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How to determine the best statistics sample size for your research.

Knowing how to determine the correct statistics sample size is critical for meaningful research outcomes. This article will guide you through the importance of sample size, the methods to calculate it, and the essential factors that influence it.

Key Takeaways

• An appropriate sample size is crucial for achieving statistically significant and reliable research results, balancing accuracy and practicality.
• Key factors influencing sample size calculation include population size, margin of error, and confidence level, which combine to determine the necessary sample size for robust data representation.
• Various tools and best practices, including online calculators and statistical software, can assist researchers in accurately determining the ideal sample size while considering study goals, cost-efficiency, and potential non-responses.

Sampling illuminates a select group like a spotlight in a vast theater, narrating a story that represents the entire audience. The art and science of choosing the right sample size—a number that can confidently speak for a larger population—are paramount in the realm of research. Whether it’s tasting a spoonful of soup to judge the whole pot or polling a random sample of voters to predict an election, the chosen sample holds the key to unlocking statistically significant insights.

Understanding Sample Size in Statistics

What gives sample size such weight in the field of research? It’s the fulcrum upon which the balance of accuracy and reliability rests. From the classrooms of academia to the boardrooms of market research, ensuring that your study’s sample size is robust enough to represent a population is the cornerstone of extracting meaningful and statistically significant results.

Understanding the nuances of sample size calculation empowers you to elevate your study from simple data collection to informed decision-making.

Definition of Sample Size

So, what exactly is this crucial concept known as sample size? It is the subset of a larger group, the chosen few who bear the responsibility of representing the collective traits, behaviors, or opinions of the entire population. Whether it’s individuals, observations, or data points, the sample size is the lens through which researchers view the broader universe of their study. And like any well-crafted lens, the clarity of the image it provides is paramount to the accuracy of the insights drawn.

Why Sample Size Matters

Overlooking the importance of an appropriate sample size risk false conclusions, mirages of non-existent trends, or oversights of pivotal truths. An adequately sized sample size serves as the foundation for statistical significance, narrowing the margin of error and bolstering the confidence in the results. It’s the difference between a guess and an educated estimate, between a shaky hypothesis and robust evidence.

The size of your sample dictates the precision of your estimates and the power of your statistical tests—making it a guardian against the randomness of chance.

Key Factors Influencing Sample Size Calculation

Identifying the ideal sample size for your study isn’t guesswork but a meticulous process influenced by various factors. These key variables—population size, margin of error, confidence level, and more—interlock to form a precise mathematical framework guiding researchers to the number that will best serve their study’s goals.

The interplay between these elements is subtle yet powerful, as small adjustments can lead to significant changes in the required size of your sample.

Population Size

The larger the population size of your study, the more samples you need to collect. A larger population whispers the need for a larger sample size to ensure the echoes of your findings reverberate with reliability. Yet, as you’ll see, this is but one piece of the puzzle in the grand scheme of sample size calculation.

Margin of Error

The margin of error signifies uncertainty, acknowledging that our estimates are educated approximations, not pinpoint accuracies. As this margin decreases, the need for a larger sample size ascends, tightening the reins on variability and enhancing the precision of our estimates. It’s a delicate balancing act: striving for a smaller margin of error without inflating the resource cost of data collection to unsustainable heights.

Confidence Level

The confidence level signifies certainty, statistically assuring that the sample’s story likely holds true for the larger population. Higher confidence levels require larger samples, as they demand more evidence to back up their claims of representation.

It’s a measure of how firmly your study can stand behind its findings, a testament to the trustworthiness of the insights drawn from the data.

How to Calculate Sample Size

With the stage set and the actors of target population size, margin of error, and confidence level ready, how then do we direct the play to calculate the ideal sample size? The script is written in the language of statistics—a formulaic approach that considers these factors and translates them into a concrete number.

By adhering to this mathematical approach, researchers can determine a minimum sample size that ideally meets their study’s requirements, thus effectively helping them determine sample size.

Sample Size Formula

The sample size formula guides our calculation, standing as a beacon amidst numerous variables. These formulas are the brainchildren of statisticians who have distilled the essence of sample size calculation into equations such as Slovin’s and Fisher’s.

By plugging in values for population size, margin of error, and desired confidence level, these formulas yield the sample size needed to navigate the waters of statistical research with precision and confidence.

Using Z-Scores in Sample Size Calculation

Z-scores, statistical indicators, measure the deviation of our data points from the mean, which is closely related to the concept of standard deviation. They are integral to the sample size calculation, as they define the confidence level for survey results. A higher z-score indicates a greater need for accuracy, thereby nudging the required sample size upward.

It’s the statistical equivalent of adjusting the focus on a microscope, ensuring that the final image is as sharp and clear as possible.

Example Calculation

Let’s illustrate this with an example. Suppose we seek to understand the proportion of U.S. supermarket shoppers who identify as vegan. Aiming for a 95% confidence level and a margin of error of 5%, the formula tells us that we need at least 385 individuals to survey. This is the number that statistically stands up to scrutiny, ensuring that the voices we hear resonate with the collective chorus of the vegan community.

Tools for Calculating Sample Size

In the digital age, advanced tools can simplify the process of sample size calculation. From the simple to the complex, a range of calculators and software is at the researcher’s disposal, each promising to streamline the journey to the optimal sample size. Whether you’re a seasoned statistician or a newcomer to the field, these tools are invaluable allies in the pursuit of statistical precision. Some of the popular tools for sample size calculation include:

• Sample Size Calculator by Creative Research Systems
• Sample Size Calculator by Raosoft
• Sample Size Calculator by SurveyMonkey

These tools can help you determine the appropriate sample size for your research study, ensuring that your results are statistically significant and reliable.

Online Sample Size Calculators

Online sample size calculators are reliable tools for time-pressed researchers. By inputting key parameters like confidence level, population size, and margin of error, these calculators churn out the minimum number of samples required in mere moments.

For example, Qualtrics offers an easy-to-use calculator that transforms the complex into the accessible, supporting researchers as they determine their ideal survey sample size.

Statistical Software

For a more hands-on approach, statistical software like R or SPSS offer advanced tools for sample size calculation. These programs can handle a plethora of variables and cater to a variety of research designs, offering functions that stretch beyond the capabilities of basic calculators.

With these programs, the possibilities are as vast as the data sets they analyze, offering a high degree of customization and precision in the calculation process.

Best Practices for Determining Sample Size

Determining the best sample size is not just a matter of mathematical prowess; it’s also an art that requires an understanding of the study’s context and constraints. Best practices balance cost, accuracy, and study objectives, ensuring the chosen sample size reflects thoughtful consideration and research integrity, not just a numerical value.

Balancing Cost and Accuracy

Cost and accuracy often pull researchers in opposite directions. The push for precise results beckons for a larger sample size, while budget constraints demand frugality. The challenge lies in finding the sweet spot where the cost of data collection aligns with the need for reliable results.

An oversized sample may drain resources, while a sample too small risks the integrity of the study. It’s about making informed choices that respect both the sanctity of data and the realities of research funding.

Considering Study Goals

The study’s objectives should guide every researcher in determining the sample size. What are the goals of the research? What insights are sought? The sample size must be tailored to answer these questions effectively, ensuring that the findings are not just statistically sound but also meaningful and actionable.

Whether it’s capturing the nuances of qualitative data or the precision of quantitative metrics, the sample size must be a fit-for-purpose tool in the researcher’s kit.

Accounting for Non-Responses

Every researcher is familiar with the issue of non-responses, the silent gaps in the data collected. To mitigate this, prudent sample size planning includes a buffer—an estimation of the likely dropout rate, which adjusts the required number upward to compensate. This foresight ensures that the final sample size retains its representativeness and reliability, reflecting a true cross-section of the population despite the inevitable no-shows.

Common Mistakes in Sample Size Calculation

Even experienced researchers can fall into traps when calculating sample size. Common missteps—whether it’s underestimating the number needed, neglecting variability, or ignoring population diversity—can skew results and compromise the integrity of the study.

Awareness of these potential blunders is the first step towards avoiding them and ensuring the robustness of research outcomes.

Underestimating Sample Size

Underestimating sample size is a costly mistake that can obscure the actual effects and complicate interpretation. A sample size too small to detect significant effects is akin to a flashlight too dim to navigate the darkness—it leaves researchers stumbling towards false conclusions and missed opportunities for discovery.

Ignoring Variability

Variability enriches data, adding nuances to findings and depth to conclusions. Ignoring this diversity can lead to an underestimation of sample size, resulting in a bland and underpowered study.

It’s essential to consider the range of responses, the highs and lows, the outliers and the averages, to ensure that your sample size is robust enough to capture the full spectrum of your population’s characteristics.

Overlooking Population Diversity

In order to accurately portray the population, it’s crucial to consider diversity. A sample that mirrors the rich tapestry of the broader population ensures that findings are not only statistically valid but also culturally and contextually relevant.

Neglecting this diversity can lead to a skewed sample that fails to represent the nuances and variations within the population, thereby undermining the generalizability of the study’s results.

Applications of Sample Size in Different Fields

Although the principles of determining sample size are universal, their application varies dramatically across different study fields. From the granular focus of market research to the broad-scale implications of public health studies, understanding the context-specific nuances of sample size is pivotal.

Each field comes with its own set of challenges and requirements, making the ability to adapt sample size calculation strategies to the unique demands of each area a valuable skill for researchers.

Market Research

In the competitive field of market research, the sample size can be the determinant of a product’s success or failure. A well-calculated sample size can unveil the deepest insights into consumer behavior, preferences, and trends, guiding businesses towards informed decisions and strategic growth.

While not all surveys require the rigorousness of a statistically significant sample size, such as those for customer feedback, the need for accuracy remains critical when the stakes are high, and the market landscape is rapidly changing.

Healthcare Studies

Given the significant implications for life and health, accurate sample size calculations in healthcare studies are of ethical importance. Whether it’s evaluating the efficacy of a new treatment or gauging patient satisfaction, the sample size must be carefully calibrated to ensure that the results are reliable and can inform clinical decisions and policy-making.

Educational Research

Educational research greatly benefits from statistically significant sample sizes, forming the basis for meaningful changes based on feedback from students and faculty. By ensuring that the sample represents the diversity of the student body, educational institutions can make data-driven decisions that enhance the learning experience and foster an environment conducive to academic success.

For additional information on related topics, you might find our articles on 250+ Country Names in Local Languages , & age range by generation.

As we draw the curtain on our exploration of sample size in research, it’s clear that the journey to determining the right number is both an art and a science. It requires a blend of statistical knowledge, practical understanding of research goals, and an appreciation of the field of study. By adhering to best practices, avoiding common mistakes, and leveraging the right tools, researchers can ensure that their findings are robust, reliable, and reflective of the population they seek to understand. May this guide serve as a compass in your research endeavors, leading you to the treasure trove of accurate and actionable insights.

Frequently Asked Questions

Why is sample size important in research.

Having an appropriate sample size is crucial in research because it impacts the accuracy of the findings, the statistical power, and the ability to generalize the results to the broader population, ultimately reducing the margin of error and increasing confidence in the outcomes.

How does population size affect sample size?

As population size increases, the sample size needed for representative and reliable research findings also increases, but there is a point where further population increase has a diminishing effect on the required sample size.

What is a margin of error and how does it impact sample size?

A smaller margin of error requires a larger sample size to achieve the desired precision in the estimates. This is because the margin of error represents the range within which the true value in the population is expected to fall.

Can I use an online calculator to determine sample size?

Yes, you can use online sample size calculators to estimate the appropriate sample size based on input parameters such as confidence level, population size, and margin of error.

What are common mistakes to avoid in sample size calculation?

To ensure accuracy and representativeness, common mistakes to avoid in sample size calculation include underestimating the needed sample size, ignoring data variability, and overlooking population diversity. Proper consideration of these factors is crucial for the validity of study results.

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Figuring Out (Determining) Sample Size for Survey Research

Table of Contents

Figuring Out Sample Size (Sample Size Determination)

Folks wanting to learn how to determine the right sample size for their research studies are badly underserved: nearly every article you can find on the internet tells, at best, just half the story. An inadequate sample size could lead to results that are far from the truth, costing your company millions in misguided investments. 

The most common advice you’ll find on the internet often leads straight to those inadequate sample sizes. There are different samples size calculations for different purposes – for means (single or multiple, independent or dependent), for proportions (single, paired, independent), for multivariate statistics (factor analysis, regression, logit, etc.) and for experiments (e.g., conjoint, MaxDiff). For brevity’s sake we’ll focus on figuring out sample size for single proportions, leaving the reader to generalize for cases of two proportions, and for single, paired and independent means.

We’ll cover some rules of thumb about multivariate statistics and experiments. We’ll also differentiate between sample size for confidence intervals (the topic of almost every other article about sample size that you’ll find) and sample size for statistical testing (a topic that is almost uniformly neglected).

In this comprehensive guide, we'll dive deep into:

• The definition of sample size and its significance in research
• Factors influencing the determination of sample size
• Step-by-step calculation methods for figuring out both sample size needs, confidence intervals and hypotheses testing. 
• Sample size advice for studies with complex analyses

Sample Size Definition

When we talk about sample size we just mean the number of respondents (people) that you include in your study . This number depends on whether you want to ensure that the results will (a) reflect the overall population's characteristics or (b) support managerially valuable hypothesis tests, or both.

Significance of Sample Size in Market Research?

Sample size is the currency with which you buy accuracy in survey research , both by generating quantifiable margins of error around any statistics we generate and by delivering credible hypothesis testing results.

Figuring out a properly defined sample size balances cost-efficiency with statistical rigor . It gives your study credibility and it offers a clearer lens through which you can understand your research findings.

To Summarize:

• Sample Size Definition : The number of observations or respondents in a study.
• Significance of Sample Size in Market Research : It directly impacts the credibility and value of the research.

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Factors Influencing Sample Size Determination

How to find the appropriate sample size depends on a few factors. Each requires careful consideration. Let's delve into these key factors.

Confidence versus power

This factor depends on whether you want your sample size scaled for precision (your margin of error or your confidence interval) or for power (i.e., for supporting hypothesis testing). Just for purposes of a sneak preview, the two formulas are slightly different (the formula for statistical power of a hypothesis test has one extra variable in it).

Population Size

Population sizes only matter in the rare case when your sample size will exceed 5% of the total population size. This happens so infrequently that we can refer anyone interested to Google “finite population correction factor,” which you can then add straightforwardly to your sample size formula.

More information about population vs sample

Margin of Error (Confidence Interval)

The margin of error is the range within which the population parameter is expected to fall. Smaller margins require larger sample sizes. Simply put, the more precise you want to be, the larger your sample size needs to be.

Confidence Level

Confidence level refers to the probability that the sample results will represent the population within the margin of error. Common levels are 90%, 95%, and 99%. Higher confidence levels require larger sample sizes.

Standard Deviation

Standard deviation measures how spread out the values in your data set are. When you expect a high variation, you'll need a larger sample size to capture it accurately.

Quick Reference Table:

Sample Size Formulas

Sample size formula for margin of error (confidence interval, precision).

You may recall when learning statistics that your professor showed a formula for a confidence interval, then did some algebra to use it to solve for sample size (n). That’s where this formula comes from, from the confidence interval around a single proportion:

• n = Sample Size
• Z a/2 = Z-value that corresponds to desired confidence level (1.96 corresponds with the typical 95% confidence level)
• p = Proportion of the population (since this is often not known, we usually use a worst case estimate of 0.5)
• d = Margin of error (the radius of the confidence interval, or the precision)

Sample size formula for hypothesis testing

What your professor didn’t show you is that there’s a different formula when you want your sample size to support statistical testing. That’s where this formula comes from:

• n, Z a/2 , p and d are as above and
• Zb =the Z-value that corresponds to the desired level of statistical power (0.84 corresponds to the commonly used 80% power)

Figuring Out Sample Size: The Process

The sample size calculation process looks harder than it is. Just break it down into systematic steps. Here's how you can approach it, complete with real-world examples.

Step 1: Determine Confidence Level—Choose Wisely

The confidence level you select specifies how confident you can be that your sample results will reflect the true population parameter (a de facto standard is to shoot for 95% confidence). A higher confidence level, such as 99%, will provide greater assurance but will demand a larger sample size. A level like 99% might be appropriate for projects that carry high stakes, such as healthcare studies or regulatory compliance assessments.

On the flip side, a lower confidence level, like 90%, may suffice for quick market assessments or pilot studies. While it reduces the sample size needed, it does come at the cost of confidence in your findings. Here you accept a slightly higher risk that your sample results may not perfectly represent the broader population.

Rule of Thumb : For most business or academic research, a confidence level of 95% is considered a good starting point. For high-stakes, mission-critical projects, aim for 99%. For more exploratory or pilot projects where you can tolerate a bit more risk, 90% might be acceptable.

Z a/2 -the Z score for Confidence Level

In the context of confidence levels, this Z-score gives us the confidence level we want to have that the population score (mean, proportion, whatever you’re measuring) is within the margin of error, or contained within the confidence interval.

To calculate the Z-score, you can look it up in the standard normal distribution table, or use statistical software. The Z-score table below shows the Z-scores for the most commonly used confidence levels in market research (90%, 95%, and 99%) .

Z-score Table for Common Confidence Levels

Remember, the choice of confidence level dictates how much risk you're willing to accept, and in turn, influences the sample size and potentially, the viability of your project.

Example : Let's say you're researching consumer preferences for a new type of organic snack bar. You decide to go with a 95% confidence level, that is a 95% chance that your margin of error will include the population’s preference for the new snack bar. This equates to a Z-score of 1.96.

Step 2: Choose the Margin of Error/Precision

The margin of error measures the precision of your survey results. Simply put, a smaller margin of error (e.g., 2%) provides more accurate insights but requires a larger sample size. This can be particularly valuable when you're working on high-stakes projects or research where even minor errors could have significant business or policy implications.

Conversely, a larger margin of error (e.g., 5% or 10%) may suffice for exploratory studies or when resource constraints are a significant concern. In these cases, the benefit of a larger sample size may not outweigh the additional time and costs involved.

Rule of Thumb: Always weigh the trade-off between precision and resources to arrive at an optimal margin of error for your study. Larger samples give you more precision but they also cost more. Your margin of error directly influences both the quality and feasibility of your market research. This selection is not merely a statistical decision; it’s a strategic one that can have a meaningful impact on your project's success.

Example : Continuing with the organic snack bar study, you decide a 5% (0.05) margin of error is acceptable: you want your estimate to be accurate to with +/- 5% of the population percentage.

Step 3: Estimate Standard Deviation 

The standard deviation is a measure of the dispersion or spread of your data points around their average value. A high standard deviation implies more variability, whereas a low standard deviation indicates that the values are more bunched around the mean.

Why Standard Deviation Matters : A high standard deviation, means that there's a larger spread in the opinions, attitudes, or behaviors of your target population. This level of variability could require a larger sample size to capture the differences adequately. In contrast, a low standard deviation simplifies things; the closer your data points are to the mean, the less sample you may need for precise results.

Rule of Thumb : If you don't have prior data to calculate the actual standard deviation, a typical approach for proportions is to assume a 50:50 split or a proportion (p) of 0.05. This conservative estimate maximizes your sample size and thereby reduces the chance of underestimating it. However, if you have historical data or pilot studies to draw from, use the observed standard deviation as it will provide a more accurate sample size tailored to your research.

Example : Given the lack of preliminary data on consumer preferences for organic snack bars, you choose p = 0.5 to maximize your sample size.

Step 4: Determine Your Level of Power (for Hypothesis Testing Only)

Power is your ability to identify a difference of a particular size in hypothesis testing. If being able to detect a difference of 5% is really important to you, then you want to have a lot of power to detect that size of difference.

Why Power Matters: In a statistical test we have to worry about both confidence and power, because we seek to avoid both false positives (through the confidence level) and false negatives (via the power level). If you calculate sample size and ignore power, your sample sill be too small to detect the things that matter to you and you increase your risk of experiencing a false negative. False negatives can be very costly in practice. Let’s say a new ad campaign will be so successful that it will increase sales by 10%. If your product has $500 million in sales, that 10% increase is $50 million. If you cut costs on sample size and get a false negative result, however, you could conclude that the new ad isn’t a success, and cost your company $50 million in lost sales.

Rule of Thumb : We usually want at least 70% or 80% power to detect differences when they are real. In truth, however, when setting both the confidence level and power, we should consider how costly are false negatives (concluding the advertising doesn’t work when in fact it does) and false positives (concluding a new ad is successful when it is not) and then tailor our confidence and power to reflect those costs.

Step 5: Apply the Appropriate Sample Size Formula

This is where determining the correct sample size formula comes into play. Let’s say we want to make sure our study can identify the percentage of respondents who want our new product. We want 95% confidence the proportion we measure will be within 10 percentage points of the population proportion, but we don’t really have a clue what that might be.

Example : Plug in the Z-score (1.96), estimated proportion (0.5), and margin of error (0.05) into the sample size formula for margin of error:

Note that we rounded our answer up to 385 because we can’t interview 0.16 of a respondent.

Actually, it turns out management wants to know the results of a statistical test. The current advertising scored 50% while it was in the testing phase, so we want to know if our new ad can beat the old one by 5%. Moreover, because we stand to lose sales if we get a false negative here, we want to have 80% power to detect a significant difference. Now we use the sample size formula for power:

Note that when we took power into account because we wanted to avoid a false negative) our sample size requirement more than doubled, from 385 to 784. Had the company gone out with a sample of 385, it would have had only a 50% chance of identifying a successful ad campaign! That’s research money very poorly spent, but it’s exactly what happens if you don’t take power into account.

Summary Checklist: Sample Size Determination Steps

• Determine Confidence Level : Usually 95%, but sometimes 90% or 99%.
• Choose Margin of Error : A small percentage (2-5%) is common.
• Estimate Proportion of Population : Often 0.5 to maximize sample size.
• Choose a level of power (hypothesis testing only) : 80% is common, 70% is usually a minimum recommendation
• Apply the Appropriate Sample Size Formula : Use the formula to find the ideal sample size.

By following these steps, you're well on your way to figuring out sample size correctly for your study. This is a cornerstone of robust and credible market research, one that balances the risks of false positives and false negatives so as to maximize the value of your findings.

Using Sample Size Calculators

Though the sample size formula is a reliable tool for manual calculations, let's face it—math can be tedious. Sample size calculators can offer a more convenient route , often giving you the same level of accuracy with just a few clicks. However, most online sample size calculators use only the sample size for precision formula and thus do not take into account power. To remedy this, you may want just to double the sample size from an online calculator (because when we chose 80% power in the example above, the sample size, 784, was about double the one that came from considering only the confidence interval.

Key Takeaway: Sample size calculators are your go-to tools for quick, accurate, and convenient calculations. Most sample size calculators neglect statistical power, however, so use them with caution.

Troubleshooting Sample Size Issues

Sometimes your calculated sample size may be impractical (unaffordable). However, there are some strategies you can employ to come up with a more affordable sample size (hopefully without compromising your research too much).

Lowering the Confidence Level

If your sample size is turning out too large for your resources, one option is to lower the confidence level . A move from a 99% to a 95% confidence level can noticeably reduce the needed sample size. Remember though, this makes your results less robust.

Lowering the Power

While this comes with risks, lowering your power to 70% from 80%, say, can reduce your sample size.

Increasing the Margin of Error

Similarly, widening the margin of error will also decrease your required sample size. While this increases the range within which your population parameter is expected to fall, it's a trade-off that can sometimes make the research process more feasible.

Key Takeaway: Tweaking your confidence level, power or margin of error can reduce sample size needs, but always weigh the pros and cons.

Troubleshooting Options

Remember, these are options to help make your study feasible, but they do come with trade-offs. Always consider the impact of these adjustments on the reliability and credibility of your findings.

Real-Life Sample Size Applications

Understanding the mechanics of how to figure out sample size is great, but what does this mean in real-world settings? How has accurate sample size determination influenced the outcomes of actual market research projects?

Success Story

Let's consider a tech company that recently launched a new feature and wanted to gauge user satisfaction. By carefully calculating a sample size that took into account a 95% confidence level and a 4% margin of error, the company was able to reliably conclude that the feature was well-received, leading to its continued investment and improvement.

Consequences of Poor Sample Size

On the flip side, another business failed to adequately figure out sample size for a similar user-satisfaction survey. They concluded there was no change in user satisfaction, but there was and they missed it leading to misguided business decisions.

Key Takeaway: Accurate sample size determination isn't just academic; it has tangible implications for your business decisions and overall strategy.

Real-Life Implications

• Success Scenarios : Precise sample size -> Reliable data -> Informed Decisions
• Failure Scenarios : Inaccurate sample size -> Unreliable Data -> Misguided Decisions

Figuring out sample size is more than a statistical necessity; it's a vital business tool that can guide a company toward success or contribute to its failure.

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Sample Sizes for Different Research Methods

The calculations above work for a single proportion. Similar equations exist for confidence intervals and statistical tests involving differences in proportions and differences in means. Complex statistical models have their own sample size requirements.

Regression analysis/driver analysis

The old rule of thumb of 10 observations per variable in the model is useful and works for data of average condition. When using particularly clean data we may get by with as few as 5 observations per variable. More common will be data with higher than average levels of multicollinearity and this will require larger sample sizes. So if our regression model has 12 variables, the basic recommendation would be n = 10k = 10(12) = 120.

Because it estimates the shape of an S-curve rather than a straight line, logit is more sample size intensive than regression. The rule of thumb is 10 times the number of variables in the model divided by the smaller of the two percentages of the binary response: n = 10k/p. So if our model has 2 predictors and we expect the response will be about 60/40 we’d go with n = 10(12)/(0.40) = 300.

Segmentation

Previous advice was a bit all over the board, but the most recent paper on the topic suggested a sample size of 100 for every basis variable included in the segmentation analysis. So if we have 20 basis variables, that suggests n=2,000.

Factor analysis 

One source suggests that samples of less than a hundred are held to be “poor,” 200 to be “fair” and 300 “good.” Others suggest that when the number of factors is small and correlations are large and reliable, samples of as few as 50 may be workable. Given the messiness of most survey research data, erring on the side of larger sample size seems prudent.

Tree-Based Segmentation

In classification or regression trees, sample is split and then split again, repeatedly. After three levels of pairwise splits, a tree model could have eight groups. For this reason, we usually recommend having at least 1000 respondents.

Conjoint Analysis/MaxDiff

Our usual recommendation about multivariate statistics (like conjoint analysis and MaxDiff analysis ) is to have at least 300 respondents, or at least 200 per separately reportable subgroup. Another way to think about conjoint analysis is to work backward from the simulator: what size differences in shares would be worth capturing, and what size of sample do you need to capture them (using a sample size formula for the difference in two proportions).

Key Takeaway : The methodology you choose can significantly impact your sample size needs, so choose wisely and calculate accordingly. Tailoring your sample size to the specific demands of your chosen methodology isn't just best practice; it's crucial for obtaining valid, actionable insights.

FAQ: Frequently Asked Questions about Figuring Out Sample Size

You've journeyed through the intricate maze of sample size determination, but you may still have lingering questions. Let's tackle some of those.

How do you define sample size?

Sample size refers to the number of individual data points or subjects that are included in a study. It's a crucial aspect of market research that impacts the reliability and credibility of your findings.

What is a good sample size?

A "good" sample size is one that allows for a high confidence level and a low margin of error (and for statistical testing, a high level of power), all while remaining manageable and cost-effective. Figuring out the ideal sample size can vary based on the research methodology.

How do I calculate sample size?

To calculate the ideal sample size, you typically use a sample size formula that takes into account the statistic you want to study, your desired levels of confidence (and power), and the acceptable margin of error. Some online calculators can also do this for you.

And there you have it—a detailed guide on Understanding and Figuring Out Sample Size for Surveys . 

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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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How many respondents do you need? Use our sample size calculator to get the right sample size for your next survey. We also answer frequently asked questions on sample size and provide suggestions to improve your surveys in this handy guide.

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What is a sample and why sample size matters.

Researching the entire population is often not feasible due to many constraints. Instead, sampling is used, which is more practical for analysis and generates results more promptly.

A sample is a subset of individuals selected from the target population to estimate the characteristics of the population. Sample size is important because it determines the accuracy and quality of your survey results. It is especially important in market research as robust data is the key to unlocking meaningful and actionable insights about your target audience .

Want to identify the number of responses required for your survey quickly? Just use our sample size calculator.

If you want to learn more about the theories behind the calculator and sample size, we also compiled everything you need to know in this guide.

Sample Size Calculator

Four important components of sample size calculation.

Here are four key components you’ll need to understand in calculating your minimum sample size:

1. Population size

The population size is the total number of people in the population (target audience) you are looking to survey. For example, if you were surveying the general population of a city with 30,000 residents, the population size for your study is 30,000.

When surveying small populations, a finite population correction is used. You can use 100,000 with caution if you do not know the exact size of a large population; the sample size remains quite static over 100,000.

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2. Confidence level

The confidence level indicates the probability that your confidence interval contains the true population value, if you were to repeat your study with a random sample selection .

For example, with a confidence level of 95%, your study could be repeated several times and your population would fall within the confidence interval on 95% of these occurrences.

The accuracy of your results is determined by how high your confidence interval is. You should also note that as your confidence level increases, so does your required sample size.

Conjointly’s default confidence level is 90% as it is most useful in business settings. However, you can easily adjust the confidence levels in your Conjointly reports.

3. Confidence interval (Margin of error)

The confidence interval is a range of values that are likely to contain your population value and is expressed in percentage points. For example, a confidence interval of ±2% means that your true population will lie either 2 percentage points above or below where it is shown in your results.

Your confidence interval will be higher or lower than your specified value as it is based on your actual sample proportion, rather than your estimated proportion. It also depends on how accurate the results you are seeking are (determined by your confidence level). A higher confidence level results in a wider confidence interval.

Check out the margin of error for different survey sample sizes under the standard 90% level of confidence.

4. Sample proportion

Your sample proportion (expressed as a percentage) indicates your estimated results and is calculated using a Quick Feedback study or previous survey results. Otherwise, 50% is a safe sample proportion to use without hindering the accuracy of your calculated sample size.

What is the formula for determining sample size?

The formula for calculating sample size is:

• n is the sample size,
• N is the population size,
• z is the confidence level (in percent, such as 90% = 0.9 ),
• p is the sample proportion (in percent, such as 50% = 0.5 ),
• e is the margin of error (in percent, such as 5% = 0.05 ).

What is a good sample size for a market research survey?

The ideal sample size for your study will depend on your population size, confidence level, and confidence interval. The survey design and methodology you use may also require you to adjust your sample size.

A good sample size will satisfy your criteria for accuracy in quantitative research results. It is usually determined by a combination of expected confidence, budget and resource availability for analysis.

Generally, the bigger the sample size, the more accurate your results will be. However, you should consider that large sample sizes are costlier and can complicate your study. You can use our sample size calculator to determine the minimum sample size for your project to ensure your survey is accurate and cost-effective.

What sample size do I need for 95 confidence?

Once you have selected your confidence level as 95%, you will need to determine your confidence interval and population size to calculate the sample size required for your study.

The sample size will be larger for 95% confidence than 90%, if all other factors remain the same.

Even though we recommend using 90% confidence level to achieve the right balance between cost and precision, you can increase it up to 99 percent. However, 99% confidence more than doubles the size of the required sample, compared to 90% confidence. This might produce unnecessary bloat of data for most quantitative research projects .

How do you find the sample size when given the margin of error?

To calculate sample size using your margin of error (confidence interval), you must also know your confidence level and population size.

The margin of error is usually expressed as ± value. This means your survey results can represent a range of values plus or minus the value of the margin of error.

Consider a survey that indicates that 40% of car owners in the USA would not consider the colour red for their next car. With a 5% margin of error, you should express your findings as 35-45% of car owners in the USA would not consider a red car. To gain more accurate insights , you could lower your margin of error to 2%, for example, and expect your findings to lie within a smaller confidence interval of 38-42%.

Why does the margin of error decrease as the sample size increases?

You will see in our sample size calculator, reducing your margin of error results in a large increase in recommended sample size.

It should be noted that this is not a linear relationship, increasing sample size will result in diminishing returns in the margin of error reduction. For example, the following chart illustrates the relationship between the margin of error and sample size, for a population of 1 million, seeking a 90% confidence interval, with a 0.5 sample proportion.

As shown above, moving from a 5% margin of error to a 1% margin of error would require a sample size over 20 times as large.

Why is a small sample size bad? Why is a larger sample size better? Why must sample size be greater than 30?

How do you justify a small sample size in quantitative research.

A small sample size can be justified when:

• The whole population is small. For example, in B2B research, when there are only 100 customers, then it is OK to sample ~30 to get a view of the opinions of the whole customer base.
• The cost of sampling is prohibitive.

Please note, it is not justifiable for most consumer surveys as they require a sample of hundreds of consumers from your product category, including current users and potential buyers. Conjointly provides numerous options and delivers quality respondents straight into your survey, starting at only $0.90 per response.

How does sample size affect validity of a study?

If sample size is not large enough for your study, the internal and external validity will be compromised and it can also result in cases of bias. A higher sample size results in more accurate results. Sample size is only one of many factors that affect the validity of your study.

You should also consider that data can still be useful in some instances even if you do not meet the required sample size for your study. For example, a customer satisfaction survey with open-ended questions can still provide meaningful insights as detailed consumer feedback is indispensable to market research.

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

6 min read How many is enough? Over the years, researchers have grappled with the problem of finding the perfect sample size for statistically sound results. Here we shed light on some methods and tools for sample size determination.

What is sample size?

Sample size is a frequently-used term in statistics and  market research , and one that inevitably comes up whenever you’re  surveying  a large population of respondents. It relates to the way research is conducted on large populations.

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So what is sampling, and why does sample size matter?

When you survey a large population of respondents, you’re interested in the entire group, but it’s not realistically possible to get answers or results from absolutely everyone. So you take a random sample of individuals which represents the population as a whole.

The size of the sample is very important for getting accurate, statistically significant results and running your study successfully.

• If your sample is too small , you may include a disproportionate number of individuals which are outliers and anomalies. These skew the results and you don’t get a fair picture of the whole population.
• If the sample is too big , the whole study becomes complex, expensive and time-consuming to run, and although the results are more accurate, the benefits don’t outweigh the costs.

If you’ve already worked out your variables you can get to the right sample size quickly with the online sample size calculator below:

Sample size calculator

If you want to start from scratch in determining the right sample size for your market research, let us walk you through the steps.

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.

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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 10 min read, sampling and non-sampling errors 10 min read, request demo.

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How To Determine Survey Sample Size: A Short Guide

Imagine you want to know how many people in the US drink coffee every morning. If you ask 10 people, that likely isn’t representative of such a large group. 

But if you want to know how many of your 50 coworkers do so, 10 respondents may be enough to get the right idea. 

That is what a survey sample size is in a nutshell. It’s not usually possible to collect feedback from an entire group you are trying to survey. So you have to decide how many people you need answers from to get reliable results.

What is Survey Sample Size?

A survey sample size is the number of participants in a study. In other words, the number of people who responded to your survey.

When conducting any survey, one of your main goals is to get results that are statistically significant. This means enough responses to infer conclusions with confidence.

Sample size usually refers to surveying large populations. So, if all you want to do is find out your 500 customers’ satisfaction, you likely won’t have trouble getting a representative sample.

On the other hand, if you want to see how many marketers in the US are potential customers for you, you’ll have to make do with a statistically significant portion of them.

PS: Check out this persona survey template to figure out where to look for potential customers!

What is a Good Sample Size for a Survey?

When the sample size is too small, you may get a disproportionately small or large number of outliers. This can skew results significantly.

On the other hand, while surveying more people will always get you more accurate results, it is often unfeasible, complex, and expensive. Oftentimes, surveying the entire population is not worth the time and effort.

So, what’s the golden mean?

Many statisticians concur that a sample size of 100 is the minimum you need for meaningful results. If your population is smaller than that, you should aim to survey all of the members. 

The same source states that the maximum number of respondents should be 10% of your population, but it should not exceed 1000. 

For instance, if you have a population of 250,000, 10% would be 25,000. Since this is higher than 1,000, a sample size of 1,000 should be enough to get you statistically significant results.

How to Determine Sample Size for a Survey

Calculating sample size can be made easier with software such as a calculator. Still, let’s have a look at what the process is like behind the scenes.

Sample Size Formula

The survey sample size is usually determined with a take on Slovin’s formula . 

Here is what you’ll need.

“P”, which is your standard deviation

This is how confident you can be that a population will select an answer within a given range. In plain English, this would be how extreme you can expect the responses to be.

A low standard deviation means that you don’t expect your respondents to be extreme. A higher standard deviation will mean that you expect respondents to choose answers from the ends of the spectrum.

Standard deviation is given as a number between 0 and 1. If you are unsure, go with 0.5, which is the exact midway point. Bear in mind, though, that this might make your results more estimated.

“Z”, which represents your “z score”

Your z score is the number of standard deviations a given group is away from the mean. 

Thankfully, you can use a cheat sheet to determine your “z score”, depending on how confident you want to be about your results. 

For example

• 99% desired confidence level would equal a z score of 2.58
• 95% would equal 1.96
• 90% is 1.65
• 85% is 1.44

According to Lisa Sullivan, Professor of Biostatistics

 “a 95% confidence interval means that if we were to take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value”.

In layman’s terms, if you calculate your sample size with a z score of 1.96, then if you were to repeat your survey 100 times, you would get the same mean result about 95 times.

“E”, which is your margin of error

The margin of error is basically how sure you need to be that the results are accurate for the entire population. The bigger the margin of error, the less reliable your results are. 

You usually want the margin of error at around 5% or less. This means you can be 95% or more sure that your results are accurate.

For example, let’s say you discover that 85% of your respondents find your customer service effective. If you assumed a 5% margin of error, you must add 5% to either side of the score. 

In essence, you can assume that 80-90% of your customer base is satisfied with your customer service.

The margin of error should be provided in decimal form. Note that the smaller margin of error you want, the larger your sample size will be.

And finally, “N”, which is your population size

The population is all the people whose attitudes or stances you are trying to learn about. 

The population could be anything from all of your customers to all people on Earth. The bigger your population, the bigger your sample will need to be in order to get reliable results.

When you know what your population is, you need to figure out how many people are in that category. 

For instance, if you wanted to get accurate survey results for the entire US, your population size would be 329.5 million (source: World Bank, 2020 ).

If you wanted to run an NPS campaign , you’d consider all of your existing customers. 

Calculation: What Sample Size is Needed for a Survey?

Determining the sample size begins with considering the population in a study.

So, let’s say I wanted to survey a population of 500, and I want to be 5% confident that I will get accurate results 95% of the time. I would need to survey 218 people.

This formula may seem confusing. You can use this spreadsheet I prepared to skip the manual labor. Make sure to copy the spreadsheet and edit only the green fields.

Let’s work with another example. We’ll assume the following values:

• 95% confidence level
• 0.5 standard deviation
• 5% margin of error
• Population of 10,000

Using our spreadsheet, you can see that you should survey at least 370 people. And Survicate is currently working on a sample size calculator, so stay tuned!

Once you have your sample size, you have to account for your response rate . You can expect it to be more or less 20-30%. If you expect to get fewer responses, send the survey to a larger number of people to reach your sample size milestone.

How to Decide Who to Include in Your Sample?

For small to medium-size businesses, the method of getting a sample is usually to send the survey to the entire customer base and hope to get enough responses.

But you may want to target your survey as well. For example, if your previous survey showed you have relatively few NPS detractors , you may want to target them specifically to find out whether their score had changed or to get more details.

Nonetheless, choosing a random sample will usually get you the most reliable results for your population.

What if You Can’t Get Enough Responses?

Sometimes, you just can’t get the number of responses to match that magical sample size you desire. Using best survey tools may help boost your response rate, but what if you still can’t get close to 100?

Calculating sample size in survey research is still important. You can benchmark how many more responses you need and thus, how you can treat incomplete results.

While your results may not be statistically significant, you can still use the feedback to fuel your business decisions. The answers will still be valuable, especially if you make good use of open-ended questions for context.

Send surveys through any channel with Survicate

Generally speaking, most surveyors want the results to be as comprehensive as possible. The more responses you get, the better. The only limiting factors are time and money.

With survey software like Survicate, you can target your audience directly through your website, email, or app, without having to manually reach out or ask bystanders. This cuts down on the required time and effort considerably.

Simply use one of our ready-to-send templates and start gathering feedback . Now, you can take advantage of our 10-day free trial to test all Business plan features with up to 25 survey responses.

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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.

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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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Sample Size Calculator

Find out the sample size.

This calculator computes the minimum number of necessary samples to meet the desired statistical constraints.

Find Out the Margin of Error

This calculator gives out the margin of error or confidence interval of observation or survey.

Related Standard Deviation Calculator | Probability Calculator

In statistics, information is often inferred about a population by studying a finite number of individuals from that population, i.e. the population is sampled, and it is assumed that characteristics of the sample are representative of the overall population. For the following, it is assumed that there is a population of individuals where some proportion, p , of the population is distinguishable from the other 1-p in some way; e.g., p may be the proportion of individuals who have brown hair, while the remaining 1-p have black, blond, red, etc. Thus, to estimate p in the population, a sample of n individuals could be taken from the population, and the sample proportion, p̂ , calculated for sampled individuals who have brown hair. Unfortunately, unless the full population is sampled, the estimate p̂ most likely won't equal the true value p , since p̂ suffers from sampling noise, i.e. it depends on the particular individuals that were sampled. However, sampling statistics can be used to calculate what are called confidence intervals, which are an indication of how close the estimate p̂ is to the true value p .

Statistics of a Random Sample

The uncertainty in a given random sample (namely that is expected that the proportion estimate, p̂ , is a good, but not perfect, approximation for the true proportion p ) can be summarized by saying that the estimate p̂ is normally distributed with mean p and variance p(1-p)/n . For an explanation of why the sample estimate is normally distributed, study the Central Limit Theorem . As defined below, confidence level, confidence intervals, and sample sizes are all calculated with respect to this sampling distribution. In short, the confidence interval gives an interval around p in which an estimate p̂ is "likely" to be. The confidence level gives just how "likely" this is – e.g., a 95% confidence level indicates that it is expected that an estimate p̂ lies in the confidence interval for 95% of the random samples that could be taken. The confidence interval depends on the sample size, n (the variance of the sample distribution is inversely proportional to n , meaning that the estimate gets closer to the true proportion as n increases); thus, an acceptable error rate in the estimate can also be set, called the margin of error, ε , and solved for the sample size required for the chosen confidence interval to be smaller than e ; a calculation known as "sample size calculation."

Confidence Level

The confidence level is a measure of certainty regarding how accurately a sample reflects the population being studied within a chosen confidence interval. The most commonly used confidence levels are 90%, 95%, and 99%, which each have their own corresponding z-scores (which can be found using an equation or widely available tables like the one provided below) based on the chosen confidence level. Note that using z-scores assumes that the sampling distribution is normally distributed, as described above in "Statistics of a Random Sample." Given that an experiment or survey is repeated many times, the confidence level essentially indicates the percentage of the time that the resulting interval found from repeated tests will contain the true result.

Confidence Interval

In statistics, a confidence interval is an estimated range of likely values for a population parameter, for example, 40 ± 2 or 40 ± 5%. Taking the commonly used 95% confidence level as an example, if the same population were sampled multiple times, and interval estimates made on each occasion, in approximately 95% of the cases, the true population parameter would be contained within the interval. Note that the 95% probability refers to the reliability of the estimation procedure and not to a specific interval. Once an interval is calculated, it either contains or does not contain the population parameter of interest. Some factors that affect the width of a confidence interval include: size of the sample, confidence level, and variability within the sample.

There are different equations that can be used to calculate confidence intervals depending on factors such as whether the standard deviation is known or smaller samples (n<30) are involved, among others. The calculator provided on this page calculates the confidence interval for a proportion and uses the following equations:

Within statistics, a population is a set of events or elements that have some relevance regarding a given question or experiment. It can refer to an existing group of objects, systems, or even a hypothetical group of objects. Most commonly, however, population is used to refer to a group of people, whether they are the number of employees in a company, number of people within a certain age group of some geographic area, or number of students in a university's library at any given time.

It is important to note that the equation needs to be adjusted when considering a finite population, as shown above. The (N-n)/(N-1) term in the finite population equation is referred to as the finite population correction factor, and is necessary because it cannot be assumed that all individuals in a sample are independent. For example, if the study population involves 10 people in a room with ages ranging from 1 to 100, and one of those chosen has an age of 100, the next person chosen is more likely to have a lower age. The finite population correction factor accounts for factors such as these. Refer below for an example of calculating a confidence interval with an unlimited population.

EX: Given that 120 people work at Company Q, 85 of which drink coffee daily, find the 99% confidence interval of the true proportion of people who drink coffee at Company Q on a daily basis.

Sample Size Calculation

Sample size is a statistical concept that involves determining the number of observations or replicates (the repetition of an experimental condition used to estimate the variability of a phenomenon) that should be included in a statistical sample. It is an important aspect of any empirical study requiring that inferences be made about a population based on a sample. Essentially, sample sizes are used to represent parts of a population chosen for any given survey or experiment. To carry out this calculation, set the margin of error, ε , or the maximum distance desired for the sample estimate to deviate from the true value. To do this, use the confidence interval equation above, but set the term to the right of the ± sign equal to the margin of error, and solve for the resulting equation for sample size, n . The equation for calculating sample size is shown below.

EX: Determine the sample size necessary to estimate the proportion of people shopping at a supermarket in the U.S. that identify as vegan with 95% confidence, and a margin of error of 5%. Assume a population proportion of 0.5, and unlimited population size. Remember that z for a 95% confidence level is 1.96. Refer to the table provided in the confidence level section for z scores of a range of confidence levels.

Thus, for the case above, a sample size of at least 385 people would be necessary. In the above example, some studies estimate that approximately 6% of the U.S. population identify as vegan, so rather than assuming 0.5 for p̂ , 0.06 would be used. If it was known that 40 out of 500 people that entered a particular supermarket on a given day were vegan, p̂ would then be 0.08.

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Consultation on Sample Size determination

Selection of a sample size, large enough to be a representative of the population that you are studying, is difficult. The principles of probability and statistical analysis must be known if you are to select the perfect sample size. Your research committee will lay emphasis on selection of the correct sample size. We help you include a valid justification for your sample size in the methodology chapter.

We take into consideration a number of factors while performing sample size calculation on behalf of our clients:

• Precision Level or Accuracy
• Need for Data for Research
• Level of Confidence
• The Degree of Variability and Deviation

Our calculations also take into consideration whether the research needs small or large population. Thus, the approaches vary depending on the necessity of the study. Two types of sampling techniques are adopted by us:

• Probability or Representative Sampling
• Non-Probability or Judgmental Sampling

The method adopted for determining the sample size under both these techniques is complicated, and PhD statisticians associated with us are able to help scholars with precision.

Determination of sample size for any study is not as simple as using the formulae on any arbitrary figure that the researcher deems fit. Request for quote today through our contact us page .

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Sample Size and its Importance in Research

Chittaranjan andrade.

Clinical Psychopharmacology Unit, Department of Clinical Psychopharmacology and Neurotoxicology, National Institute of Mental Health and Neurosciences, Bengaluru, Karnataka, India

The sample size for a study needs to be estimated at the time the study is proposed; too large a sample is unnecessary and unethical, and too small a sample is unscientific and also unethical. The necessary sample size can be calculated, using statistical software, based on certain assumptions. If no assumptions can be made, then an arbitrary sample size is set for a pilot study. This article discusses sample size and how it relates to matters such as ethics, statistical power, the primary and secondary hypotheses in a study, and findings from larger vs. smaller samples.

Studies are conducted on samples because it is usually impossible to study the entire population. Conclusions drawn from samples are intended to be generalized to the population, and sometimes to the future as well. The sample must therefore be representative of the population. This is best ensured by the use of proper methods of sampling. The sample must also be adequate in size – in fact, no more and no less.

SAMPLE SIZE AND ETHICS

A sample that is larger than necessary will be better representative of the population and will hence provide more accurate results. However, beyond a certain point, the increase in accuracy will be small and hence not worth the effort and expense involved in recruiting the extra patients. Furthermore, an overly large sample would inconvenience more patients than might be necessary for the study objectives; this is unethical. In contrast, a sample that is smaller than necessary would have insufficient statistical power to answer the primary research question, and a statistically nonsignificant result could merely be because of inadequate sample size (Type 2 or false negative error). Thus, a small sample could result in the patients in the study being inconvenienced with no benefit to future patients or to science. This is also unethical.

In this regard, inconvenience to patients refers to the time that they spend in clinical assessments and to the psychological and physical discomfort that they experience in assessments such as interviews, blood sampling, and other procedures.

ESTIMATING SAMPLE SIZE

So how large should a sample be? In hypothesis testing studies, this is mathematically calculated, conventionally, as the sample size necessary to be 80% certain of identifying a statistically significant outcome should the hypothesis be true for the population, with P for statistical significance set at 0.05. Some investigators power their studies for 90% instead of 80%, and some set the threshold for significance at 0.01 rather than 0.05. Both choices are uncommon because the necessary sample size becomes large, and the study becomes more expensive and more difficult to conduct. Many investigators increase the sample size by 10%, or by whatever proportion they can justify, to compensate for expected dropout, incomplete records, biological specimens that do not meet laboratory requirements for testing, and other study-related problems.

Sample size calculations require assumptions about expected means and standard deviations, or event risks, in different groups; or, upon expected effect sizes. For example, a study may be powered to detect an effect size of 0.5; or a response rate of 60% with drug vs. 40% with placebo.[ 1 ] When no guesstimates or expectations are possible, pilot studies are conducted on a sample that is arbitrary in size but what might be considered reasonable for the field.

The sample size may need to be larger in multicenter studies because of statistical noise (due to variations in patient characteristics, nonspecific treatment characteristics, rating practices, environments, etc. between study centers).[ 2 ] Sample size calculations can be performed manually or using statistical software; online calculators that provide free service can easily be identified by search engines. G*Power is an example of a free, downloadable program for sample size estimation. The manual and tutorial for G*Power can also be downloaded.

PRIMARY AND SECONDARY ANALYSES

The sample size is calculated for the primary hypothesis of the study. What is the difference between the primary hypothesis, primary outcome and primary outcome measure? As an example, the primary outcome may be a reduction in the severity of depression, the primary outcome measure may be the Montgomery-Asberg Depression Rating Scale (MADRS) and the primary hypothesis may be that reduction in MADRS scores is greater with the drug than with placebo. The primary hypothesis is tested in the primary analysis.

Studies almost always have many hypotheses; for example, that the study drug will outperform placebo on measures of depression, suicidality, anxiety, disability and quality of life. The sample size necessary for adequate statistical power to test each of these hypotheses will be different. Because a study can have only one sample size, it can be powered for only one outcome, the primary outcome. Therefore, the study would be either overpowered or underpowered for the other outcomes. These outcomes are therefore called secondary outcomes, and are associated with secondary hypotheses, and are tested in secondary analyses. Secondary analyses are generally considered exploratory because when many hypotheses in a study are each tested at a P < 0.05 level for significance, some may emerge statistically significant by chance (Type 1 or false positive errors).[ 3 ]

INTERPRETING RESULTS

Here is an interesting question. A test of the primary hypothesis yielded a P value of 0.07. Might we conclude that our sample was underpowered for the study and that, had our sample been larger, we would have identified a significant result? No! The reason is that larger samples will more accurately represent the population value, whereas smaller samples could be off the mark in either direction – towards or away from the population value. In this context, readers should also note that no matter how small the P value for an estimate is, the population value of that estimate remains the same.[ 4 ]

On a parting note, it is unlikely that population values will be null. That is, for example, that the response rate to the drug will be exactly the same as that to placebo, or that the correlation between height and age at onset of schizophrenia will be zero. If the sample size is large enough, even such small differences between groups, or trivial correlations, would be detected as being statistically significant. This does not mean that the findings are clinically significant.

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Survey sample size calculator

Survey sample size calculator can help you determine how many people you need to survey to be statistically significant!

Our survey sample size calculator can help determine how many people are needed to carry out a successful survey that is statistically significant.

When considering conducting a survey, one of the first questions is how many responses are needed for a statistically significant dataset. Determining the right survey sample size depends on many factors. But with our sample size calculator, you can easily find the ideal sample size for a survey—online and for free. Using it is easy, though understanding the basic principles of getting data that actually matters is the first step.

The number of people your sample will represent.

The industry standard is 95%.

Typically between 4% and 8%.

Sample Size

Why questionnaire sample size matters.

Getting an individual survey response from everyone in any sizable group is impossible. What can be done is to receive responses from a relevant portion of the group. This will provide comprehensive data from which to draw conclusions that can help achieve goals.

This is where the questionnaire sample size comes into play. Using this calculation, you know if you’ve gathered enough responses from a certain subgroup to be statistically significant. In other words, you want a representative sample that’s large enough to produce statistically significant results.

It’s required to know:

• The math behind the survey sample size formula.
• How the sample size influences results.
• How to achieve statistical significance.
• The margin of error.
• Different types of confidence levels.

How to determine the sample size for a survey

Before diving deeper into the math behind the survey sample size formula, let’s explain some basic terms:

• S = Desired sample size needed to achieve statistical significance.
• N = The total number of people in the group you're surveying.
• Z = How many standard deviations a data point is when compared to the population mean.
• Standard Deviation (σ) = Used in statistics to determine how dispersed data is compared to the average.
• Mean (μ) = Shows the average score for the characteristic being measured in a certain group, like the average IQ in the United States being 98.

When calculating sample size for survey research, it’s important to know a few facts. The first is the population of the group being researched. If you’re conducting patient surveys for your healthcare institution , it’s important to know how many patients there are. Every patient does not need to fill out the survey, though if there are 500 patients then it’s unlikely that only 10 responses will produce a statistically significant result.

Sample size for an online survey

A good sample size for an online survey can vary depending on several factors, including the population size, the level of precision desired, and the level of confidence desired. However, a sample size of at least 500-1000 respondents is recommended for online surveys.

This is because online surveys tend to have lower response rates than other surveys. A larger sample size can help compensate for this. Additionally, online surveys may have a higher degree of non-response bias, which can be mitigated by increasing the sample size.

When conducting an online survey, a sample size calculation should consider the potential non-response bias—meaning non-respondents may have different characteristics from respondents. The sample size should be adjusted accordingly.

Learn how to avoid biased survey questions by reading our blog about it .

How to calculate the survey sample size margin of error

Don’t let the statistical terminology confuse you. The margin of error is a percentage—from 0 to 100 percent—which tells you how much the results from the sample will vary compared to the entire population.

The margin of error should be as small as possible. This is achieved by having a large enough sample, since the margin of error is inversely proportional to sample size. The bigger the sample size, the smaller the margin of error.

Survey sample size confidence: Interval versus level

The survey sample size confidence interval provides the level of uncertainty in your results. Every statistic (for example, 56 percent of the US population watches TV after work) is not 100 percent certain. The confidence interval tells you how uncertain a particular statistic is.

Along with the confidence interval, there is also the confidence level, which can be 99 percent, 95 percent, 90 percent, etc. Confidence level (for example, 95 percent) tells you that, if the survey is repeated, the results will be in a certain range 95 percent of the time.

If you want a survey with a high confidence level—in the 99 to 95 percent range—a large sample is needed. Luckily, our sample size calculator returns exactly how many people will need to complete your survey based on chosen parameters.

Survey sample size: Statistical significance

It’s important to note that having statistically significant responses is not always important. If you have a retail company and you’re conducting customer surveys , then every response matters. For example, you won’t ignore a certain problem that some customers have with a product, even if only a few bring it up in a survey. In practice, every response holds immense value.

After you collect valuable data, you may find our articles on how to analyze the survey data and tips for gaining better insights useful.

Ideal versus minimum sample size formula

Now that you know the basic terminology and math behind the sample size calculator, it’s time for an actual sample size formula.

For example, if you’re surveying a population that has 1000 people—and you want your confidence level to be 95 percent (with a 5 percent margin of error)—then the minimum survey sample size for statistical significance would be 278 responses.

A good sample size for a survey depends on several factors, including the population size, the level of precision desired, and the level of confidence desired. A general rule of thumb is that a sample size of at least 30 is needed for accurate results. But for larger populations, a larger sample size may be necessary to achieve the desired level of precision and confidence.

Figuring the sample size for a survey is hassle-free with our statistically significant sample size calculator. It will tell you precisely how many responses are needed without having to make calculations manually. Try it out before focusing on which survey is the best fit.

With our tools, you’ll get the most out of the data collected. As a bonus, get started right away by combining our survey templates with our sample size calculator. These tools will help you get valuable insights from the stakeholders whose opinions matter most.

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Choose the survey type that best suits your needs, calculate the sample size needed, and then get comprehensive data that you can rely on.

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