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Determining sample size: how to make sure you get the correct sample size.

16 min read Sample size can make or break your research project. Here’s how to master the delicate art of choosing the right sample size.

What is sample size?

Sample size is the beating heart of any research project. It’s the invisible force that gives life to your data, making your findings robust, reliable and believable.

Sample size is what determines if you see a broad view or a focus on minute details; the art and science of correctly determining it involves a careful balancing act. Finding an appropriate sample size demands a clear understanding of the level of detail you wish to see in your data and the constraints you might encounter along the way.

Remember, whether you’re studying a small group or an entire population, your findings are only ever as good as the sample you choose.

Free eBook: Empower your market research efforts today

Let’s delve into the world of sampling and uncover the best practices for determining sample size for your research.

How to determine sample size

“How much sample do we need?” is one of the most commonly-asked questions and stumbling points in the early stages of  research design . Finding the right answer to it requires first understanding and answering two other questions:

How important is statistical significance to you and your stakeholders?

What are your real-world constraints.

At the heart of this question is the goal to confidently differentiate between groups, by describing meaningful differences as statistically significant.  Statistical significance  isn’t a difficult concept, but it needs to be considered within the unique context of your research and your measures.

First, you should consider when you deem a difference to be meaningful in your area of research. While the standards for statistical significance are universal, the standards for “meaningful difference” are highly contextual.

For example, a 10% difference between groups might not be enough to merit a change in a marketing campaign for a breakfast cereal, but a 10% difference in efficacy of breast cancer treatments might quite literally be the difference between life and death for hundreds of patients. The exact same magnitude of difference has very little meaning in one context, but has extraordinary meaning in another. You ultimately need to determine the level of precision that will help you make your decision.

Within sampling, the lowest amount of magnification – or smallest sample size – could make the most sense, given the level of precision needed, as well as timeline and budgetary constraints.

If you’re able to detect statistical significance at a difference of 10%, and 10% is a meaningful difference, there is no need for a larger sample size, or higher magnification. However, if the study will only be useful if a significant difference is detected for smaller differences – say, a difference of 5% — the sample size must be larger to accommodate this needed precision. Similarly, if 5% is enough, and 3% is unnecessary, there is no need for a larger statistically significant sample size.

You should also consider how much you expect your responses to vary. When there isn’t a lot of variability in response, it takes a lot more sample to be confident that there are statistically significant differences between groups.

For instance, it will take a lot more sample to find statistically significant differences between groups if you are asking, “What month do you think Christmas is in?” than if you are asking, “How many miles are there between the Earth and the moon?”. In the former, nearly everybody is going to give the exact same answer, while the latter will give a lot of variation in responses. Simply put, when your variables do not have a lot of variance, larger sample sizes make sense.

Statistical significance

The likelihood that the results of a study or experiment did not occur randomly or by chance, but are meaningful and indicate a genuine effect or relationship between variables.

Magnitude of difference

The size or extent of the difference between two or more groups or variables, providing a measure of the effect size or practical significance of the results.

Actionable insights

Valuable findings or conclusions drawn from  data analysis  that can be directly applied or implemented in decision-making processes or strategies to achieve a particular goal or outcome.

It’s crucial to understand the differences between the concepts of “statistical significance”, “magnitude of difference” and “actionable insights” – and how they can influence each other:

• Even if there is a statistically significant difference, it doesn’t mean the magnitude of the difference is large: with a large enough sample, a 3% difference could be statistically significant
• Even if the magnitude of the difference is large, it doesn’t guarantee that this difference is statistically significant: with a small enough sample, an 18% difference might not be statistically significant
• Even if there is a large, statistically significant difference, it doesn’t mean there is a story, or that there are actionable insights

There is no way to guarantee statistically significant differences at the outset of a study – and that is a good thing.

Even with a sample size of a million, there simply may not be any differences – at least, any that could be described as statistically significant. And there are times when a lack of significance is positive.

Imagine if your main competitor ran a multi-million dollar ad campaign in a major city and a huge pre-post study to detect campaign effects, only to discover that there were no statistically significant differences in  brand awareness . This may be terrible news for your competitor, but it would be great news for you.

With Stats iQ™ you can analyze your research results and conduct significance testing

As you determine your sample size, you should consider the real-world constraints to your research.

Factors revolving around timings, budget and target population are among the most common constraints, impacting virtually every study. But by understanding and acknowledging them, you can definitely navigate the practical constraints of your research when pulling together your sample.

Timeline constraints

Gathering a larger sample size naturally requires more time. This is particularly true for elusive audiences, those hard-to-reach groups that require special effort to engage. Your timeline could become an obstacle if it is particularly tight, causing you to rethink your sample size to meet your deadline.

Budgetary constraints

Every sample, whether large or small, inexpensive or costly, signifies a portion of your budget. Samples could be like an open market; some are inexpensive, others are pricey, but all have a price tag attached to them.

Population constraints

Sometimes the individuals or groups you’re interested in are difficult to reach; other times, they’re a part of an extremely small population. These factors can limit your sample size even further.

What’s a good sample size?

A good sample size really depends on the context and goals of the research. In general, a good sample size is one that accurately represents the population and allows for reliable statistical analysis.

Larger sample sizes are typically better because they reduce the likelihood of  sampling errors  and provide a more accurate representation of the population. However, larger sample sizes often increase the impact of practical considerations, like time, budget and the availability of your audience. Ultimately, you should be aiming for a sample size that provides a balance between statistical validity and practical feasibility.

4 tips for choosing the right sample size

Choosing the right sample size is an intricate balancing act, but following these four tips can take away a lot of the complexity.

1) Start with your goal

The foundation of your research is a clearly defined goal. You need to determine what you’re trying to understand or discover, and use your goal to guide your  research methods  – including your sample size.

If your aim is to get a broad overview of a topic, a larger, more diverse sample may be appropriate. However, if your goal is to explore a niche aspect of your subject, a smaller, more targeted sample might serve you better. You should always align your sample size with the objectives of your research.

2) Know that you can’t predict everything

Research is a journey into the unknown. While you may have hypotheses and predictions, it’s important to remember that you can’t foresee every outcome – and this uncertainty should be considered when choosing your sample size.

A larger sample size can help to mitigate some of the risks of unpredictability, providing a more diverse range of data and potentially more accurate results. However, you shouldn’t let the fear of the unknown push you into choosing an impractically large sample size.

3) Plan for a sample that meets your needs and considers your real-life constraints

Every research project operates within certain boundaries – commonly budget, timeline and the nature of the sample itself. When deciding on your sample size, these factors need to be taken into consideration.

Be realistic about what you can achieve with your available resources and time, and always tailor your sample size to fit your constraints – not the other way around.

4) Use best practice guidelines to calculate sample size

There are many established guidelines and formulas that can help you in determining the right sample size.

The easiest way to define your sample size is using a  sample size calculator , or you can use a manual sample size calculation if you want to test your math skills. Cochran’s formula is perhaps the most well known equation for calculating sample size, and widely used when the population is large or unknown.

Beyond the formula, it’s vital to consider the confidence interval, which plays a significant role in determining the appropriate sample size – especially when working with a  random sample  – and the sample proportion. This represents the expected ratio of the target population that has the characteristic or response you’re interested in, and therefore has a big impact on your correct sample size.

If your population is small, or its variance is unknown, there are steps you can still take to determine the right sample size. Common approaches here include conducting a small pilot study to gain initial estimates of the population variance, and taking a conservative approach by assuming a larger variance to ensure a more representative sample size.

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With this front-to-back guide, you’ll discover the latest strategies and best practices that are defining effective market research. Learn about practical insights and real-world applications that are demonstrating the value of research in driving business growth and innovation.

Learn how to determine sample size

To choose the correct sample size, you need to consider a few different factors that affect your research, and gain a basic understanding of the statistics involved. You’ll then be able to use a sample size formula to bring everything together and sample confidently, knowing that there is a high probability that your survey is statistically accurate.

The steps that follow are suitable for finding a sample size for continuous data – i.e. data that is counted numerically. It doesn’t apply to categorical data – i.e. put into categories like green, blue, male, female etc.

Stage 1: Consider your sample size variables

Before you can calculate a sample size, you need to determine a few things about the target population and the level of accuracy you need:

1. Population size

How many people are you talking about in total? To find this out, you need to be clear about who does and doesn’t fit into your group. For example, if you want to know about dog owners, you’ll include everyone who has at some point owned at least one dog. (You may include or exclude those who owned a dog in the past, depending on your research goals.) Don’t worry if you’re unable to calculate the exact number. It’s common to have an unknown number or an estimated range.

2. Margin of error (confidence interval)

Errors are inevitable – the question is how much error you’ll allow. The margin of error , AKA confidence interval, is expressed in terms of mean numbers. You can set how much difference you’ll allow between the mean number of your sample and the mean number of your population. If you’ve ever seen a political poll on the news, you’ve seen a confidence interval and how it’s expressed. It will look something like this: “68% of voters said yes to Proposition Z, with a margin of error of +/- 5%.”

3. Confidence level

This is a separate step to the similarly-named confidence interval in step 2. It deals with how confident you want to be that the actual mean falls within your margin of error. The most common confidence intervals are 90% confident, 95% confident, and 99% confident.

4. Standard deviation

This step asks you to estimate how much the responses you receive will vary from each other and from the mean number. A low standard deviation means that all the values will be clustered around the mean number, whereas a high standard deviation means they are spread out across a much wider range with very small and very large outlying figures. Since you haven’t yet run your survey, a safe choice is a standard deviation of .5 which will help make sure your sample size is large enough.

Stage 2: Calculate sample size

Now that you’ve got answers for steps 1 – 4, you’re ready to calculate the sample size you need. This can be done using an  online sample size calculator  or with paper and pencil.

1. Find your Z-score

Next, you need to turn your confidence level into a Z-score. Here are the Z-scores for the most common confidence levels:

• 90% – Z Score = 1.645
• 95% – Z Score = 1.96
• 99% – Z Score = 2.576

If you chose a different confidence level, use this  Z-score table  (a resource owned and hosted by SJSU.edu) to find your score.

2. Use the sample size formula

Plug in your Z-score, standard of deviation, and confidence interval into the  sample size calculator  or use this sample size formula to work it out yourself:

This equation is for an unknown population size or a very large population size. If your population is smaller and known, just  use the sample size calculator.

What does that look like in practice?

Here’s a worked example, assuming you chose a 95% confidence level, .5 standard deviation, and a margin of error (confidence interval) of +/- 5%.

((1.96)2 x .5(.5)) / (.05)2

(3.8416 x .25) / .0025

.9604 / .0025

385 respondents are needed

Voila! You’ve just determined your sample size.

eBook: 2022 Market Research Global Trends Report

Related resources

Convenience sampling 15 min read, non-probability sampling 17 min read, probability sampling 8 min read, stratified random sampling 13 min read, simple random sampling 10 min read, sampling methods 15 min read, sampling and non-sampling errors 10 min read, request demo.

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Sample Size Determination: Definition, Formula, and Example

Are you ready to survey your research target? Research surveys help you gain insights from your target audience. The data you collect gives you insights to meet customer needs, leading to increased sales and customer loyalty. Sample size calculation and determination are imperative to the researcher to determine the right number of respondents, keeping in mind the research study’s quality.

So, how should you do the sample size determination? How do you know who should get your survey? How do you decide on the number of the target audience?

Sending out too many surveys can be expensive without giving you a definitive advantage over a smaller sample. But if you send out too few, you won’t have enough data to draw accurate conclusions. 

Knowing how to calculate and determine the appropriate sample size accurately can give you an edge over your competitors. Let’s take a look at what a good sample includes. Also, let’s look at the sample size calculation formula so you can determine the perfect sample size for your next survey.

What is Sample Size?

‘Sample size’ is a market research term used for defining the number of individuals included in conducting research. Researchers choose their sample based on demographics, such as age, gender questions , or physical location. It can be vague or specific. 

For example, you may want to know what people within the 18-25 age range think of your product. Or, you may only require your sample to live in the United States, giving you a wide population range. The total number of individuals in a particular sample is the sample size.

What is sample size determination?

Sample size determination is the process of choosing the right number of observations or people from a larger group to use in a sample. The goal of figuring out the sample size is to ensure that the sample is big enough to give statistically valid results and accurate estimates of population parameters but small enough to be manageable and cost-effective.

In many research studies, getting information from every member of the population of interest is not possible or useful. Instead, researchers choose a sample of people or events that is representative of the whole to study. How accurate and precise the results are can depend a lot on the size of the sample.

Choosing the statistically significant sample size depends on a number of things, such as the size of the population, how precise you want your estimates to be, how confident you want to be in the results, how different the population is likely to be, and how much money and time you have for the study. Statistics are often used to figure out how big a sample should be for a certain type of study and research question.

Figuring out the sample size is important in ensuring that research findings and conclusions are valid and reliable.

Why do you need to determine the sample size?

Let’s say you are a market researcher in the US and want to send out a survey or questionnaire . The survey aims to understand your audience’s feelings toward a new cell phone you are about to launch. You want to know what people in the US think about the new product to predict the phone’s success or failure before launch.

Hypothetically, you choose the population of New York, which is 8.49 million. You use a sample size determination formula to select a sample of 500 individuals that fit into the consumer panel requirement. You can use the responses to help you determine how your audience will react to the new product.

However, determining a sample size requires more than just throwing your survey at as many people as possible. If your estimated sample sizes are too big, it could waste resources, time, and money. A sample size that’s too small doesn’t allow you to gain maximum insights, leading to inconclusive results.

LEARN ABOUT: Survey Sample Sizes

What are the terms used around the sample size?

Before we jump into sample size determination, let’s take a look at the terms you should know:

1. Population size: 

Population size is how many people fit your demographic. For example, you want to get information on doctors residing in North America. Your population size is the total number of doctors in North America. 

Don’t worry! Your population size doesn’t always have to be that big. Smaller population sizes can still give you accurate results as long as you know who you’re trying to represent.

2. Confidence level: 

The confidence level tells you how sure you can be that your data is accurate. It is expressed as a percentage and aligned to the confidence interval. For example, if your confidence level is 90%, your results will most likely be 90% accurate.

3. The margin of error (confidence interval): 

There’s no way to be 100% accurate when it comes to surveys. Confidence intervals tell you how far off from the population means you’re willing to allow your data to fall. 

A margin of error describes how close you can reasonably expect a survey result to fall relative to the real population value. Remember, if you need help with this information, use our margin of error calculator .

4. Standard deviation: 

Standard deviation is the measure of the dispersion of a data set from its mean. It measures the absolute variability of a distribution. The higher the dispersion or variability, the greater the standard deviation and the greater the magnitude of the deviation. 

For example, you have already sent out your survey. How much variance do you expect in your responses? That variation in response is the standard deviation.

Sample size calculation formula – sample size determination

With all the necessary terms defined, it’s time to learn how to determine sample size using a sample calculation formula.

Your confidence level corresponds to a Z-score. This is a constant value needed for this equation. Here are the z-scores for the most common confidence levels:

90% – Z Score = 1.645

95% – Z Score = 1.96

99% – Z Score = 2.576

If you choose a different confidence level, various online tools can help you find your score.

Necessary Sample Size = (Z-score)2 * StdDev*(1-StdDev) / (margin of error)2

Here is an example of how the math works, assuming you chose a 90% confidence level, .6 standard deviation, and a margin of error (confidence interval) of +/- 4%.

((1.64)2 x .6(.6)) / (.04)2

( 2.68x .0.36) / .0016

.9648 / .0016

603 respondents are needed, and that becomes your sample size.

Free Sample Size Calculator

How is a sample size determined?

Determining the right sample size for your survey is one of the most common questions researchers ask when they begin a market research study. Luckily, sample size determination isn’t as hard to calculate as you might remember from an old high school statistics class.

Before calculating your sample size, ensure you have these things in place:

Goals and objectives: 

What do you hope to do with the survey? Are you planning on projecting the results onto a whole demographic or population? Do you want to see what a specific group thinks? Are you trying to make a big decision or just setting a direction? 

Calculating sample size is critical if you’re projecting your survey results on a larger population. You’ll want to make sure that it’s balanced and reflects the community as a whole. The sample size isn’t as critical if you’re trying to get a feel for preferences. 

For example, you’re surveying homeowners across the US on the cost of cooling their homes in the summer. A homeowner in the South probably spends much more money cooling their home in the humid heat than someone in Denver, where the climate is dry and cool. 

For the most accurate results, you’ll need to get responses from people in all US areas and environments. If you only collect responses from one extreme, such as the warm South, your results will be skewed.

Precision level: 

How close do you want the survey results to mimic the true value if everyone responded? Again, if this survey determines how you’re going to spend millions of dollars, then your sample size determination should be exact. 

The more accurate you need to be, the larger the sample you want to have, and the more your sample will have to represent the overall population. If your population is small, say, 200 people, you may want to survey the entire population rather than cut it down with a sample.

Confidence level: 

Think of confidence from the perspective of risk. How much risk are you willing to take on? This is where your Confidence Interval numbers become important. How confident do you want to be — 98% confident, 95% confident? 

Understand that the confidence percentage you choose greatly impacts the number of completions you’ll need for accuracy. This can increase the survey’s length and how many responses you need, which means increased costs for your survey. 

Knowing the actual numbers and amounts behind percentages can help make more sense of your correct sample size needs vs. survey costs. 

For example, you want to be 99% confident. After using the sample size determination formula, you find you need to collect an additional 1000 respondents. 

This, in turn, means you’ll be paying for samples or keeping your survey running for an extra week or two. You have to determine if the increased accuracy is more important than the cost.

Population variability: 

What variability exists in your population? In other words, how similar or different is the population?

If you are surveying consumers on a broad topic, you may have lots of variations. You’ll need a larger sample size to get the most accurate picture of the population. 

However, if you’re surveying a population with similar characteristics, your variability will be less, and you can sample fewer people. More variability equals more samples, and less variability equals fewer samples. If you’re not sure, you can start with 50% variability.

Response rate: 

You want everyone to respond to your survey. Unfortunately, every survey comes with targeted respondents who either never open the study or drop out halfway. Your response rate will depend on your population’s engagement with your product, service organization, or brand. 

The higher the response rate, the higher your population’s engagement level. Your base sample size is the number of responses you must get for a successful survey.

Consider your audience: 

Besides the variability within your population, you need to ensure your sample doesn’t include people who won’t benefit from the results. One of the biggest mistakes you can make in sample size determination is forgetting to consider your actual audience. 

For example, you don’t want to send a survey asking about the quality of local apartment amenities to a group of homeowners.

Select your respondents

Focus on your survey’s objectives: 

You may start with general demographics and characteristics, but can you narrow those characteristics down even more? Narrowing down your audience makes getting a more accurate result from a small sample size easier. 

For example, you want to know how people will react to new automobile technology. Your current population includes anyone who owns a car in a particular market. 

However, you know your target audience is people who drive cars that are less than five years old. You can remove anyone with an older vehicle from your sample because they’re unlikely to purchase your product.

Once you know what you hope to gain from your survey and what variables exist within your population, you can decide how to calculate sample size. Using the formula for determining sample size is a great starting point to get accurate results. 

After calculating the sample size, you’ll want to find reliable customer survey software to help you accurately collect survey responses and turn them into analyzed reports.

LEARN MORE: Population vs Sample

In sample size determination, statistical analysis plan needs careful consideration of the level of significance, effect size, and sample size. 

Researchers must reconcile statistical significance with practical and ethical factors like practicality and cost. A well-designed study with a sufficient sample size can improve the odds of obtaining statistically significant results.

To meet the goal of your survey, you may have to try a few methods to increase the response rate, such as:

• Increase the list of people who receive the survey.
• To reach a wider audience, use multiple distribution channels, such as SMS, website, and email surveys.
• Send reminders to survey participants to complete the survey.
• Offer incentives for completing the survey, such as an entry into a prize drawing or a discount on the respondent’s next order.
• Consider your survey structure and find ways to simplify your questions. The less work someone has to do to complete the survey, the more likely they will finish it. 
• Longer surveys tend to have lower response rates due to the length of time it takes to complete the survey. In this case, you can reduce the number of questions in your survey to increase responses.  

QuestionPro’s sample size calculator makes it easy to find the right sample size for your research based on your desired level of confidence, your margin of error, and the size of the population.

FREE TRIAL         LEARN MORE

Frequently Asked Questions (FAQ)

The four ways to determine sample size are: 1. Power analysis 2. Convenience sampling, 3. Random sampling , 4. Stratified sampling

The three factors that determine sample size are: 1. Effect size, 2. Level of significance 3. Power

Using statistical techniques like power analysis, the minimal detectable effect size, or the sample size formula while taking into account the study’s goals and practical limitations is the best way to calculate the sample size.

The sample size is important because it affects how precise and accurate the results of a study are and how well researchers can spot real effects or relationships between variables.

The sample size is the number of observations or study participants chosen to be representative of a larger group

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How to Determine Sample Size for a Research Study

Frankline kibuacha | apr. 06, 2021 | 3 min. read.

This article will discuss considerations to put in place when determining your sample size and how to calculate the sample size.

Confidence Interval and Confidence Level

As we have noted before, when selecting a sample there are multiple factors that can impact the reliability and validity of results, including sampling and non-sampling errors . When thinking about sample size, the two measures of error that are almost always synonymous with sample sizes are the confidence interval and the confidence level.

Confidence Interval (Margin of Error)

Confidence intervals measure the degree of uncertainty or certainty in a sampling method and how much uncertainty there is with any particular statistic. In simple terms, the confidence interval tells you how confident you can be that the results from a study reflect what you would expect to find if it were possible to survey the entire population being studied. The confidence interval is usually a plus or minus (±) figure. For example, if your confidence interval is 6 and 60% percent of your sample picks an answer, you can be confident that if you had asked the entire population, between 54% (60-6) and 66% (60+6) would have picked that answer.

Confidence Level

The confidence level refers to the percentage of probability, or certainty that the confidence interval would contain the true population parameter when you draw a random sample many times. It is expressed as a percentage and represents how often the percentage of the population who would pick an answer lies within the confidence interval. For example, a 99% confidence level means that should you repeat an experiment or survey over and over again, 99 percent of the time, your results will match the results you get from a population.

The larger your sample size, the more confident you can be that their answers truly reflect the population. In other words, the larger your sample for a given confidence level, the smaller your confidence interval.

Standard Deviation

Another critical measure when determining the sample size is the standard deviation, which measures a data set’s distribution from its mean. In calculating the sample size, the standard deviation is useful in estimating how much the responses you receive will vary from each other and from the mean number, and the standard deviation of a sample can be used to approximate the standard deviation of a population.

The higher the distribution or variability, the greater the standard deviation and the greater the magnitude of the deviation. For example, once you have already sent out your survey, how much variance do you expect in your responses? That variation in responses is the standard deviation.

Population Size

As demonstrated through the calculation below, a sample size of about 385 will give you a sufficient sample size to draw assumptions of nearly any population size at the 95% confidence level with a 5% margin of error, which is why samples of 400 and 500 are often used in research. However, if you are looking to draw comparisons between different sub-groups, for example, provinces within a country, a larger sample size is required. GeoPoll typically recommends a sample size of 400 per country as the minimum viable sample for a research project, 800 per country for conducting a study with analysis by a second-level breakdown such as females versus males, and 1200+ per country for doing third-level breakdowns such as males aged 18-24 in Nairobi.

How to Calculate Sample Size

As we have defined all the necessary terms, let us briefly learn how to determine the sample size using a sample calculation formula known as Andrew Fisher’s Formula.

• Determine the population size (if known).
• Determine the confidence interval.
• Determine the confidence level.
• Determine the standard deviation ( a standard deviation of 0.5 is a safe choice where the figure is unknown )
• Convert the confidence level into a Z-Score. This table shows the z-scores for the most common confidence levels:
• Put these figures into the sample size formula to get your sample size.

Here is an example calculation:

Say you choose to work with a 95% confidence level, a standard deviation of 0.5, and a confidence interval (margin of error) of ± 5%, you just need to substitute the values in the formula:

((1.96)2 x .5(.5)) / (.05)2

(3.8416 x .25) / .0025

.9604 / .0025

Your sample size should be 385.

Fortunately, there are several available online tools to help you with this calculation. Here’s an online sample calculator from Easy Calculation. Just put in the confidence level, population size, the confidence interval, and the perfect sample size is calculated for you.

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• A Researcher’s Guide To Statistical Significance And Sample Size Calculations

Determining Sample Size: How Many Survey Participants Do You Need?

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How to calculate a statistically significant sample size in research, determining sample size for probability-based surveys and polling studies, determining sample size for controlled surveys, determining sample size for experiments, how to calculate sample size for simple experiments, an example sample size calculation for an a/b test, what if i don’t know what size difference to expect, part iii: sample size: how many participants do i need for a survey to be valid.

In the U.S., there is a Presidential election every four years. In election years, there is a steady stream of polls in the months leading up to the election announcing which candidates are up and which are down in the horse race of popular opinion.

If you have ever wondered what makes these polls accurate and how each poll decides how many voters to talk to, then you have thought like a researcher who seeks to know how many participants they need in order to obtain statistically significant survey results.

Statistically significant results are those in which the researchers have confidence their findings are not due to chance . Obtaining statistically significant results depends on the researchers’ sample size (how many people they gather data from) and the overall size of the population they wish to understand (voters in the U.S., for example).

Calculating sample sizes can be difficult even for expert researchers. Here, we show you how to calculate sample size for a variety of different research designs.

Before jumping into the details, it is worth noting that formal sample size calculations are often based on the premise that researchers are conducting a representative survey with probability-based sampling techniques. Probability-based sampling ensures that every member of the population being studied has an equal chance of participating in the study and respondents are selected at random.

For a variety of reasons, probability sampling is not feasible for most behavioral studies conducted in industry and academia . As a result, we outline the steps required to calculate sample sizes for probability-based surveys and then extend our discussion to calculating sample sizes for non-probability surveys (i.e., controlled samples) and experiments.

Determining how many people you need to sample in a survey study can be difficult. How difficult? Look at this formula for sample size.

No one wants to work through something like that just to know how many people they should sample. Fortunately, there are several sample size calculators online that simplify knowing how many people to collect data from.

Even if you use a sample size calculator, however, you still need to know some important details about your study. Specifically, you need to know:

• What is the population size in my research?

Population size is the total number of people in the group you are trying to study. If, for example, you were conducting a poll asking U.S. voters about Presidential candidates, then your population of interest would be everyone living in the U.S.—about 330 million people.

Determining the size of the population you’re interested in will often require some background research. For instance, if your company sells digital marketing services and you’re interested in surveying potential customers, it isn’t easy to determine the size of your population. Everyone who is currently engaged in digital marketing may be a potential customer. In situations like these, you can often use industry data or other information to arrive at a reasonable estimate for your population size.

• What margin of error should you use?

Margin of error is a percentage that tells you how much the results from your sample may deviate from the views of the overall population. The smaller your margin of error, the closer your data reflect the opinion of the population at a given confidence level.

Generally speaking, the more people you gather data from the smaller your margin of error. However, because it is almost never feasible to collect data from everyone in the population, some margin of error is necessary in most studies.

• What is your survey’s significance level?

The significance level  is a percentage that tells you how confident you can be that the true population value lies within your margin of error. So, for example, if you are asking people whether they support a candidate for President, the significance level tells you how likely it is that the level of support for the candidate in the population (i.e., people not in your sample) falls within the margin of error found in your sample.

Common significance levels in survey research are 90%, 95%, and 99%.

Once you know the values above, you can plug them into a sample size formula or more conveniently an online calculator to determine your sample size.

The table below displays the necessary sample size for different sized populations and margin of errors. As you can see, even when a population is large, researchers can often understand the entire group with about 1,000 respondents.

• How Many People Should I Invite to My Study?

Sample size calculations tell you how many people you need to complete your survey. What they do not tell you, however, is how many people you need to invite to your survey. To find that number, you need to consider the response rate.

For example, if you are conducting a study of customer satisfaction and you know from previous experience that only about 30% of the people you contact will actually respond to your survey, then you can determine how many people you should invite to the survey to wind up with your desired sample size.

All you have to do is take the number of respondents you need, divide by your expected response rate, and multiple by 100. For example, if you need 500 customers to respond to your survey and you know the response rate is 30%, you should invite about 1,666 people to your study (500/30*100 = 1,666).

Sample size formulas are based on probability sampling techniques—methods that randomly select people from the population to participate in a survey. For most market surveys and academic studies, however, researchers do not use probability sampling methods. Instead they use a mix of convenience and purposive sampling methods that we refer to as controlled sampling .

When surveys and descriptive studies are based on controlled sampling methods, how should researchers calculate sample size?

When the study’s aim is to measure the frequency of something or to describe people’s behavior, we recommend following the calculations made for probability sampling. This often translates to a sample of about 1,000 to 2,000 people. When a study’s aim is to investigate a correlational relationship, however, we recommend sampling between 500 and 1,000 people. More participants in a study will always be better, but these numbers are a useful rule of thumb for researchers seeking to find out how many participants they need to sample.

If you look online, you will find many sources with information for calculating sample size when conducting a survey, but fewer resources for calculating sample size when conducting an experiment. Experiments involve randomly assigning people to different conditions and manipulating variables in order to determine a cause-and-effect relationship. The reason why sample size calculators for experiments are hard to find is simple: experiments are complex and sample size calculations depend on several factors.

The guidance we offer here is to help researchers calculate sample size for some of the simplest and most common experimental designs: t -tests, A/B tests, and chi square tests.

Many businesses today rely on A/B tests. Especially in the digital environment, A/B tests provide an efficient way to learn what kinds of features, messages, and displays cause people to spend more time or money on a website or an app.

For example, one common use of A/B testing is marketing emails. A marketing manager might create two versions of an email, randomly send one to half the company’s customers and randomly send the second to the other half of customers and then measure which email generates more sales.

In many cases , researchers may know they want to conduct an A/B test but be unsure how many people they need in their sample to obtain statistically significant results. In order to begin a sample size calculation, you need to know three things.

1. The significance level .

The significance level represents how sure you want to be that your results are not due to chance. A significance level of .05 is a good starting point, but you may adjust this number up or down depending on the aim of your study.

2. Your desired power.

Statistical tests are only useful when they have enough power to detect an effect if one actually exists. Most researchers aim for 80% power—meaning their tests are sensitive enough to detect an effect 8 out of 10 times if one exists.

3. The minimum effect size you are interested in.

The final piece of information you need is the minimum effect size, or difference between groups, you are interested in. Sometimes there may be a difference between groups, but if the difference is so small that it makes little practical difference to your business, it probably isn’t worth investigating. Determining the minimum effect size you are interested in requires some thought about your goals and the potential impact on your business. 

Once you have decided on the factors above, you can use a sample size calculator to determine how many people you need in each of your study’s conditions.

Let’s say a marketing team wants to test two different email campaigns. They set their significance level at .05 and their power at 80%. In addition, the team determines that the minimum response rate difference between groups that they are interested in is 7.5%. Plugging these numbers into an effect size calculator reveals that the team needs 693 people in each condition of their study, for a total of 1,386.

Sending an email out to 1,386 people who are already on your contact list doesn’t cost too much. But for many other studies, each respondent you recruit will cost money. For this reason, it is important to strongly consider what the minimum effect size of interest is when planning a study.    

When you don’t know what size difference to expect among groups, you can default to one of a few rules of thumb. First, use the effect size of minimum practical significance. By deciding what the minimum difference is between groups that would be meaningful, you can avoid spending resources investigating things that are likely to have little consequences for your business.

A second rule of thumb that is particularly relevant for researchers in academia is to assume an effect size of d = .4. A d = .4 is considered by some to be the smallest effect size that begins to have practical relevance . And fortunately, with this effect size and just two conditions, researchers need about 100 people per condition.

After you know how many people to recruit for your study, the next step is finding your participants. By using CloudResearch’s Prime Panels or MTurk Toolkit, you can gain access to more than 50 million people worldwide in addition to user-friendly tools designed to make running your study easy. We can help you find your sample regardless of what your study entails. Need people from a narrow demographic group? Looking to collect data from thousands of people? Do you need people who are willing to engage in a long or complicated study? Our team has the knowledge and expertise to match you with the right group of participants for your study. Get in touch with us today and learn what we can do for you.

Continue Reading: A Researcher’s Guide to Statistical Significance and Sample Size Calculations

Part 1: What Does It Mean for Research to Be Statistically Significant?

Part 2: How to Calculate Statistical Significance

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Sample Size Considerations: Basics for Preparing Clinical or Basic Research

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• 1 Harvard Medical School, Boston, USA; Department of Orthopedic Surgery, Boston Children's Hospital, Boston, USA.
• 2 Institutional Centers for Clinical and Translational Research, Boston Children's Hospital, Boston, USA.
• PMID: 37123495
• PMCID: PMC10133938
• DOI: 10.17996/anc.20-00122

Background : Sample size estimation is an important and integral part of a research protocol. While "how large a sample?" is a simple question, the answer is only meaningful within the context of the research question. Methods : Clear definitions of the variable of interest and target population parameters are key to estimating sample size. In turn the sample must be sized such that it can accurately detect the 'effect' of interest, adequately represent the target population and maintain maximum design efficiency. Four basic pieces of information are utilized in most sample estimation across all clinical research: significance level, power, magnitude of effect and variability of the variable of interest. Results/Discussion : Preliminary determination of these will greatly facilitate work with a biostatistician or a computer application to create a sample size estimation. While applications can support relatively simple sample size calculations consultation with a biostatistician is recommended.

Keywords: Magnitude of effect; Power; Sample size; Sampling.

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4.4 Sample Size and Sampling Techniques

While there are no set guidelines to determine sample size in qualitative research, the ideal sample size depends on the questions being asked, the theoretical framework, the study design, the type of data that is gathered, the available resources, and the amount of time. 50 Some qualitative studies may involve only a single case, while others may involve a small number of cases, such as a few individuals or groups. The goal of a qualitative study is not to generalise the findings to a larger population but rather to provide a detailed and in-depth understanding of the specific case or cases being studied. A sufficient sample size in qualitative research is one that allows for the detailed, case-oriented analysis that is a characteristic of all qualitative enquiry but also not too small to result in a novel and deeply nuanced knowledge of experience. 50 The minimum number and types of sample units needed in qualitative research cannot be predetermined using calculations or power analyses. 50 Rather, the basic methodological principle in qualitative research is to achieve saturation, which means you keep sampling until you stop learning new details or insights about the phenomenon under investigation. 51 The concept of saturation originated from grounded theory but is now accepted across various approaches in qualitative research. In general, you should keep asking participants until the area of ​​interest is saturated and until you hear nothing new. 43,51 The number of participants, therefore, depends on the richness of the data. A systematic review of empirical results showed that qualitative studies that had 9-17 interviews or 4-8 focus group discussions reached saturation. 52 Nonetheless, the sampling technique is essential given that data cannot be obtained from everyone in the population.

There are four major sampling techniques:

• Purposive sampling is also known as purposeful or selective sampling. It entails the deliberate, purposeful recruitment of individuals who can offer in-depth, precise details on the topic being studied. 53 There are numerous purposive sampling techniques. Examples include typical, extreme or deviant, critical, maximum variation and homogenous sampling. 54 Typical case highlights or illustrates what is normal, typical or average in a case. The purpose is to describe what is typical to those who are unfamiliar with the concept or phenomenon. 54 Extreme or deviant is used when researchers want to explore deviations or outliers from the norm regarding a particular subject. 54 On the other hand, a critical case involves exploring one case to provide insight into other similar cases. 54 The maximum variation sampling technique is used if the research aims to uncover core and shared elements/ themes that cut across a diverse sample while simultaneously offering the opportunity to identify divergent opinions. 54 In contrast, homogenous sampling focuses on people of similar backgrounds and experiences. It reduces variation and is mainly used for focus group discussions. 54 An example of purposive sampling is the study by Adu et al., 2019 which investigated the common gaps in skills and self-efficacy for diabetes self-management and explored other factors which serve as enablers of and barriers to achieving optimal diabetes self-management. 55 The study utilised a maximum variation purposive sampling technique to recruit participants into the study. 55 Figure 4.3 illustrates purposive sampling, where researchers wish to explore the perceptions of people living with diabetes. Diabetic patients were approached and recruited into the study.

• Convenience sampling is a technique used to recruit participants who are representative of the population from which they are selected but chosen because they are easily accessible and convenient to the researchers rather than being randomly selected. 56 Often this may include utilising geographic location, association with a facility/contact and resources that make participant recruitment convenient (Figure 4.4). 56 This sampling technique saves time and effort but has low credibility. 56 While convenience sampling is used in qualitative research, it can also be utilised in quantitative research, as stated in Chapter 3. In addition, it can also be used in mixed methods research which will be discussed in Chapter 5. For example, this study by Obasola and Mabawonku, 2018 used convenience sampling to select 1001 mothers attending maternity clinics at health facilities in Nigeria. 57

• Theoretical sampling is a data collection process controlled by a theory generation process. 43 It involves the simultaneous collection, coding and analysis of data to identify the next stage of data collection and where to find the participants to develop the emerging theory. 43 It is the principal strategy for the grounded theory approach. 43 According to theoretical sampling, new goals for data collection are determined by the information gathered from the previous sample. It entails seeing emerging ideas in the data that is being produced and using those ideas to direct where, how, and from whom more data should be gathered and with what emphasis. 46 For example, the study by Ligita et al. 2019 utilised theoretical sampling in the study that sought to generate a theory to explain the process by which people with diabetes learn about their disease in Indonesia. 58 The study was conducted in three phases, with a total of twenty-six participants. In the first phase, participants were recruited via purposive sampling, and data from the first phase led to further data gathering. Theoretical sampling was used to select the next data from 17 participants based on the data analysis 58 . Phase three was directed via theoretical sampling, with two new participants recruited into the study. 58 In Figure 4.5, two examples of how theoretical sampling was used in the study have been highlighted. 59

• Snowball sampling – This technique is used when it is hard to reach potential participants e.g. members of minority groups. The researcher initially contacts a few potential participants and asks them to provide contact details of people or refer people they know who meet the selection criteria. 60 These identified or named individuals are then recruited into the study. A simple way to consider this technique is to think of how a small snowball rolls down a hill and gets bigger as it gathers more snow. 60 An example is the study by Kaplan, Korf and Sterk, 1987 which describes the temporal and social contexts of Heroin-using populations in two Dutch cities. 61 While the article may be several years old, the graphical presentation and description of the snowballing technique are still valid (Figure 4.6). 61

An Introduction to Research Methods for Undergraduate Health Profession Students Copyright © 2023 by Faith Alele and Bunmi Malau-Aduli is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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Sample Size

The sample size of a statistical sample is the number of observations that constitute it.

This article is a part of the guide:

• Non-Probability Sampling
• Convenience Sampling
• Random Sampling
• Stratified Sampling
• Research Population

Browse Full Outline

• 1 What is Sampling?
• 2.1 Sample Group
• 2.2 Research Population
• 2.3 Sample Size
• 2.4 Randomization
• 3.1 Statistical Sampling
• 3.2 Sampling Distribution
• 3.3.1 Random Sampling Error
• 4.1 Random Sampling
• 4.2 Stratified Sampling
• 4.3 Systematic Sampling
• 4.4 Cluster Sampling
• 4.5 Disproportional Sampling
• 5.1 Convenience Sampling
• 5.2 Sequential Sampling
• 5.3 Quota Sampling
• 5.4 Judgmental Sampling
• 5.5 Snowball Sampling

The sample size is typically denoted by n and it is always a positive integer. No exact sample size can be mentioned here and it can vary in different research settings. However, all else being equal, large sized sample leads to increased precision in estimates of various properties of the population.

What Should Be the Sample Size?

Determining the sample size to be selected is an important step in any research study. For example let us suppose that some researcher wants to determine prevalence of eye problems in school children and wants to conduct a survey .

The important question that should be answered in all sample surveys is "How many participants should be chosen for a survey"? However, the answer cannot be given without considering the objectives and circumstances of investigations.

The choosing of sample size depends on non-statistical considerations and statistical considerations. The non-statistical considerations may include availability of resources, manpower, budget, ethics and sampling frame . The statistical considerations will include the desired precision of the estimate of prevalence and the expected prevalence of eye problems in school children.

Following three criteria need to be specified to determine the appropriate samples size:

1. The Level of Precision

Also called sampling error , the level of precision, is the range in which the true value of the population is estimated to be. This is range is expressed in percentage points. Thus, if a researcher finds that 70% of farmers in the sample have adopted a recommend technology with a precision rate of ±5%, then the researcher can conclude that between 65% and 75% of farmers in the population have adopted the new technology.

2. The Confidence Level

The confidence interval is the statistical measure of the number of times out of 100 that results can be expected to be within a specified range.

For example, a confidence interval of 90% means that results of an action will probably meet expectations 90% of the time.

The basic idea described in Central Limit Theorem is that when a population is repeatedly sampled, the average value of an attribute obtained is equal to the true population value. In other words, if a confidence interval is 95%, it means 95 out of 100 samples will have the true population value within range of precision.

3. Degree of Variability

Depending upon the target population and attributes under consideration, the degree of variability varies considerably. The more heterogeneous a population is, the larger the sample size is required to get an optimum level of precision. Note that a proportion of 55% indicates a high level of variability than either 10% or 80%. This is because 10% and 80% means that a large majority does not or does, respectively, have the attribute under consideration.

There are number of approaches to determine the sample size including: using a census for smaller populations, using published tables, imitating a sample size of similar studies, and applying formulas to calculate a sample size.

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Estimation of Multidimensional Poverty in Morocco: A Small Area Estimation Approach Using Meteorological and Socio-economic Covariates

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• Published: 09 May 2024

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• Gianni Betti 1 ,
• Federico Crescenzi   ORCID: orcid.org/0000-0002-0701-4398 2 ,
• Vasco Molini 3 &
• Lorenzo Mori 4  

In this paper we estimate the Head Count Ratio (HCR) and two fuzzy poverty measures at provincial level in Morocco using data from the Household Budget Survey (HBS). As the sample size is not always sufficient to provide reliable direct estimates, we use a Fay–Herriot model with additive logistic transformation and meteorological covariates to obtain estimates with lower mean squared errors. Among our main results, we find out that the Fuzzy Monetary measure provides more accurate estimates than the Head Count Ratio when conducting small area estimation exercises. Also, we empirically notice that the set of covariates at our disposal allows us to obtain better estimates for each supplementary poverty measure that we identify.

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These are known as area-level small area methods to distinguish from unit-level methods where the subscript denotes a unit of the sample and not an area.

The use of covariates with error on SAE is an open field of research and only few articles have been published (see:Chandra et al., 2018 ; Datta et al., 2018 ; Würz et al., 2022 )

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Eurostat ( 2013 ) discourage the use of CV for percentages or proportions. Although this applies to statistics like the head count ratio, the statistic that we report here is slightly different in that it is an average of a membership function. Kvålseth ( 2017 ) proposes to use a second-order alternative (CV2) that is not influenced by values near 0. However, in this context, we still prefer to use the CV as it is more common and widely used in the SAE context. Readers interested in computing the CV2 can refer to the values in the Appendix; the results are almost identical.

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Betti, G., Crescenzi, F., Molini, V. et al. Estimation of Multidimensional Poverty in Morocco: A Small Area Estimation Approach Using Meteorological and Socio-economic Covariates. Soc Indic Res (2024). https://doi.org/10.1007/s11205-024-03340-9

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