How to Calculate Sample Sizes for Research Studies
In the realm of research, where knowledge is the ultimate treasure, the quest for the right sample size is a critical step on the path to discovery. Determining how many participants or data points to include in a study is not a mere guess; it is a calculated decision with far-reaching implications for the validity and generalizability of your findings. This comprehensive guide will delve into the intricacies of sample size calculation, illuminating the factors at play, the methods employed, and the practical considerations that researchers must navigate.
The Significance of Sample Size
The sample size in a research study is akin to a lens through which you observe a larger population. If the lens is too small, your view will be limited and distorted. If it is too large, the cost and effort of data collection might outweigh the benefits. The right sample size strikes a balance, allowing you to capture the essence of the population with a reasonable degree of precision and confidence.
The Perils of an Inadequate Sample Size
An inadequate sample size can undermine the entire research endeavor. It can lead to:
- Low Statistical Power: The ability to detect a true effect if it exists. With a small sample, even a meaningful difference might be obscured by random variation.
- Inaccurate Estimates: The sample might not be representative of the population, leading to biased or misleading results.
Difficulty in Generalizing: Findings might not be applicable to the broader population, limiting their impact and significance.
The Price of an Overly Large Sample Size
While a larger sample generally provides more precise estimates, it comes with its own drawbacks:
- Increased Costs: Data collection, analysis, and management become more expensive and time-consuming.
Ethical Concerns: Exposing more participants to potential risks or inconveniences without a clear benefit.
Diminishing Returns: Beyond a certain point, the gains in precision from a larger sample become negligible.
Factors Influencing Sample Size
The ideal sample size is not a one-size-fits-all proposition. It depends on a constellation of factors, each requiring careful consideration:
- Research Design: The type of study (experimental, observational, survey, etc.), the number of groups or variables, and the complexity of the analysis influence the required sample size.
Effect Size: The magnitude of the difference or relationship you expect to find. A larger effect size can be detected with a smaller sample.
Significance Level: The probability of rejecting a true null hypothesis (Type I error). Typically set at 0.05, it represents the acceptable risk of a false positive.
Power: The probability of detecting a true effect if it exists. Typically set at 0.80 or higher, it represents the desired sensitivity of the study.
Variability: The degree of heterogeneity within the population. A more diverse population requires a larger sample to capture its nuances.
Practical Constraints: Budget, time, availability of participants, and logistical limitations can influence the feasible sample size.
Methods for Sample Size Calculation
Several methods and tools are available for calculating sample sizes. The choice depends on the specific research design and the statistical tests to be employed. Here are some common approaches:
- Power Analysis: This statistical method estimates the required sample size to achieve a desired level of power for a specific effect size and significance level. It is widely used in experimental and quasi-experimental studies.
Confidence Interval Approach: This method determines the sample size needed to estimate a population parameter (e.g., mean, proportion) with a specified level of confidence and margin of error.
Formula-Based Approaches: Specific formulas are available for different types of studies, such as comparing means, proportions, or correlations. These formulas often involve parameters like standard deviation, effect size, and desired precision.
Sample Size Calculators: Many online calculators and software packages simplify the process of sample size estimation by providing user-friendly interfaces and pre-programmed formulas.
Examples of Sample Size Calculations
Let’s explore a few examples to illustrate how sample size calculations are applied in practice:
Example 1: Comparing Two Means
Suppose you are conducting a randomized controlled trial to compare the effectiveness of two drugs in lowering blood pressure. You want to detect a mean difference of 5 mmHg with a power of 0.80 and a significance level of 0.05. Assuming a standard deviation of 10 mmHg, a power analysis would reveal that you need approximately 64 participants per group.
Example 2: Estimating a Population Proportion
Imagine you are conducting a survey to estimate the proportion of people in a city who support a new policy. You want to achieve a margin of error of 3% with a 95% confidence level. Using the confidence interval approach, you would find that you need a sample size of around 1068 participants.
Example 3: Correlation Analysis
Suppose you are investigating the relationship between hours of study and exam scores. You expect a moderate correlation (r = 0.30) and want to detect it with a power of 0.80 and a significance level of 0.05. A formula-based approach or a sample size calculator would indicate that you need a sample size of approximately 85 participants.
Practical Considerations and Tips
Beyond the theoretical calculations, several practical aspects warrant attention:
- Pilot Studies: Conducting a small-scale pilot study can help refine the research design, estimate effect sizes, and inform the sample size calculation for the main study.
Response Rates: Anticipate non-response or attrition, especially in longitudinal studies. Inflating the initial sample size can help ensure a sufficient final sample.
Subgroup Analysis: If you plan to analyze subgroups within the sample, ensure that each subgroup has a sufficient sample size for meaningful comparisons.
Expert Consultation: Seek guidance from a statistician or experienced researcher to ensure the appropriateness of the chosen methods and the accuracy of the calculations.
The quest for the right sample size is a journey of balancing precision, practicality, and the pursuit of knowledge. By understanding the factors at play, employing appropriate methods, and considering practical constraints, researchers can navigate this journey with confidence, ensuring that their studies are equipped to uncover meaningful insights and contribute to the ever-evolving tapestry of human understanding. Remember, the sample size is not merely a number; it is a gateway to unlocking the secrets hidden within the vast expanse of data.
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How to Determine Sample Size for a Research Study
Frankline kibuacha | apr. 06, 2021 | 3 min. read.
This article will discuss considerations to put in place when determining your sample size and how to calculate the sample size.
Confidence Interval and Confidence Level
As we have noted before, when selecting a sample there are multiple factors that can impact the reliability and validity of results, including sampling and non-sampling errors . When thinking about sample size, the two measures of error that are almost always synonymous with sample sizes are the confidence interval and the confidence level.
Confidence Interval (Margin of Error)
Confidence intervals measure the degree of uncertainty or certainty in a sampling method and how much uncertainty there is with any particular statistic. In simple terms, the confidence interval tells you how confident you can be that the results from a study reflect what you would expect to find if it were possible to survey the entire population being studied. The confidence interval is usually a plus or minus (±) figure. For example, if your confidence interval is 6 and 60% percent of your sample picks an answer, you can be confident that if you had asked the entire population, between 54% (60-6) and 66% (60+6) would have picked that answer.
Confidence Level
The confidence level refers to the percentage of probability, or certainty that the confidence interval would contain the true population parameter when you draw a random sample many times. It is expressed as a percentage and represents how often the percentage of the population who would pick an answer lies within the confidence interval. For example, a 99% confidence level means that should you repeat an experiment or survey over and over again, 99 percent of the time, your results will match the results you get from a population.
The larger your sample size, the more confident you can be that their answers truly reflect the population. In other words, the larger your sample for a given confidence level, the smaller your confidence interval.
Standard Deviation
Another critical measure when determining the sample size is the standard deviation, which measures a data set’s distribution from its mean. In calculating the sample size, the standard deviation is useful in estimating how much the responses you receive will vary from each other and from the mean number, and the standard deviation of a sample can be used to approximate the standard deviation of a population.
The higher the distribution or variability, the greater the standard deviation and the greater the magnitude of the deviation. For example, once you have already sent out your survey, how much variance do you expect in your responses? That variation in responses is the standard deviation.
Population Size
As demonstrated through the calculation below, a sample size of about 385 will give you a sufficient sample size to draw assumptions of nearly any population size at the 95% confidence level with a 5% margin of error, which is why samples of 400 and 500 are often used in research. However, if you are looking to draw comparisons between different sub-groups, for example, provinces within a country, a larger sample size is required. GeoPoll typically recommends a sample size of 400 per country as the minimum viable sample for a research project, 800 per country for conducting a study with analysis by a second-level breakdown such as females versus males, and 1200+ per country for doing third-level breakdowns such as males aged 18-24 in Nairobi.
How to Calculate Sample Size
As we have defined all the necessary terms, let us briefly learn how to determine the sample size using a sample calculation formula known as Andrew Fisher’s Formula.
- Determine the population size (if known).
- Determine the confidence interval.
- Determine the confidence level.
- Determine the standard deviation ( a standard deviation of 0.5 is a safe choice where the figure is unknown )
- Convert the confidence level into a Z-Score. This table shows the z-scores for the most common confidence levels:
| 80% | 1.28 | |
| 85% | 1.44 | |
| 90% | 1.65 | |
| 95% | 1.96 | |
| 99% | 2.58 | |
- Put these figures into the sample size formula to get your sample size.
Here is an example calculation:
Say you choose to work with a 95% confidence level, a standard deviation of 0.5, and a confidence interval (margin of error) of ± 5%, you just need to substitute the values in the formula:
((1.96)2 x .5(.5)) / (.05)2
(3.8416 x .25) / .0025
.9604 / .0025
Your sample size should be 385.
Fortunately, there are several available online tools to help you with this calculation. Here’s an online sample calculator from Easy Calculation. Just put in the confidence level, population size, the confidence interval, and the perfect sample size is calculated for you.
GeoPoll’s Sampling Techniques
With the largest mobile panel in Africa, Asia, and Latin America, and reliable mobile technologies, GeoPoll develops unique samples that accurately represent any population. See our country coverage here , or contact our team to discuss your upcoming project.
Related Posts
Sample Frame and Sample Error
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Statistics By Jim
Making statistics intuitive
Sample Size Essentials: The Foundation of Reliable Statistics
By Jim Frost 4 Comments
What is Sample Size?
Sample size is the number of observations or data points collected in a study. It is a crucial element in any statistical analysis because it is the foundation for drawing inferences and conclusions about a larger population .
Imagine you’re tasting a new brand of cookies. Sampling just one cookie might not give you a true sense of the overall flavor—what if you picked the only burnt one? Similarly, in statistical analysis , the sample size determines how well your study represents the larger group. A larger sample size can mean the difference between a snapshot and a panorama, providing a clearer, more accurate picture of the reality you’re studying.
In this blog post, learn why adequate sample sizes are not just a statistical nicety but a fundamental component of trustworthy research. However, large sample sizes can’t fix all problems. By understanding the impact of sample size on your results, you can make informed decisions about your research design and have more confidence in your findings .
Benefits of a Large Sample Size
A large sample size can significantly enhance the reliability and validity of study results. We’re primarily looking at how well representative samples reflect the populations from which the researchers drew them. Here are several key benefits.
Increased Precision
Larger samples tend to yield more precise estimates of the population parameters . Larger samples reduce the effect of random fluctuations in the data, narrowing the margin of error around the estimated values.
Estimate precision refers to how closely the results obtained from a sample align with the actual population values. A larger sample size tends to yield more precise estimates because it reduces the effect of random variability within the sample. The more data points you have, the smaller the margin of error and the closer you are to capturing the correct value of the population parameter.
For example, estimating the average height of adults using a larger sample tends to give an estimate closer to the actual average than using a smaller sample.
Learn more about Statistics vs. Parameters , Margin of Error , and Confidence Intervals .
Greater Statistical Power
The power of a statistical test is its capability to detect an effect if there is one, such as a difference between groups or a correlation between variables. Larger samples increase the likelihood of detecting actual effects.
Statistical power is the probability that a study will detect an effect when one exists. The sample size directly influences it; a larger sample size increases statistical power . Studies with more data are more likely to detect existing differences or relationships.
For instance, in testing whether a new drug is more effective than an existing one, a larger sample can more reliably detect small but real improvements in efficacy .
Better Generalizability
With a larger sample, there is a higher chance that the sample adequately represents the diversity of the population, improving the generalizability of the findings to the population.
Consider a national survey gauging public opinion on a policy. A larger sample captures a broader range of demographic groups and opinions.
Learn more about Representative Samples .
Reduced Impact of Outliers
In a large sample, outliers have less impact on the overall results because many observations dilute their influence. The numerous data points stabilize the averages and other statistical estimates, making them more representative of the general population.
If measuring income levels within a region, a few very high incomes will distort the average less in a larger sample than in a smaller one .
Learn more about 5 Ways to Identify Outliers .
The Limits of Larger Sample Sizes: A Cautionary Note
While larger sample sizes offer numerous advantages, such as increased precision and statistical power, it’s important to understand their limitations. They are not a panacea for all research challenges. Crucially, larger sample sizes do not automatically correct for biases in sampling methods , other forms of bias, or fundamental errors in study design. Ignoring these issues can lead to misleading conclusions, regardless of how many data points are collected.
Sampling Bias
Even a large sample is misleading if it’s not representative of the population. For instance, if a study on employee satisfaction only includes responses from headquarters staff but not remote workers, increasing the number of respondents won’t address the inherent bias in missing a significant segment of the workforce.
Learn more about Sampling Bias: Definition & Examples .
Other Forms of Bias
Biases related to data collection methods, survey question phrasing, or data analyst subjectivity can still skew results. If the underlying issues are not addressed, a larger sample size might magnify these biases instead of mitigating them.
Errors in Study Design
Simply adding more data points will not overcome a flawed experimental design . For example, increasing the sample size will not clarify the causal relationships if the design doesn’t control a confounding variable .
Large Sample Sizes are Expensive!
Additionally, it is possible to have too large a sample size. Larger sizes come with their own challenges, such as higher costs and logistical complexities. You get to a point of diminishing returns where you have a very large sample that will detect such small effects that they’re meaningless in a practical sense.
The takeaway here is that researchers must exercise caution and not rely solely on a large sample size to safeguard the reliability and validity of their results. An adequate amount of data must be paired with an appropriate sampling method, a robust study design, and meticulous execution to truly understand and accurately represent the phenomena being studied .
Sample Size Calculation
Statisticians have devised quantitative ways to find a good sample size. You want a large enough sample to have a reasonable chance of detecting a meaningful effect when it exists but not too large to be overly expensive.
In general, these methods focus on using the population’s variability . More variable populations require larger samples to assess them. Let’s go back to the cookie example to see why.
If all cookies in a population are identical (zero variability), you only need to sample one cookie to know what the average cookie is like for the entire population. However, suppose there’s a little variability because some cookies are cooked perfectly while others are overcooked. You’ll need a larger sample size to understand the ratio of the perfect to overcooked cookies.
Now, instead of just those two types, you have an entire range of how much they are over and undercooked. And some use sweeter chocolate chips than others. You’ll need an even larger sample to understand the increased variability and know what an average cookie is really like.
Power and sample size analysis quantifies the population’s variability. Hence, you’ll often need a variability estimate to perform this type of analysis. These calculations also frequently factor in the smallest practically meaningful effect size you want to detect, so you’ll use a manageable sample size.
To learn more about determining how to find a sample size, read my following articles :
- How to Calculate Sample Size
- What is Power in Statistics?
Sample Size Summary
Understanding the implications of sample size is fundamental to conducting robust statistical analysis. While larger samples provide more reliable and precise estimates, smaller samples can compromise the validity of statistical inferences.
Always remember that the breadth of your sample profoundly influences the strength of your conclusions. So, whether conducting a simple survey or a complex experimental study, consider your sample size carefully. Your research’s integrity depends on it.
Consequently, the effort to achieve an adequate sample size is a worthwhile investment in the precision and credibility of your research .
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Reader Interactions
September 11, 2024 at 10:09 am
Hi Jim, thanks for your post.
It’s clear that a small sample size could take to a type 2 error. But Could it put my study in risk to make a type 1 error? I mean, compared to a correct sample size based on proper calculations?
September 11, 2024 at 1:33 pm
That’s a great question! The surprising answer is that increasing or decreasing the sample size actually does not affect the type 1 error rate! The reason why is because as you increase or decrease the sample size, the detectable effect size changes to maintain an error rate that equals your significance level. Controlling the false positives is built right into the equations and process.
So, if you’re studying a certain subject and you have a sample size of 10 or 1000, your false positive error rate is constant. However, as you mention, the type 2, false negative error will decrease as sample size increases.
August 29, 2024 at 7:00 am
A problem which ought to be considered when running an opinion poll: Is the group of people who consent to answer strictly comparable to the group who do not consent?. If not, then there may be systematic bias
July 17, 2024 at 11:11 am
When I used survey data, we had a clear, conscious sampling method and the distinction made sense. However, with other types of data such as performance or sales data, I’m confused about the distinction. We have all the data of everyone who did the work, so by that understanding, we aren’t doing any sampling. However, is there a ‘hidden’ population of everyone who could potentially do that work? If we take a point in time, such as just first quarter performance, is that a sample or something else? I regularly see people just go ahead and apply the same statistics to both, suggesting that this is a ‘sample’, but I’m not sure what it’s a sample of or how!
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Determining sample size: how to make sure you get the correct sample size.
16 min read Sample size can make or break your research project. Here’s how to master the delicate art of choosing the right sample size.
What is sample size?
Sample size is the beating heart of any research project. It’s the invisible force that gives life to your data, making your findings robust, reliable and believable.
Sample size is what determines if you see a broad view or a focus on minute details; the art and science of correctly determining it involves a careful balancing act. Finding an appropriate sample size demands a clear understanding of the level of detail you wish to see in your data and the constraints you might encounter along the way.
Remember, whether you’re studying a small group or an entire population, your findings are only ever as good as the sample you choose.
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Let’s delve into the world of sampling and uncover the best practices for determining sample size for your research.
How to determine sample size
“How much sample do we need?” is one of the most commonly-asked questions and stumbling points in the early stages of research design . Finding the right answer to it requires first understanding and answering two other questions:
How important is statistical significance to you and your stakeholders?
What are your real-world constraints.
At the heart of this question is the goal to confidently differentiate between groups, by describing meaningful differences as statistically significant. Statistical significance isn’t a difficult concept, but it needs to be considered within the unique context of your research and your measures.
First, you should consider when you deem a difference to be meaningful in your area of research. While the standards for statistical significance are universal, the standards for “meaningful difference” are highly contextual.
For example, a 10% difference between groups might not be enough to merit a change in a marketing campaign for a breakfast cereal, but a 10% difference in efficacy of breast cancer treatments might quite literally be the difference between life and death for hundreds of patients. The exact same magnitude of difference has very little meaning in one context, but has extraordinary meaning in another. You ultimately need to determine the level of precision that will help you make your decision.
Within sampling, the lowest amount of magnification – or smallest sample size – could make the most sense, given the level of precision needed, as well as timeline and budgetary constraints.
If you’re able to detect statistical significance at a difference of 10%, and 10% is a meaningful difference, there is no need for a larger sample size, or higher magnification. However, if the study will only be useful if a significant difference is detected for smaller differences – say, a difference of 5% — the sample size must be larger to accommodate this needed precision. Similarly, if 5% is enough, and 3% is unnecessary, there is no need for a larger statistically significant sample size.
You should also consider how much you expect your responses to vary. When there isn’t a lot of variability in response, it takes a lot more sample to be confident that there are statistically significant differences between groups.
For instance, it will take a lot more sample to find statistically significant differences between groups if you are asking, “What month do you think Christmas is in?” than if you are asking, “How many miles are there between the Earth and the moon?”. In the former, nearly everybody is going to give the exact same answer, while the latter will give a lot of variation in responses. Simply put, when your variables do not have a lot of variance, larger sample sizes make sense.
Statistical significance
The likelihood that the results of a study or experiment did not occur randomly or by chance, but are meaningful and indicate a genuine effect or relationship between variables.
Magnitude of difference
The size or extent of the difference between two or more groups or variables, providing a measure of the effect size or practical significance of the results.
Actionable insights
Valuable findings or conclusions drawn from data analysis that can be directly applied or implemented in decision-making processes or strategies to achieve a particular goal or outcome.
It’s crucial to understand the differences between the concepts of “statistical significance”, “magnitude of difference” and “actionable insights” – and how they can influence each other:
- Even if there is a statistically significant difference, it doesn’t mean the magnitude of the difference is large: with a large enough sample, a 3% difference could be statistically significant
- Even if the magnitude of the difference is large, it doesn’t guarantee that this difference is statistically significant: with a small enough sample, an 18% difference might not be statistically significant
- Even if there is a large, statistically significant difference, it doesn’t mean there is a story, or that there are actionable insights
There is no way to guarantee statistically significant differences at the outset of a study – and that is a good thing.
Even with a sample size of a million, there simply may not be any differences – at least, any that could be described as statistically significant. And there are times when a lack of significance is positive.
Imagine if your main competitor ran a multi-million dollar ad campaign in a major city and a huge pre-post study to detect campaign effects, only to discover that there were no statistically significant differences in brand awareness . This may be terrible news for your competitor, but it would be great news for you.
With Stats iQ™ you can analyze your research results and conduct significance testing
As you determine your sample size, you should consider the real-world constraints to your research.
Factors revolving around timings, budget and target population are among the most common constraints, impacting virtually every study. But by understanding and acknowledging them, you can definitely navigate the practical constraints of your research when pulling together your sample.
Timeline constraints
Gathering a larger sample size naturally requires more time. This is particularly true for elusive audiences, those hard-to-reach groups that require special effort to engage. Your timeline could become an obstacle if it is particularly tight, causing you to rethink your sample size to meet your deadline.
Budgetary constraints
Every sample, whether large or small, inexpensive or costly, signifies a portion of your budget. Samples could be like an open market; some are inexpensive, others are pricey, but all have a price tag attached to them.
Population constraints
Sometimes the individuals or groups you’re interested in are difficult to reach; other times, they’re a part of an extremely small population. These factors can limit your sample size even further.
What’s a good sample size?
A good sample size really depends on the context and goals of the research. In general, a good sample size is one that accurately represents the population and allows for reliable statistical analysis.
Larger sample sizes are typically better because they reduce the likelihood of sampling errors and provide a more accurate representation of the population. However, larger sample sizes often increase the impact of practical considerations, like time, budget and the availability of your audience. Ultimately, you should be aiming for a sample size that provides a balance between statistical validity and practical feasibility.
4 tips for choosing the right sample size
Choosing the right sample size is an intricate balancing act, but following these four tips can take away a lot of the complexity.
1) Start with your goal
The foundation of your research is a clearly defined goal. You need to determine what you’re trying to understand or discover, and use your goal to guide your research methods – including your sample size.
If your aim is to get a broad overview of a topic, a larger, more diverse sample may be appropriate. However, if your goal is to explore a niche aspect of your subject, a smaller, more targeted sample might serve you better. You should always align your sample size with the objectives of your research.
2) Know that you can’t predict everything
Research is a journey into the unknown. While you may have hypotheses and predictions, it’s important to remember that you can’t foresee every outcome – and this uncertainty should be considered when choosing your sample size.
A larger sample size can help to mitigate some of the risks of unpredictability, providing a more diverse range of data and potentially more accurate results. However, you shouldn’t let the fear of the unknown push you into choosing an impractically large sample size.
3) Plan for a sample that meets your needs and considers your real-life constraints
Every research project operates within certain boundaries – commonly budget, timeline and the nature of the sample itself. When deciding on your sample size, these factors need to be taken into consideration.
Be realistic about what you can achieve with your available resources and time, and always tailor your sample size to fit your constraints – not the other way around.
4) Use best practice guidelines to calculate sample size
There are many established guidelines and formulas that can help you in determining the right sample size.
The easiest way to define your sample size is using a sample size calculator , or you can use a manual sample size calculation if you want to test your math skills. Cochran’s formula is perhaps the most well known equation for calculating sample size, and widely used when the population is large or unknown.
Beyond the formula, it’s vital to consider the confidence interval, which plays a significant role in determining the appropriate sample size – especially when working with a random sample – and the sample proportion. This represents the expected ratio of the target population that has the characteristic or response you’re interested in, and therefore has a big impact on your correct sample size.
If your population is small, or its variance is unknown, there are steps you can still take to determine the right sample size. Common approaches here include conducting a small pilot study to gain initial estimates of the population variance, and taking a conservative approach by assuming a larger variance to ensure a more representative sample size.
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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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- A Researcher’s Guide To Statistical Significance And Sample Size Calculations
Determining Sample Size: How Many Survey Participants Do You Need?
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How to calculate a statistically significant sample size in research, determining sample size for probability-based surveys and polling studies, determining sample size for controlled surveys, determining sample size for experiments, how to calculate sample size for simple experiments, an example sample size calculation for an a/b test, what if i don’t know what size difference to expect, part iii: sample size: how many participants do i need for a survey to be valid.
In the U.S., there is a Presidential election every four years. In election years, there is a steady stream of polls in the months leading up to the election announcing which candidates are up and which are down in the horse race of popular opinion.
If you have ever wondered what makes these polls accurate and how each poll decides how many voters to talk to, then you have thought like a researcher who seeks to know how many participants they need in order to obtain statistically significant survey results.
Statistically significant results are those in which the researchers have confidence their findings are not due to chance . Obtaining statistically significant results depends on the researchers’ sample size (how many people they gather data from) and the overall size of the population they wish to understand (voters in the U.S., for example).
Calculating sample sizes can be difficult even for expert researchers. Here, we show you how to calculate sample size for a variety of different research designs.
Before jumping into the details, it is worth noting that formal sample size calculations are often based on the premise that researchers are conducting a representative survey with probability-based sampling techniques. Probability-based sampling ensures that every member of the population being studied has an equal chance of participating in the study and respondents are selected at random.
For a variety of reasons, probability sampling is not feasible for most behavioral studies conducted in industry and academia . As a result, we outline the steps required to calculate sample sizes for probability-based surveys and then extend our discussion to calculating sample sizes for non-probability surveys (i.e., controlled samples) and experiments.
Determining how many people you need to sample in a survey study can be difficult. How difficult? Look at this formula for sample size.
No one wants to work through something like that just to know how many people they should sample. Fortunately, there are several sample size calculators online that simplify knowing how many people to collect data from.
Even if you use a sample size calculator, however, you still need to know some important details about your study. Specifically, you need to know:
- What is the population size in my research?
Population size is the total number of people in the group you are trying to study. If, for example, you were conducting a poll asking U.S. voters about Presidential candidates, then your population of interest would be everyone living in the U.S.—about 330 million people.
Determining the size of the population you’re interested in will often require some background research. For instance, if your company sells digital marketing services and you’re interested in surveying potential customers, it isn’t easy to determine the size of your population. Everyone who is currently engaged in digital marketing may be a potential customer. In situations like these, you can often use industry data or other information to arrive at a reasonable estimate for your population size.
- What margin of error should you use?
Margin of error is a percentage that tells you how much the results from your sample may deviate from the views of the overall population. The smaller your margin of error, the closer your data reflect the opinion of the population at a given confidence level.
Generally speaking, the more people you gather data from the smaller your margin of error. However, because it is almost never feasible to collect data from everyone in the population, some margin of error is necessary in most studies.
- What is your survey’s significance level?
The significance level is a percentage that tells you how confident you can be that the true population value lies within your margin of error. So, for example, if you are asking people whether they support a candidate for President, the significance level tells you how likely it is that the level of support for the candidate in the population (i.e., people not in your sample) falls within the margin of error found in your sample.
Common significance levels in survey research are 90%, 95%, and 99%.
Once you know the values above, you can plug them into a sample size formula or more conveniently an online calculator to determine your sample size.
The table below displays the necessary sample size for different sized populations and margin of errors. As you can see, even when a population is large, researchers can often understand the entire group with about 1,000 respondents.
| Population Size | Sample Size Based on ±3% Margin of Error | Sample Size Based on ±5% Margin of Error | Sample Size Based on ±10% Margin of Error | |
|---|---|---|---|---|
| 500 | 345 | 220 | 80 | |
| 1,000 | 525 | 285 | 90 | |
| 3,000 | 810 | 350 | 100 | |
| 5,000 | 910 | 370 | 100 | |
| 10,000 | 1,000 | 385 | 100 | |
| 100,00+ | 1,100 | 400 | 100 |
| # | Type | Purpose | Example | Formative or Summative |
|---|---|---|---|---|
| Problem Discovery | Finding Problems and/or Insights | What are the for the check-out flow? | Formative | |
| Estimation | Estimating a Value/Parameter | What is the | Summative | |
| Comparison | Making a Comparison | Is there a or is the score ? | Summative |
In contrast to the focus on measurements taken during summative user research (study types 2 and 3), the goal of problem discovery usability studies (type 1) is to discover and enumerate the problems that users have when performing tasks with a product. It’s considered a formative type of evaluation .
So, what’s the sample size for each study type? 5, 50, 100?
One Size Does Not Fit All Even Within Study Types
While defining the study type helps narrow the proper approach to sample size estimation, it still doesn’t warrant recommending one number. Because there’s math involved, it’s understandable that people seek a simple single number. We’ve been trained to find a single answer to simple math problems: 2+2 always equals 4. The square root of 9 is always 3. The answer is determined because there aren’t any variables—life is great!
As soon as you introduce variables, however, things get more complicated. The hypotenuse of a triangle is always equal to the square root of the sum of the squares of the two other sides ( a 2 + b 2 = c 2 ), but the actual length of the hypotenuse depends on the length of the two sides.
The methods for finding sample sizes for summative studies are typically taught in university statistics classes. Those methods include several variables whose values can differ from study to study, including alpha and beta decision criteria (which control the long-run probability of Type I and Type II errors), the standard deviation of the metric, and the smallest difference that you need to detect to make the necessary decisions (i.e., the critical difference ). Changing any of these variables will change the sample size needed to meet the requirements.
Problem discovery sample sizes use a less familiar approach. We’ve discussed in previous articles the mathematics commonly used to derive sample sizes for formative problem discovery usability studies and how well that math matches reality .
So, what is the formula for finding sample sizes for problem discovery studies?
Sample Size Formula for Discovery Studies
While you don’t need to fully understand the derivation of the formula to use it, it helps to know how to use it. It has only two elements: n and p .
P (at least once) = 1 − (1 − p) n
The p is how likely a problem (or event) is to occur in the tested population and n is the sample size. In this formula, they compute the probability of seeing the problem at least once in a formative usability study with n participants.
Technical note : We manipulated the binomial probability formula to get to 1 − (1 − p ) n , but there are other ways to arrive at this formula, including the Poisson probability formula and capture-recapture models .
The formula above computes the probability of detecting a problem given a sample size and its frequency in the population. It can be rearranged using algebra to solve for the sample size.
Because n is an exponent in the formula, it’s necessary to use logarithms to manipulate the formula to focus on the sample size instead of the probability of discovering the event of interest at least once. The resulting formula is:
Don’t worry too much about the formula other than to note that it shows that the sample size for a discovery study is driven by the discovery goal ( P (at least once)) and how likely an event is to happen during the discovery ( p ).
As mentioned above, in the best-known rule of thumb for usability study sample sizes, the “magic number 5,” the claim is that five participants are enough for the discovery of 85% of usability problems (strictly speaking, 85% of the problems that are available for discovery given the constraints of the study regarding the sampled population and tasks).
Nothing is inherently right or wrong with a discovery goal of 85%. It deviates from the more expected convention of 95% or 90% used in confidence intervals , but like a confidence level, the discovery goal can take any value from 1% to 99%. So, where did 85% originally come from?
Several early investigations into using these formulas to predict problem discovery rates as a function of sample size (e.g., Virzi, 1990 ; Nielsen & Landauer, 1993 ) reported finding that four or five participants discover 80–85% of the problems in large-sample usability studies. Over time, these findings became the simplified “magic number 5” rule.
An early test of the simple goal of 85% discovery was an economic ROI simulation published in 1994 (by Jim) that estimated the costs associated with running additional participants, fixing problems, and failing to discover problems in formative usability studies. Although all the independent variables influenced the sample size at the maximum ROI, the variable with the broadest influence was the average likelihood of problem discovery ( p ), which also had the strongest influence on the percentage of problems discovered at the maximum ROI. The results indicated that, when the target value of p is small (e.g., 10%), practitioners should plan to discover about 86% of the problems available for discovery in the study. When p is greater (e.g., 25–50%), the appropriate goal is about 98% discovery.
Things get trickier determining how often events of interest occur during the study. A common estimate of that likelihood is 31%. But where did that come from?
In the research Jakob Nielsen and Thomas Landauer published in 1993 , which was the basis of their recommendation for running formative usability studies with five participants, the value they computed for the likelihood of problem occurrence was .31.
This was the average of the problem discovery rates reported in 11 usability studies they had conducted or had acquired from other researchers at the time (including one from Jim Lewis—see Figure 1 for the correspondence between Nielsen and Lewis in 1991). When they used their version of 1 − (1 − p ) n and graphed the expected percentage of discovery for sample sizes from 1 to 15 and p = 31%, their estimated discovery rate was 85% when n = 5.
Figure 1: Correspondence between Jakob Nielsen and Jim Lewis in 1991. (Oh, the days of formal correspondence.…)
If you plug .85 and .31 into the sample size formula, you get:
n = ln(1 − .85)/ln(1 − .31) = (−1.897)/(−0.371) = 5.11
So, math supports running five participants in a discovery study if (1) the discovery goal is 85% and (2) the probability of the occurrence of an event of interest is 31%. (You can also use our online calculator , which will do the math for you.)
But as mentioned above, one size does not fit all . What if, in your research context, you need to discover more or fewer than 85% of the events of interest, and what if their probability of occurrence is less or greater than 31%?
In those cases, you need a size chart, analogous to shopping for a men’s dress shirt to fit a given neck size and sleeve length (desired discovery rate and problem likelihood). We’ll publish that size chart in a future article.
Summary and Discussion
How many participants do you need for a usability study?
It depends first on the study type. There are three study types—discovery, estimation, and comparison. In contrast to estimation and comparison studies, sample size estimation for discovery studies uses a different mathematical approach.
It still depends within study types. Don’t rely on averaging together recommendations or looking for a single number that will always work even when focusing within a study type such as discovery.
What about the “magic number 5?” The controversial claim based on the research of Nielsen and Landauer that “five is enough” turns out to sometimes be true, but only for a limited range of research contexts.
What about any other magic number? Because the appropriate sample size for discovery studies depends on two factors, no one magic number will be appropriate for all research contexts. In fact, there is no magic number for sample sizes for any type of usability study, formative or summative.
Use the formula for problem discovery. The problem discovery formula can be used to find the sample size based on expected problem occurrences ( p ) and the likelihood of seeing a problem at least once. You can also use the online calculator .
Parameters have defaults but should be changed when necessary to fit the research needs. The typical parameter for discovering problems is 85%, but this can be increased or decreased depending on the context. The parameter of 31% for the probability of problem occurrence came from an average across datasets from the 1990s. It’s not a bad place to start, but it shouldn’t be the only value for this parameter. Using values of 10%, 20%, and even 5% may make sense depending on how important it is to discover uncommon problems.
If there isn’t a magic number, should we give up on sample size estimation for formative usability studies? Giving up on magic numbers doesn’t mean you have to give up on sample size estimation for formative usability studies (or any other type of discovery study). You just need to be able to make decisions about (1) how rare of an event you need to be able to detect at least once and (2) what percentage of those events you need to discover in the study.
Bottom line: It would be nice if this process were simpler, but unfortunately, one sample size does not fit all research requirements. Fortunately, there is a mathematical model that can guide UX professionals to make reasoned decisions about sample size requirements for formative usability studies.
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- Indian J Anaesth
- v.60(9); 2016 Sep
Sample size calculation: Basic principles
Sabyasachi das.
Department of Anaesthesiology and Critical Care, Medical College, Kolkata, West Bengal, India
Mohanchandra Mandal
1 Department of Anaesthesiology and Critical Care, North Bengal Medical College, Sushrutanagar, Darjeeling, West Bengal, India
Addressing a sample size is a practical issue that has to be solved during planning and designing stage of the study. The aim of any clinical research is to detect the actual difference between two groups (power) and to provide an estimate of the difference with a reasonable accuracy (precision). Hence, researchers should do a priori estimate of sample size well ahead, before conducting the study. Post hoc sample size computation is not encouraged conventionally. Adequate sample size minimizes the random error or in other words, lessens something happening by chance. Too small a sample may fail to answer the research question and can be of questionable validity or provide an imprecise answer while too large a sample may answer the question but is resource-intensive and also may be unethical. More transparency in the calculation of sample size is required so that it can be justified and replicated while reporting.
INTRODUCTION
Besides scientific justification and validity, the calculation of sample size (‘just large enough’) helps a medical researcher to assess cost, time and feasibility of his project.[ 1 ] Although frequently reported in anaesthesia journals, the details or the elements of calculation of sample size are not consistently provided by the authors. Sample size calculations reported do not match with replication of sample size in many studies.[ 2 ] Most trials with negative results do not have a large enough sample size. Hence, reporting of statistical power and sample size need to be improved.[ 3 , 4 ] There is a belief that studies with small sample size are unethical if they do not ensure adequate power. However, the truth is that for a study to be ethical in its design, its predicted value must outweigh the projected risks to its participants. In studies, where the risks and inconvenience borne by the participants outweigh the benefits received as a result of participation, it is the projected burden. A study may still be valid if the projected benefit to the society outweighs the burden to society. If there is no burden, then any sample size may be ideal.[ 5 ] Many different approaches of sample size design exist depending on the study design and research question. Moreover, each study design can have multiple sub-designs resulting in different sample size calculation.[ 6 ] Addressing a sample size is a practical issue that has to be solved during planning and designing stage of the study. It may be an important issue in approval or rejection of clinical trial results irrespective of the efficacy.[ 7 ]
By the end of this article, the reader will be able to enumerate the prerequisite for sample size estimation, to describe the common lapses of sample size calculation and the importance of a priori sample size estimation. The readers will be able to define the common terminologies related to sample size calculation.
IMPORTANCE OF PILOT STUDY IN SAMPLE SIZE ESTIMATION
In published literature, relevant data for calculating the sample size can be gleaned from prevalence estimates or event rates, standard deviation (SD) of the continuous outcome, sample size of similar studies with similar outcomes. The idea of approximate ‘effect’ estimates can be obtained by reviewing meta-analysis and clinically meaningful effect. Small pilot study, personal experience, expert opinion, educated guess, hospital registers, unpublished reports support researcher when we have insufficient information in the existing/available literature. A pilot study not only helps in the estimation of sample size but also its primary purpose is to check the feasibility of the study.
The pilot study is a small scale trial run as a pre-test, and it tries out for the proposed major trial. It allows preliminary testing of the hypotheses and may suggest some change, dropping some part or developing new hypotheses so that it can be tested more precisely.[ 8 ] It may address many logistic issues such as checking that instructions are comprehensive, and the investigators are adequately skilled for the trial. The pilot study almost always provides enough data for the researcher to decide whether to go ahead with the main study or to abandon. Many research ideas that seem to show great promise are unproductive when actually carried out. From the findings of pilot study, the researcher may abandon the main study involving large logistic resources, and thus can save a lot of time and money.[ 8 ]
METHODS FOR SAMPLE SIZE CALCULATION
Sample size can be calculated either using confidence interval method or hypothesis testing method. In the former, the main objective is to obtain narrow intervals with high reliability. In the latter, the hypothesis is concerned with testing whether the sample estimate is equal to some specific value.
Null hypothesis
This hypothesis states that there is no difference between the control and the study group in relation to randomized controlled trial (RCT). Rejecting or disproving the null hypothesis – and thus concluding that there are grounds for believing that there is a difference between the two groups, is a central task in the modern practice of science, and gives a precise criterion for rejecting a hypothesis.[ 9 , 10 ]
Alternative hypothesis
This hypothesis is contradictory to null hypothesis, i.e., it assumes that there is a difference among the groups, or there is some association between the predictor and the outcome [ Figure 1 ].[ 9 , 10 ] Sometimes, it is accepted by exclusion if the test of significance rejects the null hypothesis. It may be one-sided (specifies the difference in one direction only) or two-sided (specifies the difference in both directions).
Result possibilities during hypothesis tasting. H 0 – Null hypothesis; H 1 – The alternative hypothesis
Type I error (α error) occur if the null hypothesis is rejected when it is true. It represents the chance that the researcher detects a difference between two groups when in reality no difference exists. In other words, it is the chance of false-positive conclusion. A value of 0.05 is most commonly used.
Type II error (β error) is the chance of a false-negative result. The researcher does not detect the difference between the two groups when in reality the difference exists. Conventionally, it is set at a level of 0.20, which translates into <20% chance of a false-negative conclusion. Power is the complement of beta, i.e., (1-beta). In other words, power is 0.80 or 80% when beta is set at 0.20. The power represents the chance of avoiding a false-negative conclusion, or the chance of detecting an effect if it really exists.[ 11 ]
TYPES OF TRIALS
Parallel arm RCTs are most commonly used, that means all participants are randomized in two or more arms of different interventions treated concurrently. Various types of parallel RCTs are used in accordance with the need: Superiority trials which verify whether a new approach is more effective than the conventional from statistically or clinical point of view. Here, the concurrent null hypothesis is that the new approach is not more effective than the conventional approach. Equivalence trials which are designed to ascertain that the new approach and the standard approach are equally effective. Corresponding null hypothesis states that the difference between both approaches is clinically relevant. Non-inferiority trials which are designed to ascertain that the new approach is equal if not superior to the conventional approach. Corresponding null hypothesis is that the new approach is inferior to the conventional one.
PREREQUISITES FOR SAMPLE SIZE ESTIMATION
At the outset, primary objectives (descriptive/analytical) and primary outcome measure (mean/proportion/rates) should be defined. Often there is a primary research question that the researcher wants to investigate. It is important to choose a primary outcome and lock that for the study. The minimum difference that investigator wants to detect between the groups makes the effect size for the sample size calculation.[ 7 ] Hence, if the researcher changes the planned outcome after the start of the study, the reported P value and inference becomes invalid.[ 11 ] The level of acceptable Type I error (α) and Type II error (β) should also be determined. The error rate of Type I error (alpha) is customarily set lower than Type II error (beta). The philosophy behind this is the impact of a false positive error (Type I) is more detrimental than that of false negative (Type II) error. So they are protected against more rigidly.
Besides, the researcher needs to know the control arm mean/event rates/proportion, and the smallest clinically important effect that one is trying to detect.
THE RELATION BETWEEN PRIMARY OBJECTIVE AND THE SAMPLE SIZE
The type of primary outcome measure with its clear definition help computing correct sample size as there are definite ways to reach sample size for each outcome measure. It needs special attention as it principally influences how impressively the research question is answered. The type of primary outcome measure also is the basis for the mode of estimation regarding population variance. For continuous variable (e.g., mean arterial pressure [MAP]), population SD is incorporated in the formula whereas the SD needs to be worked out from the proportion of outcomes for binomial variables (e.g., hypotension - yes/no). In literature, there can be several outcomes for each study design. It is the responsibility of the researcher to find out the primary outcome of the study. Mostly sample size is estimated based on the primary outcome. It is possible to estimate sample size taking into consideration all outcome measures, both primary and secondary at the cost of much larger sample size.
ESSENTIAL COMPONENTS OF SAMPLE SIZE ESTIMATION
The sample size for any study depends on certain factors such as the acceptable level of significance ( P value), power (1 − β) of the study, expected ‘clinically relevant’ effect size, underlying event rate in the population, etc.[ 7 ] Primarily, three factors P value (depends on α), power (related with β) and the effect size (clinically relevant assumption) govern an appropriate sample size.[ 12 , 13 , 14 ] The ‘effect size’ means the magnitude of clinically relevant effect under the alternative hypothesis. It quantifies the difference in the outcomes between the study and control groups. It refers to the smallest difference that would be of clinical importance. Ideally, the basis of effect size selection should be on clinical judgement. It varies with different clinical trials. The researcher has to determine this effect size with scientific knowledge and wisdom. Available previous publications on related topic might be helpful in this regard. ‘Minimal clinically important difference’ is the smallest difference that would be worth testing. Sample size varies inversely with effect size.
The ideal study to make a researcher happy is one where power of the study is high, or in other words, the study has high chance of making a conclusion with reasonable confidence, be it accepting or rejecting null hypothesis.[ 9 ] Sample size matrix, includes different values of sample sizes using varying dimensions of alpha, power (1-β), and effect size. It is often more useful for the research team to choose the sample size number that fits conveniently to the need of the researcher [ Table 1 ].
The matrix showing changes of sample size with varying dimensions of alpha, power (1-β), and effect size
FORMULAE AND SOFTWARE
Once these three factors are fixed, there are many ways (formulae, nomogram, tables and software) for estimating the optimum sample size. At present, there are a good number of softwares, available in the internet. It is prudent to be familiar with the instructions of any software to get sample size of one arm of the study. Perhaps the most important step is to check with the most appropriate formula to get a correct sample size. Websites of some of the commonly used softwares are provided in Table 2 .[ 2 , 6 ]
Websites for some useful statistical software
The number of formulae for calculating the sample size and power, to answer precisely different study designs and research questions are no less than 100. It is wise to check appropriate formula even while using software. Although there are more than 100 formulae, for RCTs numbers of formulae are limited. It essentially depends on the primary outcome measure such as mean ± SD, rate and proportion.[ 6 ] Interested readers may access all relevant sample size estimation formulae using the relevant links.
Calculating the sample size by comparing two means
A study to see the effect of phenylephrine on MAP as continuous variable after spinal anaesthesia to counteract hypotension.
MAP as continuous variable:
- n = Sample size in each of the groups
μ2 = Population mean in treatment Group 2
- μ1−μ2 = The difference the investigator wishes to detect
- ℧ = Population variance (SD)
b = Conventional multiplier for power = 0.80.
Value of a = 1.96, b = 0.842 [ Table 3 ]. If a difference of 15 mmHg in MAP is considered between the phenylephrine and the placebo group as clinically significant (μ1− μ2) and be detected with 80% power and a significance level alpha of 0.05.[ 7 ] n = 2 × ([1.96 + 0.842] 2 × 20 2 )/15 2 = 27.9. That means 28 subjects per group is the sample size.
The constant Z values for conventional α and β values
Calculating the sample size by comparing two proportions
A study to see the effect of phenylephrine on MAP as a binary variable after spinal anaesthesia to counteract hypotension.
MAP as a binary outcome, below or above 60 mmHg (hypotension – yes/no):
- n = The sample size in each of the groups
- p 1 = Proportion of subjects with hypotension in treatment Group 1
- q 1 = Proportion of subjects without hypotension in treatment Group 1 (1 − p1)
- p 2 = Proportion of subjects with hypotension in treatment Group 2
- q 2 = Proportion of subjects without hypotension in treatment Group 2 (1 − p2)
- x = The difference the investigator wishes to detect
- a = Conventional multiplier for alpha = 0.05
- b = Conventional multiplier for power = 0.8.
Considering a difference of 10% as clinically relevant and from the recent publication the proportion of subjects with hypotension in the treated group will be 20% ( p 1 = 0.2) and in the control group will be 30% ( p 2 = 0.3), and thus q 1 and q 2 are 0.80 and 0.70, respectively.[ 7 ] Assuming a power of 80%, and an alpha of 0.05, i.e. 1.96 for a and 0.842 for b [ Table 3 ] we get:
([1.96 + 0.842] 2 × [0.20 × 0.80 + 0.30 × 0.70])/0.10 2 = 290.5. Thus, 291 is the sample size.
Researcher may follow some measures like using continuous variables as the primary outcome, measuring the outcome precisely or choose outcomes that can be measured properly. Use of a more common outcome, making one-sided hypothesis may help achieving this target. Published literature and pilot studies are the basis of sample size calculation. At times, expert opinions, personal experience with event rates and educated guess becomes helpful. Variance, effect size or event rates may be underestimated during calculation of the sample size at the designing phase. If the investigator realizes that this underestimation has led to ‘too small a sample size’ recalculation can be tried based on interim data.[ 15 ]
Sample size calculation can be guided by previous literature, pilot studies and past clinical experiences. The collaborative effort of the researcher and the statistician is required in this stage. Estimated sample size is not an absolute truth, but our best guess. Issues such as anticipated loss to follow-up, large subgroup analysis and complicated study designs, demands a larger sample size to ensure adequate power throughout the trial. A change in sample size is proportional to variance (square of SD) and inversely proportional to the detected difference.
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Everything to Know About Sample Size Determination
A step-by-step interactive guide including common pitfalls
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Download and explore the data yourself. Data files include:
- Blinded Sample Size Re-estimation.nqt
- Blinded SiteAndSubject.nqt
- Center Covariate Reducing Sample Size.nqt
- Cluster Randomized Extension.nqt
- External Pilot Study Sample Size Example.nqt
- Log-Rank Test Everolimus.nqt
- Log-Rank Test with Dropout.nqt
- MaxCombo Model Selection with Delayed Effect.nqt
- Responder Analysis Higher Sample Size Chi-Squared.nqt
- Two Means Group Sequential Replication.nqt
- Two Proportions Inequality Difference Scale.nqt
- Two Proportions Inequality Ratio Scale.nqt
- Two Proportions Non-inferiority Difference Scale.nqt
- Two Proportions Non-inferiority Ratio Scale.nqt
- Two Sample t-test Simvastin.nqt
- Win Ratio for Composite Endpoint.nqt
Designing a trial involves considering and balancing a wide variety of clinical, logistical and statistical factors.
One decision out of many is how large a study needs to be to have a reasonable chance of success. Sample size determination is the process by which trialists can find the ideal number of participants to balance the statistical and practical aspects that inform study design.
In this interactive webinar, we provided a comprehensive overview of sample size determination, the key steps to successfully finding the appropriate sample size and cover several common pitfalls researchers fall into when finding the sample size for their study.
In this free webinar we will cover
- What is sample size determination?
- A step-by-step guide to sample size determination
- Common sample size pitfalls and solutions
+ Q&A about your sample size issues!
In most clinical trials, sample size determination is found by reaching a predefined statistical power - typically defined as the Type II error or how likely a significant p-value is under a given treatment effect.
Power calculations require pre-study knowledge about the study design, statistical error rates, nuisance parameters (such as the variance) and effect size with each of these adding additional complexity.
Sample size determination has a number of common pitfalls which can lead to inappropriately small or large sample sizes with issues ranging from poor design decisions, misspecifying nuisance parameters or choosing the effect size inappropriately.
In this interactive webinar, we explore these and some solutions to avoid these mistakes and help maximise the efficiency of your clinical trial.
We provide a comprehensive overview of sample size determination, the key steps to successfully finding the appropriate sample size and cover several common pitfalls researchers fall into when finding the sample size for their study.
Looking for more trial design and sample size resources? Check out webinars to improve clinical trial designs & practical examples of sample size determination
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A case controlled study of risk factors for metastatic squamous cell carcinoma in organ transplant recipients: single academic medical center
- ORIGINAL PAPER
- Published: 11 September 2024
- Volume 316 , article number 612 , ( 2024 )
Cite this article
- Cynthia F. Griffith ORCID: orcid.org/0000-0002-0566-8611 1 ,
- Anthony Solhjoo 1 ,
- Luke Mahan 2 &
- Rajiv I. Nijhawan 1
Solid organ transplant recipients (SOTRs) are at high risk of cutaneous squamous cell carcinoma (cSCC) metastasis. Despite prior studies identifying risk factors, mortality remains high. Understanding additional risk factors may aid in reducing mortality in this population. This study aimed to investigate risk factors and predictive variables for metastatic cSCC in SOTRs. The primary goal was to accurately identify transplant patients at increased risk of metastatic cSCC. A retrospective case–control study in a single institution of 3576 cases of organ transplants were identified from January 1991 to July 2022. A cohort of metastatic cancer patients and two randomly generated age and organ matched control cohorts were identified. 16 SOTR patients developed metastatic cSCC. The majority were male, with high-risk tumor sites. Tumor depth varied and half exhibited perineural invasion. Cylex® (p = 0.05) and white blood cell counts (p = 0.04) were significantly lower in these patients compared to control. Lung transplants were at highest risk relative to other solid organ transplants. Voriconazole exposure was also associated with increased metastatic risk (p = 0.04). Small sample size at a single institution. Close monitoring of SOTR, especially those with lung transplants given their increased risk, reducing immunosuppression, and limiting exposure to voriconazole can improve outcomes in SOTRs with metastatic cSCC.
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Acknowledgements
Thank you to Dr. Ahmed Shalaby for statistical analysis. Research reported in this publication was supported by the National Center for Advancing Translational Sciences of the National Institutes of Health under award Number UL1 TR003163. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH (National Institutes of Health). Thank you to Anusha Mithani, PA-C, Yadaris Bonilla, PA-C and Rafael Basa PA-C for data collection.
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Department of Dermatology, University of Texas Southwestern Medical Center, Harry Hines, Dallas, TX, 75390, USA
Cynthia F. Griffith, Anthony Solhjoo & Rajiv I. Nijhawan
Department of Lung Transplant, University of Texas Southwestern Medical Center, Dallas, TX, 75390, USA
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C.G., A.S., and L.M. wrote the main manuscript text, prepared figures/tables, and made substantial contributions to the conception of the work, acquisition, analysis, and interpretation of data. R.I.N. revised the manuscript text critically for important intellectual content. All authors reviewed the manuscript. C.G. approved the version to be published.
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Griffith, C.F., Solhjoo, A., Mahan, L. et al. A case controlled study of risk factors for metastatic squamous cell carcinoma in organ transplant recipients: single academic medical center. Arch Dermatol Res 316 , 612 (2024). https://doi.org/10.1007/s00403-024-03284-7
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Published : 11 September 2024
DOI : https://doi.org/10.1007/s00403-024-03284-7
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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 ...
It is the ability of the test to detect a difference in the sample, when it exists in the target population. Calculated as 1-Beta. The greater the power, the larger the required sample size will be. A value between 80%-90% is usually used. Relationship between non-exposed/exposed groups in the sample.
Introduction. Sample size calculation or estimation is an important consideration which necessitate all researchers to pay close attention to when planning a study, which has also become a compulsory consideration for all experimental studies ().Moreover, nowadays, the selection of an appropriate sample size is also drawing much attention from researchers who are involved in observational ...
sample size would be determined thus: From the above example, the sample size for a study population of 1,024 is approximately 400, which also is approximately 39% of the population.
Overall Guetterman (2015) found that the mean sample size was 87 participants. However the range of participants was from 1-700. Regarding differences by methodology, he found case studies had a mean sample size of 188; ethnographies 128; grounded theory, 59; narrative inquiry, 18; and phenomenology, 21. (Guetterman, 2015: 10-13). So there ...
Pilot Studies: Conducting a small-scale pilot study can help refine the research design, estimate effect sizes, and inform the sample size calculation for the main study. Response Rates: Anticipate non-response or attrition, especially in longitudinal studies. Inflating the initial sample size can help ensure a sufficient final sample.
Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample.The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting ...
size determination is a critical aspect of research design, ensuring the validity, reliability, and generalizability. of study findings. Adequate sample sizes are essential for achieving statist ...
2.58. Put these figures into the sample size formula to get your sample size. Here is an example calculation: Say you choose to work with a 95% confidence level, a standard deviation of 0.5, and a confidence interval (margin of error) of ± 5%, you just need to substitute the values in the formula: ( (1.96)2 x .5 (.5)) / (.05)2.
Sample size is the number of observations or data points collected in a study. It is a crucial element in any statistical analysis because it is the foundation for drawing inferences and conclusions about a larger population. When delving into the world of statistics, the phrase "sample size" often pops up, carrying with it the weight of ...
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.
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).
Approaches to sample size calculation according to study design are presented with examples in health research. For sample size estimation, researchers need to (1) provide information regarding the statistical analysis to be applied, (2) determine acceptable precision levels, (3) decide on study power, (4) specify the confidence level, and (5 ...
Sample size determination is an essential step in planning a clinical study. It is critical to understand that different study designs need different methods of sample size estimation. Although there is a vast literature discussing sample size estimation, incorrect or improper formulas continue to be applied. This article reviews basic statistical concepts in sample size estimation, discusses ...
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 ...
The sample size of a quantitative study is the number of people who complete questionnaires in a research project. It is a representative sample of the target audience in which you are interested. ... Determining a good sample size for quantitative research. Sample size, as we've seen, is an important factor to consider in market research ...
However, in some fields of study, such as pharmacology or biological research, a minimum of five per group is recommended and considered acceptable by academic journals in the field. 4 Recommendations for minimum sample sizes for clinical studies suggest having at least 100 in each group. 40 However, recent advances in sample size calculation ...
For sample size estima-tion, researchers need to (1) provide information regarding the statistical analysis to be applied, (2) determine acceptable precision levels, (3) decide on study power, (4) specify the confidence level, and (5) determine the magnitude of practical significance differences (effect size).
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:
Characterising and justifying sample size sufficiency in interview-based studies: systematic analysis of qualitative health research over a 15-year period. BMC Medical Research Methodology. 18(1 ...
An appropriate sample renders the research more efficient: Data generated are reliable, resource investment is as limited as possible, while conforming to ethical principles. The use of sample size calculation directly influences research findings. Very small samples undermine the internal and external validity of a study.
Sample size and power analyses in clinical studies. In clinical research, sample size is calculated in line with the hypothesis and study design. The cross-over study design and parallel study design apply different approaches for sample size estimation. Unlike pre-clinical studies, a significant number of clinical journals necessitate sample ...
Not much of a surprise there. But there is a way to get to a sample size that doesn't involve democracy or demagoguery. The first step in finding a sample size is to define the study type. For the purposes of sample size estimation, there are three types of usability studies: Problem Discovery, Estimation, and Comparison (Table 1). #
The sample size for any study depends on certain factors such as the acceptable level of significance (P value), power (1 − β) of the study, expected 'clinically relevant' effect size, underlying event rate in the population, etc. Primarily, three factors P value (depends on α), power (related with β) and the effect size (clinically ...
In this interactive webinar, we provided a comprehensive overview of sample size determination, the key steps to successfully finding the appropriate sample size and cover several common pitfalls researchers fall into when finding the sample size for their study. In this free webinar we will cover. What is sample size determination?
Limitations in this study that could be improved upon in future research include a small sample size. A multi-institutional study could yield a larger sample size to provide more accurate analysis of the predictive variables. In addition, several patients in our cohort had incomplete medical histories prior to starting care at our institution.
Objective: Clinical theories suggest that narcissists have a compromised self-concept. However, empirical investigation on attributes of the self that would be impaired in pathological narcissism is limited and inconsistent. The present study aims at detecting distinctive profiles of narcissistic manifestations on facets of the self that have been indicated as relevant in clinical and ...