Here are some situations where simple random sampling works well:

Opinion polls

Few situations are more vital than elections for getting a good picture of public opinion. Opinion polls are widely used to get a flavor of how the electorate is thinking, and simple random sampling helps do that. Samples with participants from different backgrounds, age groups, and political leanings give a more accurate picture of overall voter sentiment.

Market research

Want to open a specialist restaurant in your local town? Find out if there is enough demand for what you intend to offer by taking a simple random sample of the population and asking about dining preferences. With a well-designed questionnaire and a good-sized sample, you can make sure of your plans before you start. A good-sized sample is so important because it directly affects the accuracy of your results. The larger the sample, the smaller the margin of error and the more confident you can be that your findings reflect the population as a whole.

Quality control

Modern factories can produce huge amounts of products every day, but how do you ensure the quality stays up to standard? Take a simple random sample to pass an inspection, either on a single product basis or in batches, depending on the output. This should give a good picture of how the production line is working and, if done correctly, can point to where any flaws are coming from.

Medical studies

If you’re conducting drug trials and start with a population list of those who have the condition your drug is designed to work on, simple random sampling can create a list of participants for you—one that reflects the broader population. In this domain, regulatory guidelines often mandate specific sample sizes to ensure that safety and efficacy conclusions are reliable, making it important to balance randomness with the required number of participants.

 How to create a simple random sample

Ready to use simple random sampling? Here’s how to go about it:

Define the population

The first step is to define the population you want to study. This could be anywhere from a school year to a nation. A key consideration is ensuring you have access to every member of that population so your random selections can be valid and contactable. It’s also important to factor in ethical considerations, such as obtaining consent from participants and safeguarding their privacy throughout the process.

Create a sampling frame

This is just another way of saying a list of everyone in your population. It could be a physical list, a database, or any other way of storing and organizing data.

Assign a unique identifier

Give each member of your population a unique number. This could be a pre-existing piece of data like a National Insurance/Social Security number or one you allocate. This gives you your units to select from.

Define your sample size

The sample size you need will depend on your population size, confidence level, and the interval required for the results. In statistics, confidence is another way of saying probability. There are many statistically solid ways to define your confidence interval and confidence level, but for the sake of this article, let’s consider 10% of your population size as a good marker.

Another important consideration is population variance—how much individuals in the population are expected to differ in their responses. The greater the variance, the larger your sample size needs to be to achieve reliable results. Statistical techniques such as power analysis can help determine the minimum sample size required to detect an effect with a given level of confidence, ensuring your sample is both efficient and robust.

Make your selection

This is where you choose your participants at random. Select the number of participants you need from your sampling frame using a statistically sound random number generator. Using a reliable generator ensures your selection is truly random and not influenced by patterns or biases, which is important for maintaining the integrity of your sample. 

Remember: The key to simple random sampling is ensuring every member of the population has a completely equal chance of being chosen.

Advantages and disadvantages of simple random sampling

Advantages:

It’s unbiased

Everyone has an equal chance of being selected, reducing the risk of selection bias in your results.

It’s easy to understand

The concept is straightforward and doesn't require complex software or methods to get results.

Disadvantages:

Practical challenges

Simple random sampling needs a complete and robust sampling frame. Without this, you can’t be assured of a representative sample.

Unequal representation of strata

If your population has distinct strata (subgroups like age, gender, or ethnicity), simple random sampling might not guarantee a proportional representation of each group in your sample. This can be problematic if you're trying to understand matters specific to these subgroups.

Simple random sampling vs. other sampling methods

Is simple random sampling the method to use for your study? Here’s a brief rundown of some other methods to compare:

Systematic sampling

This is a probability (based on random chance) method where selections are made from a random starting point but at a fixed interval. This means starting at a randomly chosen point but picking every, for example, 10th person on a list and continuing until you have the sample size you need. It can be easier to implement than simple random sampling, but it can be prone to bias if there are underlying patterns in the data.

Stratified sampling

With stratified sampling, you divide your population into subgroups (strata) based on relevant characteristics, then use a probability method (like simple random sampling) to sample from each subgroup. This can help your sample to reflect the proportions of those subgroups in the population.

Cluster sampling

In cluster sampling, you divide your population into smaller groups called clusters and randomly select from these clusters to get your sample. This method is useful when a population is large or geographically dispersed, but it depends on each cluster being representative of the population as a whole.

Making sense of simple random sampling

When done correctly, simple random sampling is a relatively reliable and unbiased way to create a group of study participants. By understanding its strengths and limitations, you can decide whether it's the right tool for your research. 

Remember, the key is choosing a sampling method that helps you gather the most accurate and representative information possible for your work.