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Sample Size Determination: Definition, Formula & 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, considering the research study’s quality.

So, how should you determine the sample size? 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 accurately calculate and determine the appropriate sample size 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 to define the number of individuals included in research. Researchers choose their sample based on demographics, such as age,  gender , or physical location. The term 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 choosing the correct 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 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 determine a sample size 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 who fit into the  consumer panel  requirement. The responses can help you determine how your audience will react to the new product.

However, determining a sample size requires more than just sending your survey to as many people as possible. If your estimated sample size is 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, a .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:

1. 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 to projecting your survey results on a larger population. You’ll want to ensure it’s balanced and reflects the community as a whole. However, the sample size isn’t as critical if you’re trying to understand 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 in Denver, where the climate is dry and cool. 

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

2. 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 will 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.

3. 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 the number of responses you need, which means increased costs for your survey. 

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

For example, you want to be 99% confident. After using the sample size determination formula, 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.

4. 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, there may be many variations. To get the most accurate picture of the population, you’ll need a larger sample size. 

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.

5. Response rate: 

You want everyone to respond to your survey. Unfortunately, every survey has targeted respondents who either never open the study or drop out halfway through. 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 survey to be successful.

6. 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 would not want to send a survey to a group of homeowners asking about the quality of local apartment amenities.

7. 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 it easier to get a more accurate result from a small sample size. 

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 will unlikely 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 the sample size. Using the formula to determine sample size is a great starting point for getting 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 determining sample size, the  statistical analysis plan  needs to carefully consider 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 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 population size.

LEARN MORE         FREE TRIAL

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

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

The sample size is important because it affects how precise and accurate a study’s results 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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Basic concepts for sample size calculation: Critical step for any clinical trials!

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Address for correspondence: Dr. Kewal Krishan Gupta, House No. 204, Medical Campus, Faridkot - 151 203, Punjab, India. E-mail: [email protected]

This is an open access article distributed under the terms of the Creative Commons Attribution NonCommercial ShareAlike 3.0 License, which allows others to remix, tweak, and build upon the work non commercially, as long as the author is credited and the new creations are licensed under the identical terms.

Quality of clinical trials has improved steadily over last two decades, but certain areas in trial methodology still require special attention like in sample size calculation. The sample size is one of the basic steps in planning any clinical trial and any negligence in its calculation may lead to rejection of true findings and false results may get approval. Although statisticians play a major role in sample size estimation basic knowledge regarding sample size calculation is very sparse among most of the anesthesiologists related to research including under trainee doctors. In this review, we will discuss how important sample size calculation is for research studies and the effects of underestimation or overestimation of sample size on project's results. We have highlighted the basic concepts regarding various parameters needed to calculate the sample size along with examples.

Keywords: Clinical trial, power of study, sample size

Introduction

Proper study design that is an integral component of any randomized clinical trial (i.e., the highest level of evidence available for evaluating new therapies), appears infrequently in the anesthesia literature.[ 1 , 2 , 3 ] Lack of sample size calculations in prospective studies and power analysis in studies with negative results have sufficiently supported this finding.[ 4 , 5 ] Two possible reasons for its absence in anesthesia research are followings:

Rare training on subjects like sample size calculation and power analysis among resident doctors.

Complex appearance of mathematical expression which are used for this.

To plan a research project and to understand the contents of a research paper, we need to be familiar with the fundamental concepts of medical statistics. While designing a study, we need to interact with a statistician. Understanding the basic concepts will help the anesthesiologist to interact with him in a more meaningful way. One of the pivotal aspects of planning a clinical study is the calculation of the sample size. Hence in this article, we will discuss the importance of sample size estimation for a clinical trial and different parameters that impact sample size along with basic rules for these parameters.

As we know, it is naturally neither practical nor feasible to study the whole population in any study. Hence, the sample is a set of participants (lesser in number) which adequately represents the population from which it is drawn so that true inferences about the population can be made from the results obtained. The sample size is, simply put, the number of patients or experimental units in a sample. Every individual in the chosen population should have an equal chance to be included in the sample.

Why Sample Size Calculations?

The sample size is one of the first practical steps and statistical principal in designing a clinical trial to answer the research question.[ 6 ] With smaller sample size in a study, it may not be able to detect the precise difference between study groups, making the study unethical. Moreover, the results of the study cannot be generalized to the population, as this sample will be inadequate to represent the target population. On the other hand, by taking larger sample size in the study, we put more population to the risk of the intervention and also making the study unethical. It also results in wastage of precious resources and the researchers' time.

Hence, sample size is an important factor in approval/rejection of clinical trial results irrespective of how clinically effective/ineffective, the intervention may be.

Components of sample size calculation

One of the most common questions any statistician gets asked is “How large a sample size do I need?” Researchers are often surprised to find out that the answer depends on a number of factors, and they have to give the statistician some information before they can get an answer! Thus calculating the sample size for a trial requires four basic components that are following.[ 7 , 8 ]

P value (or alpha)

Everybody is familiar with the term of P value. This is also known as level of significance and in every clinical trial we set an acceptable limit for P value. For example, we assume P < 0.05 is significant, it means that we are accepting that probability of difference in studying target due to chance is 5% or there are 5% chances of detection in difference when actually there was no difference exist (false positive results). This type of error in clinical research is also known as Type I error or alpha. Type I error is inversely proportional to sample size.

Sometimes we may commit another type of error where we may fail to detect the difference when actually there is the difference. This is known as Type II error that detects false negative results, exactly opposite to mentioned above where we find false positive results when actually there was no difference. To accept or reject null hypothesis by adequate power, acceptable limit for the false negative rate must be decided before conducting the study.

In another term, Type II error is the probability of failing to find the difference between two study groups when actually a difference exist and it is termed as beta (β). By convention, maximum acceptable value for β in bio-statistical literature is 0.20 or a 20% chance that null hypothesis is falsely accepted. The “power” of the study then is equal to (1-β) and for a β of 0.2, the power is 0.8, which is the minimum power required to accept the null hypothesis. Usually, most of clinical trial uses the power of 80% which means that we are accepting that one in five times (i.e., 20%) we will miss a real difference. The power of a study increases as the chances of committing a Type II error decrease.

The effect size

Effect size (ES) is the minimal difference that investigator wants to detect between study groups and is also termed as the minimal clinical relevant difference. We can estimate the ES by three techniques that is, pilot studies, previously reported data or educated guess based on clinical experiences.

To understand the concept of ES, here we take one example. Suppose that treatment with Drug A results in a reduction of mean blood pressure (MBP) by 10 mm of Hg and with Drug B results in a reduction of MBP by 20 mm of Hg. Then, absolute ES will be 10 mm of Hg in this case. ES can be expressed as the absolute or relative difference. As in above example, relative difference/reduction with drug intervention is 10/20 or 50%. In other word, for continuous outcome variables the ES will be numerical difference and for binary outcome e.g., effect of drug on development of stress response (yes/no), researcher should estimate a relevant difference between the event rates in both treatment groups and could choose, for instance, a difference of 10% between both the groups as ES. In statistics, the difference between the value of the variable in the control group and that in the test drug group is known as ES. Even a small change in the expected difference with treatment has a major effect on the estimated sample size, as the sample size is inversely proportional to the square of the difference. For larger ES, smaller sample size would be needed to prove the effect but for smaller ES, sample size should be large.

The variability

Finally for the sample size calculation, researcher needs to anticipate the population variance of a given outcome variable which is estimated by means of the standard deviation (SD). Investigators often use an estimate obtained from information in previous studies because the variance is usually an unknown quantity. For a homogenous population, we need smaller sample size as variance or SD will be less in this population. Suppose for studying the effect of diet program A on the weight, we include a population with weights ranging from 40 to 105 kg. Now, it is easy to understand that the SD in this group will be more and we would need a larger sample size to detect a difference between interventions, else the difference between the study groups would be concealed by the inherent difference between them because of the SD. If, on the other hand, we take a sample from a population with weights between 60 and 80 kg we would naturally get a more homogenous group, thus reducing the SD and, therefore, the sample size.

Other factors affecting the sample size calculation are dropout rate and underlying event rate in the population.

Dropout rate

Dropout rate means that estimate of a number of subjects those can leave out the study/clinical trial due to some reason. Normally the sample size calculation will give a number of study subjects required for achieving target statistical significance for a given hypothesis. However in clinical practice, we may need to enroll more subjects to compensate for these potential dropouts.[ 9 ]

If n is the sample size required as per formula and if d is the dropout rate then adjusted sample size N1 is obtained as N1 = n /(1-d).

Event rate in population

Prevalence rate or underlying event rate of the condition under study in population is very important while calculating sample size. It is usually estimated from previous literature. For example studying the association of smoking and brain tumor, the prevalence rate for a brain tumor in studying population should be known prior to the study. Sometimes, we have to readjust the sample size after starting the trial because of unexpectedly low event rate in the population.

Examples of sample size calculations

Example 1: comparing two means.

A placebo-controlled randomized trial proposes to assess the effectiveness of Drug A in preventing the stress response to laryngoscopy. A previous study showed that there is the average rise of 20 mm of Hg in systolic blood pressure during laryngoscopy (with SD of 15 mm of Hg). What should be the sample size to study the difference in mean systolic blood pressure between two groups with a significant P < 0.05 and power of study of 90%.

Level of significance = 5%, Power = 80%, Zα = Z is constant set by convention according to accepted α error and Z (1-β) = Z is constant set by convention according to power of study which is calculated from Table 1 .

Showing constant values for convention values of α and β values

Formula of calculating sample size is:

n = 2 (Zα + Z [1-β]) 2 × SD 2 /d 2

Zα = 1.96, Z (1-β) = 1.28, SD = 15, d (effect size) = 20

So n = 2 (1.96 + 1.28) 2 × 15 2 /20 2 = 11.82

Twelve individuals in each group should be recruited in the study.

Example 2: Comparing two proportions

A study is planned to check the effectiveness of dexmedtomidine in preventing postoperative shivering. From previous studies, it was found that incidence of postoperative shivering is 60%. Reduction in the incidence of shivering up to 20% will be considered significant for the effectiveness of the drug. What should be the sample size for the study with alpha value, that is, Type I error of 5% (0.05) and power of 95%.

The parameters for sample size calculation are:

P1 = 60%, P2 = 20%, Effect size (d) = 40%, Zα = 1.96, Z (1-β) = 1.64

Average of P1 and P2 will be P = P1 + P2/2 60 + 20/2 = 40

q = 1-p = 1-40 = 60%

Formula will be: n = 2 (Zα + Z [1-β]) 2 × P × q/d 2

n = 2 (1.96 + 1.64) 2 × 40 × 60/(40) 2 = 38.88

In this example, we need 40 persons to be included in the each group for the study.

Some basic rules for on sample size estimations are

Power—It should be ≥80%. Sample size increases as power increases. Higher the power, lower the chance of missing a real effect.[ 10 ]

Level of significance—It is typically taken as 5%. The sample size increases as level of significance decreases.[ 10 ]

Clinically meaningful difference—To detect a smaller difference, one needs a sample of large sample size and vice a versa.[ 10 ]

Post-hoc power calculations—After the study is conducted, one should not perform any “ post-hoc ” power calculations. The power should always be calculated prior to a study to determine the required sample size, since it is the prestudy probability that the study will detect a minimum effect regarded as clinically significant. Once the effect of the study is known, investigators should use the 95% confidence interval (CI) to express the amount of uncertainty around the effect estimate instead of power.[ 11 , 12 ]

Reporting of sample size

According to the CONSORT statement, sample size calculations should be reported and justified in all published RCTs. Many studies only include statements like “we calculated that the sample size in each treatment group should be 150 at an alpha of 0.05 and a power of 0.80.” However, such a statement is almost meaningless because it neglects the estimates for the effect of interest and the variability. The best way to express sample size from IDEAL clinical trial should be “A clinically significant effect of 10% or more over the 3 years would be of interest. Assuming 3-year survival rates in the control group and the intervention group of 64% and 74% respectively, with a two-sided significance of 0.05 and a power of 0.8, a total of 800-1000 patients will be required.”[ 13 ]

The sample size is first and important step in planning a clinical trial and any negligence in its estimation may lead to rejection of an efficacious drug and an ineffective drug may get approval. Although techniques for sample size calculation are described in various statistical books, performing these calculations can be complicated and it is desirable to consult an experienced statistician in estimation of this vital study parameter. To have meaningful dialogue with the statistician every research worker should be familiar with the basic concepts of sample size calculations.

Financial support and sponsorship

Conflicts of interest.

There are no conflicts of interest.

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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.

GeoPoll’s Sampling Techniques

With the largest mobile panel in Africa, Asia, and Latin America, and reliable mobile technologies, GeoPoll develops unique samples that accurately represent any population. See our country coverage  here , or  contact  our team to discuss your upcoming project.

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• Tags market research , Market Research Methods , sample size , survey methodology

Calculate your ideal sample size

Last updated

11 May 2023

Reviewed by

Miroslav Damyanov

Whether you're conducting market research , medical trials, or social science studies, understanding how to calculate your ideal sample size is essential for a successful research project .

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• What is a sample size?

The sample size is the number of participants or data points a researcher needs to collect to make inferences about a larger population. Researchers use sample size to conclude a population. 

For example, if a researcher wants to know the average height of adult males in the United States, the population would be all adult males in the US. The researcher would collect a sample of adult males, measure their height, and use this information to estimate the average size of all adult males in the US. 

• Understanding sample size

Comprehending sample size is vital for conducting meaningful research that provides reliable and accurate results. Here are some key concepts that can help you better understand this critical aspect of research:

Representativeness

A sample is considered emblematic if it accurately reflects the population characteristics from which it’s drawn. To ensure representativeness, researchers should use appropriate sampling methods , such as random or stratified sampling .

Confidence level

This is the degree of certainty the results obtained from a sample accurately represent the population. A confidence level of 95% means there is a 95% chance the population parameter falls within the confidence interval .

The margin of error

The margin of error is the sampling error expected in the results due to using a cross-section instead of the entire population. 

This refers to the ability of a study to detect an actual effect—if it exists. A study with high power has a greater chance of detecting a significant impact, while a study with low power may fail to see the effect, even if it exists.

Effect size

This is the magnitude of the difference between groups or the strength of the relationship between variables. The larger the effect size, the stronger the relationship.

By selecting an appropriate sample size, researchers can ensure their findings represent the population being studied and have the necessary level of precision and confidence.

Does having a statistically significant sample size matter?

A statistically significant sample size is the minimum number of participants required to detect a meaningful difference in the studied population. Statistical significance doesn't guarantee the validity or importance of the study results. 

However, it provides evidence that the observed differences in the sample are unlikely coincidental. Therefore, a statistically significant sample size is vital in drawing valid conclusions and making informed decisions based on the study results.

• How to calculate sample size

Quantifying the ideal sample size requires careful consideration of several factors, including the research question , the desired accuracy, and the confidence level. Here's a general overview of how to calculate sample size:

Power analysis is a statistical method used to determine the ideal sample size based on the effect size, the significance level, and the study's desired power. 

Confidence intervals are an analytical method used to estimate the range of values probable to contain the actual population variable with a certain confidence level. 

The margin of error is a demographic method used to gauge the scope of values likely to have the true population parameter with a certain precision level. 

The sample size calculation may differ depending on the statistical method and study design.

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Maximize your research’s impact with the right sample size and get an accurate representation of your target audience.

Sample size

The total number of people whose opinion or behavior your sample will represent.

The probability that your sample accurately reflects the attitudes of your population. The industry standard is 95%.

The range (measured as a percentage) that your population’s responses may deviate from your sample’s.

Sample size formula

The formulas for calculating sample size depend on the statistical method used. Here are the commonly used formulas:

Power analysis : N = [(Zα/2 + Zβ) / ES] ^ 2

N = sample size

Zα/2 = the critical value of the standard normal distribution for a specified level of significance

Zβ = the critical value of the standard normal distribution for a particular power of the study

ES = the effect size, representing the magnitude of the difference or effect the study tries to detect

Confidence intervals :  n = [(z * σ) / E] ^ 2

z = the critical value of the standard normal distribution for a specified level of confidence

σ = the standard deviation of the population

E = the desired margin of error

The margin of error : MOE = Z * (σ / √n)

Z = the z-score associated with the desired level of confidence (e.g., for 95% confidence, Z = 1.96)

n = the sample size

Margin of error calculator

Optimize your research’s impact when you improve the margin of error.

Margin of error

The number of people who took your survey.

These formulas are general guidelines, and researchers should consult with a statistician or use statistical software to ensure the sample size calculation is appropriate for their particular research question and study design.

Is a larger sample size better?

Yes, a larger sample size is better. A larger sample size increases the statistical power of a study, meaning it's more likely to detect actual effects or differences between groups.

Why use a sample size calculator?

A sample size calculator is used to determine the optimal sample size needed to obtain reliable and valid results in a study. It considers several factors, including the desired level of statistical power, the expected effect size, and the significance level.

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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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