# data[].attributes.headline
YouTube Video: The Sample Size Explained in One Minute: From Definition to Examples and Research Tips (1:51) 

# data[].attributes.subject
YouTube Video: The Sample Size Explained in One Minute: From Definition to Examples and Research Tips (1:51) 

# data[].attributes.attachment_link.title
The Sample Size Explained in One Minute: From Definition to Examples and Research Tips

# data[].attributes.headline
Qualtrics Sample Size Calculator & Blog post about Sample Sizes 

# data[].attributes.subject
Qualtrics Sample Size Calculator & Blog post about Sample Sizes 

# data[].attributes.attachment_link.readable_text
How many people do you need to interview to get results representative of the target population with the level of confidence that you are willing to accept?
Discover how to maximize business ROI for market research.
Introductions to Sample Size

How can you calculate sample size, reduce the margin of error and produce surveys with statistically significant results? In this short guide, we explain how you can improve your surveys and showcase some of the tools and resources you can leverage in the process.

But first, when it comes to market research, how many people do you need to interview to get results representative of the target population with the level of confidence that you are willing to accept?
Download our step-by-step guide to make sure you're getting the right sample size.
However, if all of this sounds new to you, let's start with what sample size is.

What is sample size?

Sample size is a term used in market research to define the number of subjects included in a survey, study, or experiment. In surveys with large populations, sample size is incredibly important. The reason for this is because it's unrealistic to get answers or results from everyone - instead, you can take a random sample of individuals that represent the population as a whole.

For example, we might want to compare the performance of long-distance runners that eat Weetabix for breakfast versus those who don't. Since it's impossible to track the dietary habits of every long-distance runner across the globe, we would have to focus on a segment of the survey population. This might mean selecting 1,000 runners for the study.

How can sample size influence results?

That said, no matter how diligent we are with our selection, there will always be some margin of error (also referred to as confidence interval) in the study results, that's because we can't speak to every long-distance runner or be confident of how Weetabix influences (in every possible scenario), the performance of long-distance runners. This is known as a "sampling error."

Larger sample sizes will help to mitigate the margin of error, helping to provide more statistically significant and meaningful results. In other words, a more accurate picture of how eating Weetabix can influence the performance of long-distance runners.
So what do you need to know when calculating sample size?

What you need to know to calculate survey sample size

Confidence interval (or margin of error)

The confidence interval is the plus-or-minus figure that represents the accuracy of the reported. Consider the following example:

A Canadian national sample showed "Who Canadians spend their money on for Mother's Day." Eighty-two percent of Canadians expect to buy gifts for their mom, compared to 20 percent for their wife and 15 percent for their mother-in-law. In terms of spending, Canadians expect to spend $93 on their wife this Mother's Day versus $58 on their mother. The national findings are accurate, plus or minus 2.75 percent, 19 times out of 20.

For example, if you use a confidence interval of 2.75 and 82% percent of your sample indicates they will "buy a gift for mom" you can be "confident (95% or 99%)" that if you had asked the question to ALL CANADIANS, somewhere between 79.25% (82%-2.75%) and 84.75% (82%+2.75%) would have picked that answer.

Confidence interval is also called the "margin of error."

Confidence level

The confidence level tells you how confident you are of this result. It is expressed as a percentage of times that different samples (if repeated samples were drawn) would produce this result. The 95% confidence level means that 19 times out of twenty that results would fall in this - + interval confidence interval. The 95% confidence level is the most commonly used.

When you put the confidence level and the confidence interval together, you can say that you are 95% (19 out of 20) sure that the true percentage of the population that will "buy a gift for mom" is between 79.25% and 84.75%.

Wider confidence intervals increase the certainty that the true answer is within the range specified. These wider confidence intervals come from smaller sample sizes. When the costs of an error is extremely high (a multi-million dollar decision is at stake) the confidence interval should be kept small. This can be done by increasing the sample size.

Population size

Population size is the total amount of people in the group you're trying to study. If you were taking a random sample of people across the U.K., then your population size would be just over 68 million (as of 09 August 2021).

Standard deviation

This refers to how much individual responses will vary between each other and the mean. If there's a low standard deviation, scores will be clustered near the mean with minimal variation. A higher standard deviation means that when plotted on a graph, responses will be more spread out.

Standard deviation is expressed as a decimal, and 0.5 is considered a "good" standard deviation to set to ensure a sample size that represents the population.

How can you calculate sample size?

After you've considered the four above variables, you should be able to calculate your sample size.

However, if you don't know your population size, you can still calculate your sample size. To do this, you need two pieces of information: a z-score and the sample size formula.

What is a z-score?

A z-score is simply the numerical representation of your desired confidence level. It tells you how many standard deviations from the mean your score is.

The most common percentages are 90%, 95%, and 99%.

As the formula shows, the z-score is simply the raw score minus the population mean and divided by the population's standard deviation.

Using a sample size calculation

Once you have your z-score, you can fill out your sample size formula, which is:

Is there an easier way to calculate sample size?

If you want an easier option, Qualtrics offers an online sample size calculator that can help you determine your ideal survey sample size in seconds. Just put in the confidence level, population size, margin of error, and the perfect sample size is calculated for you.

Sample Size Calculator

Best-practice tips for sample size

There are lots of variables to consider when it comes to generating a specific sample size. That said, there are a few best-practice tips (or rules) to ensure you get the best possible results:

1) Balance cost and confidence level

To increase confidence level or reduce the margin of error, you have to increase your sample size. Larger sizes almost invariably lead to higher costs. Take the time to consider what results you want from your surveys and what role it plays in your overall campaigns.

2) You don't always need statistically significant results

Depending on your target audience, you may not be able to get enough responses (or a large enough sample size) to achieve "statistically significant" results.

If it's for your own research and not a wider study, it might not be that much of a problem, but remember that any feedback you get from your surveys is important. It might not be statistically significant, but it can aid your activities going forward.

Ultimately, you should treat this on a case-by-case basis. Survey samples can still give you valuable answers without having sample sizes that represent the general population.
But more on this in the section below.

3) Ask open-ended questions

Yes and no questions provide certainty, but open-ended questions provide insights you would have otherwise not received. To get the best results, it's worth having a mix of closed and open-ended questions.
For a deeper dive into survey question types, check out our handbook.

Different types of surveys

From market research to customer satisfaction, there are plenty of different surveys that you can carry out to get the information you need, corresponding with your sample size.

The great thing about what we do at Qualtrics is that we offer a comprehensive collection of pre-made, customer, product, employee, and brand survey templates. This includes Net Promoter Score (NPS) surveys, manager feedback surveys, customer service surveys, and more.

The best part? You can access all of these templates for free. Each one is designed by our specialist team of subject matter experts and researchers so you can be sure that our best-practice question choices and clear designs will get more engagement and better quality data.

As well as offering free survey templates, you can check out our free survey builder. Trusted by over 11,000 brands and 99 of the top 100 business schools, our tool allows you to create, distribute and analyze surveys to find customer, employee, brand, product, and market research insights.

Drag-and-drop functionality means anyone can use it, and wherever you need to gather and analyze data, our platform can help.

What next?

Once you have determined your sample size, you're ready for the next step in the research journey. market research.

Market research is the process of gathering information about consumers' needs and preferences, and it can provide incredible insights that help elevate your business (or your customers') to the next level.

If you want to learn more, we've got you covered. Just download our free guide and find out how you can:

Identify use cases for market research

Create and deliver effective market research campaigns

Take action on research findings

We've got you covered. Download our guide to conducting market research

# data[].attributes.attachment_link.title
Sample Size Calculator (Use in 60 Seconds) // Qualtrics

# data[].attributes.attachment_link.description
How many people do you need to interview to get results representative of the target population with the level of confidence that you are willing to accept? Discover how to maximize business ROI for market research. How can you calculate sample size, reduce the margin of error and produce surveys with statistically significant results?

# data[].attributes.attachment_link.description
How many people do you need for saturation in qualitative research? Use our sample size calculator and see how the formula works for interviews, diary studies, etc.

# data[].attributes.headline
6 Types of Mixed-Methods Designs Brief Review 

# data[].attributes.subject
6 Types of Mixed-Methods Designs Brief Review 

# data[].attributes.attachment_link.title
GSU Library Research Guides: Mixed Methods: Mixed Methods Designs

# data[].attributes.attachment_link.description
Mixed Methods explanation of four mixed methods designs

# data[].attributes.headline
Mixed Methods Research Guide With Examples

# data[].attributes.subject
Mixed Methods Research Guide With Examples

# data[].attributes.attachment_link.title
Mixed Methods Research Guide With Examples

# data[].attributes.attachment_link.description
Mixed method research is an approach where researchers collect and analyze both quantitative and qualitative data within the same study. Know its types, strengths, and challenges, along with how…

# data[].attributes.headline
ClinCalc: Sample Size Calculator for study Power (Includes Citation)

# data[].attributes.subject
ClinCalc: Sample Size Calculator for study Power (Includes Citation)

# data[].attributes.attachment_link.readable_text
Determines the minimum number of subjects for adequate study power

ClinCalc.com » Statistics » Sample Size Calculator

Study Group Design

vs.
Two independent
study groups
vs.
One study group
vs. population

Two study groups will each receive different treatments.

Primary Endpoint

Dichotomous
(yes/no)

Continuous
(means)

The primary endpoint is binomial - only two possible outcomes.
Eg, mortality (dead/not dead), pregnant (pregnant/not)

Statistical Parameters

Anticipated Incidence

Known population | %
Study group | %

Anticipated Mean

Known population | ±
Study group |

Type I/II Error Rate

Alpha |
Power |

Press 'Calculate' to view calculation results.

About This Calculator

This calculator uses a number of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect.¹

Before a study is conducted, investigators need to determine how many subjects should be included. By enrolling too few subjects, a study may not have enough statistical power to detect a difference (type II error). Enrolling too many patients can be unnecessarily costly or time-consuming.

Generally speaking, statistical power is determined by the following variables:

Baseline Incidence: If an outcome occurs infrequently, many more patients are needed in order to detect a difference.

Population Variance: The higher the variance (standard deviation), the more patients are needed to demonstrate a difference.

Treatment Effect Size: If the difference between two treatments is small, more patients will be required to detect a difference.

Alpha: The probability of a type-I error -- finding a difference when a difference does not exist. Most medical literature uses an alpha cut-off of 5% (0.05) -- indicating a 5% chance that a significant difference is actually due to chance and is not a true difference.

Beta: The probability of a type-II error -- not detecting a difference when one actually exists. Beta is directly related to study power (Power = 1 - β). Most medical literature uses a beta cut-off of 20% (0.2) -- indicating a 20% chance that a significant difference is missed.

Post-Hoc Power Analysis

To calculate the post-hoc statistical power of an existing trial, please visit the post-hoc power analysis calculator.

References and Additional Reading

1. Rosner B. Fundamentals of Biostatistics. 7th ed. Boston, MA: Brooks/Cole; 2011.

# data[].attributes.attachment_link.description
Press 'Calculate' to view calculation results. This calculator uses a number of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect. Before a study is conducted, investigators need to determine how many subjects should be included.

# data[].attributes.body
Definitions and explanations for common terms and concepts

# data[].attributes.attachment_link.description
Definitions and explanations for common terms and concepts

# data[].attributes.headline
Definitions of Statistics, Probability, and Key Terms

# data[].attributes.subject
Definitions of Statistics, Probability, and Key Terms

# data[].attributes.attachment_link.readable_text
The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives.

In this course, you will learn how to organize and summarize data. Organizing and summarizing data is called descriptive statistics. Two ways to summarize data are by graphing and by using numbers (for example, finding an average). After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from "good" data. The formal methods are called inferential statistics. Statistical inference uses probability to determine how confident we can be that our conclusions are correct.

Effective interpretation of data (inference) is based on good procedures for producing data and thoughtful examination of the data. You will encounter what will seem to be too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.

Probability

Probability is a mathematical tool used to study randomness. It deals with the chance (the likelihood) of an event occurring. For example, if you toss a fair coin four times, the outcomes may not be two heads and two tails. However, if you toss the same coin 4,000 times, the outcomes will be close to half heads and half tails. The expected theoretical probability of heads in any one toss is or 0.5. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. After reading about the English statistician Karl Pearson who tossed a coin 24,000 times with a result of 12,012 heads, one of the authors tossed a coin 2,000 times. The results were 996 heads. The fraction is equal to 0.498 which is very close to 0.5, the expected probability.

The theory of probability began with the study of games of chance such as poker. Predictions take the form of probabilities. To predict the likelihood of an earthquake, of rain, or whether you will get an A in this course, we use probabilities. Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent. A stockbroker uses probability to determine the rate of return on a client's investments. You might use probability to decide to buy a lottery ticket or not. In your study of statistics, you will use the power of mathematics through probability calculations to analyze and interpret your data.

Key Terms

In statistics, we generally want to study a population. You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a sample. The idea of sampling is to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population.

Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students' grade point averages. In presidential elections, opinion poll samples of 1,000-2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16 ounce can contains 16 ounces of carbonated drink.

From the sample data, we can calculate a statistic. A statistic is a number that represents a property of the sample. For example, if we consider one math class to be a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. The statistic is an estimate of a population parameter, in this case the mean. A parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.

One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. The accuracy really depends on how well the sample represents the population. The sample must contain the characteristics of the population in order to be a representative sample. We are interested in both the sample statistic and the population parameter in inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population parameter.

A variable, or random variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. Variables may be numerical or categorical. Numerical variables take on values with equal units such as weight in pounds and time in hours. Categorical variables place the person or thing into a category. If we let X equal the number of points earned by one math student at the end of a term, then X is a numerical variable. If we let Y be a person's party affiliation, then some examples of Y include Republican, Democrat, and Independent. Y is a categorical variable. We could do some math with values of X (calculate the average number of points earned, for example), but it makes no sense to do math with values of Y (calculating an average party affiliation makes no sense).

Data are the actual values of the variable. They may be numbers or they may be words. Datum is a single value.

Two words that come up often in statistics are mean and proportion. If you were to take three exams in your math classes and obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing by three (your mean score would be 84.3 to one decimal place). If, in your math class, there are 40 students and 22 are men and 18 are women, then the proportion of men students is and the proportion of women students is . Mean and proportion are discussed in more detail in later chapters.

# data[].attributes.attachment_link.title
1.1 Definitions of Statistics, Probability, and Key Terms - Introductory Business Statistics 2e | OpenStax

# data[].attributes.attachment_link.description
Probability is a mathematical tool used to study randomness. It deals with the chance (the likelihood) of an event occurring. For example, if you toss a...

# data[].attributes.body
Submissions

Articles»

Announcements

Lesson Plans

Resources

Events

What Is Power?

# data[].attributes.body
Sample size determination is the essential step of research methodology. It is an act of choosing the number of observers or replicates to include in a statistical sample. In some situations, an increase in precision for a larger sample size is minimal or even nonexistent. Sample sizes are judged based on the quality of the resulting estimates. Sample size determination in descriptive studies is different than experimental studies. Sample size determination helps in increasing the quality of evidence-based research.

# data[].attributes.headline
NIH Grant Applications: The Anatomy of a Specific Aims Page

# data[].attributes.subject
NIH Grant Applications: The Anatomy of a Specific Aims Page

# data[].attributes.body
The Anatomy of a Specific Aims Page

# data[].attributes.attachment_link.description
The specific aims page, especially the aims themselves, are the crux of your grant application. Use the following tips to write a strong, clear specific aims page. Use the Specific Aims Page Checklist to assess your writing and to ensure that you have included all of the necessary components.

# data[].attributes.headline
Grant drafting support with guided generative AI software Godwin et al 2024

# data[].attributes.subject
Grant drafting support with guided generative AI software Godwin et al 2024

# data[].attributes.attachment_link.title
Grant drafting support with guided generative AI software Godwin et al 2024

# data[].attributes.body
Retrieved from: https://www.uab.edu/medicine/cfar/images/Specific_Aims_Examples.pdf

# data[].attributes.headline
ChatGPT for Research & Publication: A Step-by-Step Guide

# data[].attributes.subject
ChatGPT for Research & Publication: A Step-by-Step Guide

# data[].attributes.body
Retrieved from: https://pmc.ncbi.nlm.nih.gov/articles/PMC10731938/

# data[].attributes.attachment_link.title
ChatGPT for Research and Publication - A Step-by-Step Guide

# data[].attributes.headline
Elsevier's new OpenEvidence AI Medical Research APP ( Free to Healthcare Professionals) 

# data[].attributes.subject
Elsevier's new OpenEvidence AI Medical Research APP ( Free to Healthcare Professionals) 

# data[].attributes.body
OpenEvidence is what we always imagined when we used to talk about someone finally solving medical search.

Information overload is an extreme challenge in medicine.

The amount of medical research published annually is doubling every 5 years.[1] Such a rate of change makes it nearly impossible for the world’s physicians, medical researchers, and healthcare professionals to monitor and understand all the latest research literature and clinical evidence relevant to their work.

To tame the medical information firehose, we built OpenEvidence, an artificial intelligence system to aggregate, synthesize, and visualize clinically relevant evidence in understandable, accessible formats that can be used to make more evidenced-based decisions and improve patient outcomes.

# data[].attributes.attachment_link.description
The world’s leading AI-powered medical search platform.

# data[].attributes.headline
YouTube Video: Mixed-Methods Research Designs Review (2:52)

# data[].attributes.subject
YouTube Video: Mixed-Methods Research Designs Review (2:52)

# data[].attributes.attachment_link.title
Mixed Method Research | Mixed Methods Research Designs | Types of Mixed Methods Research Designs