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How To Determine Sample Size for Quantitative Research

This blog post looks at how large a sample size should be for reliable, usable market research findings.

Table of Contents: 

What is sample size , why do you need to determine sample size , variables that impact sample size.

• Determining sample size

The sample size of a quantitative study is the number of people who complete questionnaires in a research project. It is a representative sample of the target audience in which you are interested.

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You need to determine how big of a sample size you need so that you can be sure the quantitative data you get from a survey is reflective of your target population as a whole - and so that the decisions you make based on the research have a firm foundation. Too big a sample and a project can be needlessly expensive and time-consuming. Too small a sample size, and you risk interviewing the wrong respondents - meaning ultimately you miss out on valuable insights.

There are a few variables to be aware of before working out the right sample size for your project.

Population size

The subject matter of your research will determine who your respondents are - chocolate eaters, dentists, homeowners, drivers, people who work in IT, etc. For your respective group of interest, the total of this target group (i.e. the number of chocolate eaters/homeowners/drivers that exist in the general population) will guide how many respondents you need to interview for reliable results in that field.

Ideally, you would use a random sample of people who fit within the group of people you’re interested in. Some of these people are easy to get hold of, while others aren‘t as easy. Some represent smaller groups of people in the population, so a small sample is inevitable. For example, if you’re interviewing chocolate eaters aged 5-99 you’ll have a larger sample size - and a much easier time sampling the population - than if you’re interviewing healthcare professionals who specialize in a niche branch of medicine.

Confidence interval (margin of error)

Confidence intervals, otherwise known as the margin of error, indicate the reliability of statistics that have been calculated by research; in other words, how certain you can be that the statistics are close to what they would be if it were possible to interview the entire population of the people you’re researching.

Confidence intervals are helpful since it would be impossible to interview all chocolate eaters in the US. However, statistics and research enable you to take a sample of that group and achieve results that reflect their opinions as a total population. Before starting a research project, you can decide how large a margin of error you will allow between the mean number of your sample and the mean number of its total population. The confidence interval is expressed as +/- a number, indicating the margin of error on either side of your statistic. For example, if 35% of chocolate eaters say that they eat chocolate for breakfast and your margin of error is 5, you’ll know that if you had asked the entire population, 30-40% of people would admit to eating chocolate at that time of day.

Confidence level

The confidence level indicates how probable it is that if you were to repeat your study multiple times with a random sample, you would get the same statistics and they would fall within the confidence interval every time.

In the example above, if you were to repeat the chocolate study over and over, you would have a certain level of confidence that those eating chocolate for breakfast would always fall within the 30-40% parameters. Most research studies have confidence intervals of 90% confident, 95% confident, or 99% confident. The number you choose will depend on whether you are happy to accept a broadly accurate set of data or whether the nature of your study demands one that is almost completely reliable.

Standard deviation

Standard deviation represents how much the results will vary from the mean number and from each other. A high standard deviation means that there is a wide range of responses to your research questions, while a low standard deviation indicates that responses are more similar to each other, clustered around the mean number. A standard deviation of 0.5 is a safe level to pick to ensure that the sample size is large enough.

Population variability 

If you already know anything about your target audience, you should have a feel for the degree to which their opinions vary. If you’re interviewing the entire population of a city, without any other criteria, their views are going to be wildly diverse so you’ll want to sample a high number of residents. If you’re honing in on a sample of chocolate breakfast eaters - there’s probably a limited number of reasons why that’s their meal of choice, so you can feel confident with a much smaller sample.

Project scope

The scope and objectives of the research will have an influence on how big the sample is. If the project aims to evaluate four different pieces of stimulus (an advert, a concept, a website, etc.) and each respondent is giving feedback on a single piece, then a higher number of respondents will need to be interviewed than if each respondent were evaluating all four; the same would be true when looking for reads on four different sub-audiences vs. not needing any sub-group data cuts.

Determining a good sample size for quantitative research

Sample size, as we’ve seen, is an important factor to consider in market research projects. Getting the sample size right will result in research findings you can use confidently when translating them into action. So now that you’ve thought about the subject of your research, the population that you’d like to interview, and how confident you want to be with the findings, how do you calculate the appropriate sample size?

There are many factors that can go into determining the sample size for a study, including z-scores, standard deviations, confidence levels, and margins of error. The great thing about quantilope is that your research consultants and data scientists are the experts in helping you land on the right target so you can focus on the actual study and the findings. 

To learn more about determining sample size for quantitative research, get in touch below: 

Get in touch to learn more about quantitative sample sizes!

Related posts, quantilope & wire webinar: solving the research dilemma with ai, a full year of better brand health tracking in the soda category, non-probability sampling: when and how to use it effectively, survey results: how to analyze data and report on findings.

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How many participants for quantitative usability studies: a summary of sample-size recommendations.

July 25, 2021 2021-07-25

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In This Article:

Introduction, the intuition behind the 40-participants guideline: why you need 40 participants, the assumptions behind the 40-participant guideline, when you may get away with fewer participants, what if your metric is continuous.

The exact number of participants required for quantitative usability testing can vary. Apparently contradictory recommendations (ranging from 20 to 30 to 40 or more) often confuse new quantitative UX researchers. (In fact, we’ve recommended different numbers over the years.)

Where do these recommendations come from and how many participants do you really need? This is an important question. If you test with too few , your results may not be statistically reliable . If you test with too many, you’re essentially throwing your money away. We want to strike the perfect balance — collecting enough data points to be confident in our results, but not so many that we’re wasting precious research funding.

In most cases, we recommend 40 participants for quantitative studies. If you don’t really care about the reasoning behind that number, you can stop reading here. Read on if you do want to know where that number comes from, when to use a different number, and why you may have seen different recommendations.

Since this is a common confusion, let’s clarify: there are two kinds of studies, qualitative and quantitative. Qual aims at insights, not numbers , so statistical significance doesn’t come into play. In contrast, quant does focus on collecting UX metrics , so we need to ensure that these numbers are correct. And the key point: this article is about quant, not qual . ( Qualitative studies only need a small number of users , but that’s not what we’re discussing here.)

When we conduct quantitative usability studies, we’re collecting UX metrics — numbers that represent some aspect of the user experience.

For example, we might want to know what percentage of our users are able to book a hotel room on Expedia, a travel-booking site. We won’t be able to ask every Expedia user to try to book a hotel room. Instead, we will run a study in which will ask a subset of our target population of Expedia users to make a reservation.

Then, we’ll count how many participants in that study are able to complete the task and we’ll use that percentage to estimate the percentage of our population. Of course, what we get from the study is not going to be exactly the same as our population success rate (there is always going to be some amount of measurement error), but we hope that it will be close enough.

When the number of people we include in the study is small, the percentage from the study will be unlikely to predict the success rate of the whole population — that number will simply be too noisy.

As another example, image you want to figure out the average daily temperature in Berlin, Germany during the summer. You decide to estimate that average by looking only at three random daily temperatures. Those three days probably will not give you a very accurate number, will they? This is the problem with small samples for quantitative studies.

In a quantitative usability study, to get a reasonably trustworthy prediction for the behavior of your overall population, you need around 40 data points. There are nuances depending on how much risk you are willing to take and what exactly you are trying to measure.

The 40-participant recommendation comes from a calculation . That calculation estimates the minimum number of users needed to produce a reasonable prediction of your population behavior based on one study. It has specific assumptions, but it will work for many quantitative usability studies .

If you don’t care about statistics, you can stop reading at this point (or jump directly to the conclusion ). Otherwise, if you’re curious about the nuances behind this recommendation, keep reading.

In statistical terms, the 40-participant guideline comes from a very specific situation, which may or may not apply to your particular scenario. It assumes that you have a considerable user population (over 500 people) and that the following are true:

• You want to estimate a binary metric such as success rate or conversion rate based on a study with a sample of your user population.
• You aim for a 15% margin of error — namely, you want your true score (e.g., the success rate or conversion rate for your whole population) to be within 15% of the observed score (the percentage you obtained from your study).
• You want to take very little risk of being wrong in this prediction (that is, you will use a confidence level of 95% for computing your margin of error).

If all the above are true, it turns out that you can calculate the number of participants you need for your study, and it is 39. We round it up to 40 — hence the above recommendation. (These estimates are often rounded up by a few participants. First, rounding up makes the numbers more memorable. Second, slight overrecruiting helps if something goes wrong with one or two participants and their data has to be removed. For example, you may discover during the study that you accidentally recruited an unrepresentative user or a cheater.)

It is possible to need fewer participants if the last two of the assumptions above are not true. Specifically, if you are:

• Willing to have a margin of error that is bigger than 15% 
• Willing to take a larger risk  

Willing to Have a Margin of Error Bigger than 15% 

The margin of error tells you how much you can expect your overall population rate to vary as a function of the observed score. Any time you collect a metric you should compute a margin of error (or, equivalently, a confidence interval). In other words, if in your Expedia study, 70% of your study participants were able to book a room and your margin of error was 15%, it means that your whole-population completion rate (the true score) is 70% ± 15% — that is, it could be anywhere from 55% to 85%.

That range is 30% wide and it represents the precision of your estimate; it could, however, be the case that in some situations you don’t care if it’s a little wider and your margin of error is bigger (for example, if you want to be able to say that most people can use a certain feature of your UI). We don’t recommend going for margins of error bigger than 20% because your confidence interval for the true score will be quite wide and unlikely to be useful. 

Willing to Take a Larger Risk  

A 95% confidence level means that your margin of error computations will be wrong only 5% of the time. It is the gold standard for published academic research. However, most UX researchers work in applied research, not academic research. For practical purposes, you may be willing to take a little bit more risk.

(Taking more risk is cheaper and is a good idea if the risks of a somewhat unreliable result won’t be catastrophic. However, bear in mind that UX teams often use quantitative usability testing to inform prioritization and resource allocation, so unreliable data may be quite problematic.)

If you are willing to drop the confidence level to 90%, then a margin of error of 15% will require 28 users and a margin of error of 20% will require 15 users . Again, you may consider rounding these up for many good reasons (for example, you may end up having to remove some of your trials when you clean up the data). This is the origin of the 30-user guideline that you may have encountered elsewhere — that recommendation accepts more risk.

This table shows the number of participants needed for different confidence levels and desired margins of error for binary metrics. The lower the confidence level, the riskier the study. The bigger the margin of error, the lower your precision and the less useful the numbers will be.

If your metric is continuous or can be treated as continuous (e.g., task time, satisfaction or other types of rating, SUS score ), the formula for the number of participants will depend on an additional factor: the variability of your target population. (It will also depend, like for binary metrics, on the desired margin of error and the confidence level used). That is something that you could estimate separately for your population by running a pilot study.

Of course, a pilot study to estimate the standard deviation is quite expensive and it will itself involve a fairly large number of participants. On the other hand, in most quantitative usability studies, there are several metrics involved and usually at least one of them is binary. Therefore, we recommend using that binary metric as a constraint in deciding the number of users. In other words, if you are collecting success, task time, and satisfaction, then you can simply say I want a 15% margin of error for success at a 90% or 95% confidence level (and recruit 30 or 40 users respectively). That will usually result in good margins of error for the other metrics involved.

If, however, you collect only continuous metrics (this is unusual) and you cannot afford to estimate the standard deviation of your population, you must first settle on a desired value for your margin of error. Of course, your desired value will depend on what you are measuring and the range for a task. We usually recommend using as a desired value 15% or 20% of the mean — in other words, if your task time is around 1 minute, you would like a margin of error no bigger than 0.15–0.20 minutes (9 to 12 seconds); if your task time is around 10 minutes, your margin of error should be no bigger than 1.5–2 minutes.

Next, you can use Jakob Nielsen’s estimate of variability for website- and intranet-related continuous metrics . That estimate is 52% of the mean .  In other words, if the mean task time is 1 min, your estimated standard deviation is 0.52 x 1 min = 0.52 minutes. If the mean task time is 10 minutes, then your estimated standard deviation will be 0.52 x 10 min = 5.2 minutes. With that supplementary assumption, you would need 47 users for a 15% margin of error at 95% confidence level, 33 users for a 15% margin of error at 90% confidence level, 26 users for a 20% margin of error at 95% confidence level and 19 users for a 20% margin of error at 90% confidence level. (Note that a 15% margin of error of 1 minute translates into 0.15 minutes — that is, 9 seconds.)

This table shows the required number of participants needed for a study involving continuous metrics such as time on task or satisfaction. Different numbers of participants are appropriate for different confidence levels and desired margins of error.

In general, the number of users can be determined using the following formula:

The variables in that formula are:

• K is a constant (1.96 for 95% confidence level or 1.645 for 90% confidence level)
• s is your standard deviation as a proportion of the mean
• m is your desired margin of error, also expressed as a proportion of the mean (0.15 corresponding to 15% or 0.20 corresponding to 20%)

If you estimate your standard deviation as a 52% (or 0.52) of the mean, then you can use the formula below:

Even though there are many different recommendations for sample sizes in quantitative usability testing, they are all consistent with each other — they simply make slightly different assumptions. We think the 40-user guideline is the simplest and the most likely to lead to good results — namely, a relatively small margin of error with a high confidence level.

However, you may settle for a lower number of users (around 30) if you want to take slightly more risk that your findings will not represent the behavior of your user population and thus decrease your confidence level to 90%. Moreover, if you also have tolerance for a larger margin of error, you can drop the number of users to 20 or even fewer, but that is generally a lot riskier.

An acceptable strategy (especially if you are on a tight budget and mostly interested in continuous metrics such as task time and satisfaction) is to start with as many users as you can comfortably afford — say, 20–25 users. Once you’ve collected your data from these users, calculate your margins of error and determine if they are tight enough for your purposes. If they are too wide, then consider adding more users. This approach, however, requires that you work fast: you’ll need to do your analysis in a matter of a few days in order to be able to run the extra participants very soon after the first batch. Otherwise, you risk compromising the validity of your study.

Choose the right sample size for your situation to ensure you’ll optimize your quantitative study: collecting just enough data, but not too much.

Jeff Sauro, James Lewis. 2016. Quantifying the User Experience: Practical Statistics for User Research . Elsevier.

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How to choose a sample size (for the statistically challenged)

One of the most common questions I get asked by people doing surveys in international development is “how big should my sample size be?”. While there are many  sample size calculators and statistical guides available, those who never did statistics at university (or have forgotten it all) may find them intimidating or difficult to use.

If this sounds like you, then keep reading. This guide will explain how to choose a sample size for a basic survey without any of the complicated formulas. For more easy rules of thumb regarding sample sizes for other situations, I highly recommend  Sample size: A rough guide  by Ronán Conroy and   The Survey Research Handbook  by Pamela Alreck and Robert Settle.

This article is a short introduction to the topic for a more in-depth coverage of the topic consider enrolling in the free online course offered by University of Florida .

This advice is for:

• Basic surveys such as feedback forms, needs assessments, opinion surveys, etc. conducted as part of a program.
• Surveys that use random sampling.

This advice is NOT for:

• Research studies conducted by universities, research firms, etc.
• Complex or very large surveys, such as national household surveys.
• Surveys to compare between an intervention and control group or before and after a program (for this situation  Sample size: A rough guide ).
• Surveys that use non-random sampling, or a special type of sampling such as cluster or stratified sampling (for these situations see  Sample size: A rough guide  and the UN guidelines on household surveys ).
• Surveys where you plan to use fancy statistics to analyse the results, such as multivariate analysis (if you know how to do such fancy statistics then you should already know how to choose a sample size).

The minimum sample size is 100

Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100. If your population is less than 100 then you really need to survey all of them.

A good maximum sample size is usually 10% as long as it does not exceed 1000

A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000. This exceeds 1000, so in this case the maximum would be 1000.

Even in a population of 200,000, sampling 1000 people will normally give a fairly accurate result. Sampling more than 1000 people won’t add much to the accuracy given the extra time and money it would cost.

Choose a number between the minimum and maximum depending on the situation

Suppose that you want to survey students at a school which has 6000 pupils enrolled. The minimum sample would be 100. This would give you a rough, but still useful, idea about their opinions. The maximum sample would be 600, which would give you a fairly accurate idea about their opinions.

Choose a number closer to the  minimum  if:

• You have limited time and money.
• You only need a rough estimate of the results.
• You don’t plan to divide the sample into different groups during the analysis, or you only plan to use a few large subgroups (e.g. males / females).
• You think most people will give similar answers.
• The decisions that will be made based on the results do not have significant consequences.

Choose a number closer to the  maximum  if:

• You have the time and money to do it.
• It is very important to get accurate results.
• You plan to divide the sample into many different groups during the analysis (e.g. different age groups, socio-economic levels, etc).
• You think people are likely to give very different answers.
• The decisions that will be made based on the results of the survey are important, expensive or have serious consequences.

In practice most people normally want the results to be as accurate as possible, so the limiting factor is usually time and money. In the example above, if you had the time and money to survey all 600 students then that will give you a fairly accurate result. If you don’t have enough time or money then just choose the largest number that you can manage, as long as it’s more than 100.

If you would like to learn more about Survey Data Collection consider taking the free course offered by University of Michigan and University of Maryland. Enroll here.

If you want to be a bit more scientific then use this table

While the previous rules of thumb are perfectly acceptable for most basic surveys, sometimes you need to sound more “scientific” in order to be taken seriously. In that case you can use the following table. Simply choose the column that most closely matches your population size. Then choose the row that matches the level of error you’re willing to accept in the results.

You will see on this table that the smallest samples are still around 100, and the biggest sample (for a population of more than 5000) is still around 1000. The same general principles apply as before – if you plan to divide the results into lots of sub-groups, or the decisions to be made are very important, you should pick a bigger sample.

Note: This table can only be used for basic surveys to measure what proportion of the population have a particular characteristic (e.g. what proportion of farmers are using fertiliser, what proportion of women believe myths about family planning, etc). It can’t be used if you are trying to compare two groups (e.g. control versus intervention) or two points in time (e.g. baseline and endline surveys). See  Sample size: A rough guide  for other tables that can be used in these cases.

Relax and stop worrying about the formulas

It’s a dirty little secret among statisticians that sample size formulas often require you to have information in advance that you don’t normally have. For example, you typically need to know (in numerical terms) how much the answers in the survey are likely to vary between individuals (if you knew that in advance then you wouldn’t be doing a survey!).

So even though it’s theoretically possible to calculate a sample size using a formula, in many cases experts still end up relying rules of thumb plus a good deal of common sense and pragmatism. That means you shouldn’t worry too much if you can’t use fancy maths to choose your sample size – you’re in good company.

Once you’ve chosen a sample size, don’t forget to write good survey questions ,  design the survey form properly  and   pre-test and pilot your questionnaire .

Photo by  James Cridland

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The Quantitative Research Sample Size Calculator

Chris martin, market research room 101: round 2.

On Thursday 9th May 2024, Team Russell and Team Hudson duelled in a panel debate modelled off the po...

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We may love our in-depth qualitative research tools, but we know the value of integrating both qual and quant methods. That’s why we have built our DIY quantitative research sample size calculator. From some basic information, this tool displays the recommended sample size required for your research to be statistically significant.

Use the calculator to work out how many people you need to complete your survey or poll to be confident in the accuracy of your results.

Not sure what values to use? This brief guide explains the terms used in our sample size calculator, in addition to providing recommended values for optimum results.

Sample Size:   Your sample size is the amount of consumers in your target population that you will be researching. This calculator provides a recommended sample size – i.e. the minimum amount of consumers you need to research for your results to be statistically significant within your defined parameters.

Population Size:   The population size is the approximate amount of consumers in the group that you want to research. For example, if you want to understand the internet usage habits of the entire UK population, your population would be all UK consumers ( 64.6 million  at the latest estimate).

Confidence Level:   A confidence level is defined as the statistical probability that the value of a parameter falls within a specified range of values. Therefore a confidence level of N% means you can be N% sure that your results contain the true mean average of the designated population.

In market research, the most commonly used confidence level is 95%. A higher confidence level indicates a higher probability that your results are accurate, but increasing it can dramatically increase the required sample size. Finding a balance between confidence and an achievable research goal is crucial.

In this calculation, each confidence level is translated to a   z-score. A z-score is a statistical method for rescaling data that helps researchers draw comparisons easier. The following table details the z-score generated from each confidence level:

Margin of Error:   The margin of error is the maximum acceptable difference in results between the population and sample. On a basic level, if a poll were to ask 1,000 people if they drive a car and 70% of people were to answer yes – a margin of error of +/- 5% would indicate that in the total population, between 66.5% and 73.5% would answer in the same way.

The smaller the margin of error, the more representative of the total population the results will be. However, decreasing the margin of error will also result in a sharp increase in sample size. We recommend using a 5% margin of error as standard, which should never be increased above 10%.

The DIY Sample Size Calculation

Want to work out your required sample size by hand? Our free calculator uses the following equation. Simply follow the steps below to work out how many research participants you need to complete your research.

S = (z 2  (d(1 - d))/ e 2 ) / 1 + (z 2  (d(1 - d)) / e 2 )

S   = sample size |  P   = population size  |  z   = z-score  |  e   = margin of error  |  d  = standard deviation

Please note that our calculator assumes a standard deviation of 0.5. Use the manual equation to change the standard deviation.

Now that you have calculated the recommended amount of participants required to make your results statistically significant, the next step is to invite participants. In our experience, a typical panel based survey will yield a 15%-20% response rate without an incentive, but approximately a 30% response rate when a relevant incentive is offered. There are a multitude of factors that can affect survey response rate, from length to design, acessibility to relevance.

However, by using an estimate of 30% survey completion and the minimum sample provided by our calculator, it is possible to work out how many consumers you'll need to reach. For example, if you need to reach a minimum sample of 1,000 consumers - you'll need to invite approximately 3,334 consumers within your target population   (S (1 - 0.7) . 

What are your top tips for improving survey response rates? Let us know in the comments below and start a discussion.

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Chris is an experienced executive and marketing strategist in the insight and technology sectors. He also hosts our MRX Lab podcast.

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It’s safe to say artificial intelligence, and more specifically generative AI, has had a transformative impact on the market research sector. From the contentious emergence of synthetic participants t...

How to Use Digital Ethnography and ...

In one way or another, we’ve all encountered social media spaces. Whether you’ve had a Facebook account since it first landed on the internet, created different accounts to keep up with relatives duri...