How to Calculate Sample Size

One of the most challenging things for marketers and researchers is determining and defining the right sample size. Generating accurate data means researchers can gain insights into how the overall population responds to companies, clinical trials and much more. Here’s our guide on how to calculate sample size.

What is a sample size?

The sample size is the term used to describe the number of participants taking part in a research project. In most cases, subjects are selected from a range of people and are representative of the general population during a study. It would be impossible to ask every member of the public to take part in a study, so sample sizes are crucial if you want to generate credible results.

For example, if a new estate agency wanted to find out what peoples most significant pain points are when selling their home, they could survey people who have recently sold their house. Now, it would be impractical to study every single person, but by choosing a smaller number that represents the age, gender, profession and location of your target market can offer a good representation of the general public.

Sample size definitions

When companies conduct market research, they refer to the sample size as “n”. This represents the number of participants in the study. It’s important to remember at this point that the size of your sample can influence:

• How accurate the estimates are.
• The conclusions you can draw from them.

For example, if a burger company wanted to get feedback on people’s favourite current burger chain, they’d need to make sure they were targeting the right people to get a comprehensive view. If they fail to choose the right participants, they could be left with vegans or vegetarians, so the results wouldn’t reflect the general population.

Similarly, suppose the company conducted their research in an area with a high population of meat-eaters. In that case, it doesn’t mean they’d achieve the same results in the next town, which might have higher level of vegetarians and vegans.

For anyone undertaking primary research there are some vital definitions you need to know, including margin of error, confidence level, population size, sample ratio definition and sample size:

Margin of error

The margin of error refers to the amount of accuracy your study requires. You might have heard of it as the confidence interval, but it’s the plus or minus number that comes with a percentage. The larger your margin of error is, the less likely it is that your study reflects the general population.

Confidence level

The confidence level refers to how sure you can be that the margin of error contains the right proportion. What this means is that if you repeated a study and used the range each time to make your calculations, the actual value should lie inside the same ranges 95% of the time.

Population size

Population size is the total amount of people in the group you’re trying to study. For example, if you’re conducting a study about a city, the population size would be the total number of residents living there.

Sample size

Sample size is the number of people you need to estimate an accurate analysis of the whole population. If people don’t respond to your survey or research, you’ll need to increase your sample size to gauge a precise calculation.

Why is sample size important?

When you conduct research, it is often impractical to get answers from every member of your population. This might be plausible if you are surveying your employees, but it can be logistically or economically impractical to fully survey customers and impossible to cover the general public. Instead, you should take a sample size to generate an accurate impression of what the entire community might think. For this reason, the sample size is critical to any research study.

Choosing the correct sample size enables you to get an idea of what the general population thinks, and it adds credibility to your study. Research studies that use a small sample size are a waste of time and money because no useful conclusions can be drawn from them.

For example, if a medical research trial tested a new medication on 50 people, and there were no side effects, it doesn’t mean the drug is safe. An individual with a medical condition could receive treatment and become very unwell. Not only does a large sample size make your results more realistic, but it can also protect you from legal action.

How to determine sample size

Now for the most important part; how do you determine sample size? Well, there are three ways you can go about this, including using a sample size from a similar study, doing it manually or using a calculator.

Conduct a census

If your population size is relatively small, you might be able to take a census instead of using a sample. Keeping track of a team of 100 people is relatively easy, so you could conduct a census and create a statistically robust study.

However, if your study involves thousands of people, then it’s almost impossible to survey everyone, let alone make sure each person answers the questions.

Use a similar study

There are so many studies around; it’s more than likely one will be similar to yours. You can use their sample size to create your own, but be aware that if the researchers didn’t do their calculations correctly, it would impact the credibility of your study.

The best way to find similar studies is by looking at the best academic research databases.

Refer to a table

While some studies are specifically detailed, others are more general. If your research is measuring results from clinical or other popular research fields, there’s a chance that you’ll be able to generate a sample size by referring to a table.

DIY

If you have strong maths skills, then you might be able to calculate your sample size formula manually. There are many different formulas, including Cochran’s.

• Use it to calculate an accurate sample size
• Most appropriate for large population sizes

If your population size is ambiguous, you can use Slovin’s formula. Calculating your sample size is difficult, and even statisticians struggle with manual calculations.

Most people struggle with how to calculate sample size in research. For accuracy, we recommend you use a calculator.

Use a sample size calculator

Perhaps the easiest way to define your sample size is by using a calculator. Smart Survey’s calculator allows you to input the data for your population size, confidence level and margin of error. And a calculator means you don’t need to worry about the maths, because everything is done for you. You can find our sample size calculator here.

The bottom line

It isn’t easy, but once you know how to calculate sample size, you can conduct studies to evaluate how your team is performing, the general attitude towards your business and highlight your target audience.

If you found this article useful, check out our guide to carrying out a survey. The six-step guide offers a comprehensive look at the best ways to conduct online surveys and includes a section on reporting your results.