Sample Size Calculator
Find out the sample size.
This calculator computes the minimum number of necessary samples to meet the desired statistical constraints.
| Confidence Level: | ||
| Margin of Error: | ||
| Population Proportion: | Use 50% if not sure | |
| Population Size: | Leave blank if unlimited population size. | |
Find Out the Margin of Error
This calculator gives out the margin of error or confidence interval of observation or survey.
| Confidence Level: | ||
| Sample Size: | ||
| Population Proportion: | ||
| Population Size: | Leave blank if unlimited population size. | |
Related Standard Deviation Calculator | Probability Calculator
In statistics, information is often inferred about a population by studying a finite number of individuals from that population, i.e. the population is sampled, and it is assumed that characteristics of the sample are representative of the overall population. For the following, it is assumed that there is a population of individuals where some proportion, p , of the population is distinguishable from the other 1-p in some way; e.g., p may be the proportion of individuals who have brown hair, while the remaining 1-p have black, blond, red, etc. Thus, to estimate p in the population, a sample of n individuals could be taken from the population, and the sample proportion, p̂ , calculated for sampled individuals who have brown hair. Unfortunately, unless the full population is sampled, the estimate p̂ most likely won't equal the true value p , since p̂ suffers from sampling noise, i.e. it depends on the particular individuals that were sampled. However, sampling statistics can be used to calculate what are called confidence intervals, which are an indication of how close the estimate p̂ is to the true value p .
Statistics of a Random Sample
The uncertainty in a given random sample (namely that is expected that the proportion estimate, p̂ , is a good, but not perfect, approximation for the true proportion p ) can be summarized by saying that the estimate p̂ is normally distributed with mean p and variance p(1-p)/n . For an explanation of why the sample estimate is normally distributed, study the Central Limit Theorem . As defined below, confidence level, confidence intervals, and sample sizes are all calculated with respect to this sampling distribution. In short, the confidence interval gives an interval around p in which an estimate p̂ is "likely" to be. The confidence level gives just how "likely" this is – e.g., a 95% confidence level indicates that it is expected that an estimate p̂ lies in the confidence interval for 95% of the random samples that could be taken. The confidence interval depends on the sample size, n (the variance of the sample distribution is inversely proportional to n , meaning that the estimate gets closer to the true proportion as n increases); thus, an acceptable error rate in the estimate can also be set, called the margin of error, ε , and solved for the sample size required for the chosen confidence interval to be smaller than e ; a calculation known as "sample size calculation."
Confidence Level
The confidence level is a measure of certainty regarding how accurately a sample reflects the population being studied within a chosen confidence interval. The most commonly used confidence levels are 90%, 95%, and 99%, which each have their own corresponding z-scores (which can be found using an equation or widely available tables like the one provided below) based on the chosen confidence level. Note that using z-scores assumes that the sampling distribution is normally distributed, as described above in "Statistics of a Random Sample." Given that an experiment or survey is repeated many times, the confidence level essentially indicates the percentage of the time that the resulting interval found from repeated tests will contain the true result.
| Confidence Level | z-score (±) |
| 0.70 | 1.04 |
| 0.75 | 1.15 |
| 0.80 | 1.28 |
| 0.85 | 1.44 |
| 0.92 | 1.75 |
| 0.95 | 1.96 |
| 0.96 | 2.05 |
| 0.98 | 2.33 |
| 0.99 | 2.58 |
| 0.999 | 3.29 |
| 0.9999 | 3.89 |
| 0.99999 | 4.42 |
Confidence Interval
In statistics, a confidence interval is an estimated range of likely values for a population parameter, for example, 40 ± 2 or 40 ± 5%. Taking the commonly used 95% confidence level as an example, if the same population were sampled multiple times, and interval estimates made on each occasion, in approximately 95% of the cases, the true population parameter would be contained within the interval. Note that the 95% probability refers to the reliability of the estimation procedure and not to a specific interval. Once an interval is calculated, it either contains or does not contain the population parameter of interest. Some factors that affect the width of a confidence interval include: size of the sample, confidence level, and variability within the sample.
There are different equations that can be used to calculate confidence intervals depending on factors such as whether the standard deviation is known or smaller samples (n<30) are involved, among others. The calculator provided on this page calculates the confidence interval for a proportion and uses the following equations:
| where is z score is the population proportion and are sample size is the population size |
Within statistics, a population is a set of events or elements that have some relevance regarding a given question or experiment. It can refer to an existing group of objects, systems, or even a hypothetical group of objects. Most commonly, however, population is used to refer to a group of people, whether they are the number of employees in a company, number of people within a certain age group of some geographic area, or number of students in a university's library at any given time.
It is important to note that the equation needs to be adjusted when considering a finite population, as shown above. The (N-n)/(N-1) term in the finite population equation is referred to as the finite population correction factor, and is necessary because it cannot be assumed that all individuals in a sample are independent. For example, if the study population involves 10 people in a room with ages ranging from 1 to 100, and one of those chosen has an age of 100, the next person chosen is more likely to have a lower age. The finite population correction factor accounts for factors such as these. Refer below for an example of calculating a confidence interval with an unlimited population.
EX: Given that 120 people work at Company Q, 85 of which drink coffee daily, find the 99% confidence interval of the true proportion of people who drink coffee at Company Q on a daily basis.
Sample Size Calculation
Sample size is a statistical concept that involves determining the number of observations or replicates (the repetition of an experimental condition used to estimate the variability of a phenomenon) that should be included in a statistical sample. It is an important aspect of any empirical study requiring that inferences be made about a population based on a sample. Essentially, sample sizes are used to represent parts of a population chosen for any given survey or experiment. To carry out this calculation, set the margin of error, ε , or the maximum distance desired for the sample estimate to deviate from the true value. To do this, use the confidence interval equation above, but set the term to the right of the ± sign equal to the margin of error, and solve for the resulting equation for sample size, n . The equation for calculating sample size is shown below.
| where is the z score is the margin of error is the population size is the population proportion |
EX: Determine the sample size necessary to estimate the proportion of people shopping at a supermarket in the U.S. that identify as vegan with 95% confidence, and a margin of error of 5%. Assume a population proportion of 0.5, and unlimited population size. Remember that z for a 95% confidence level is 1.96. Refer to the table provided in the confidence level section for z scores of a range of confidence levels.
Thus, for the case above, a sample size of at least 385 people would be necessary. In the above example, some studies estimate that approximately 6% of the U.S. population identify as vegan, so rather than assuming 0.5 for p̂ , 0.06 would be used. If it was known that 40 out of 500 people that entered a particular supermarket on a given day were vegan, p̂ would then be 0.08.
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Sample Size Calculator (Creative Research Systems)
This Sample Size Calculator is presented as a public service of Creative Research Systems survey software. You can use it to determine how many people you need to interview in order to get results that reflect the target population as precisely as needed. You can also find the level of precision you have in an existing sample.
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Creative Research Systems Sample Size Calculator
This free interactive web-based sample size calculator can be used to understand the relationship between number of samples, variation in indicators and confidence in survey results.
Sample Size Calculator
Do you know how many people have to answer your survey no problem. use our sample size calculator to know the exact number of surveys to run in your study..
Whenever you’re running and planning a research study, there’s nothing as important as knowing the exact number of surveys that you need for the study to be considered valid research material. This is when we need to know what’s the best way to you’ll be able to determine the sample size for your research.
We’re lovers of technology and automation here at QuesionPro. This is why we’ve created a simple sample calculator, so that just a few clicks away, determine the exact number of surveys to run.
If you’d like to know a bit more about how to use this sample calculator, please read the following part, and you’ll become an expert in Sample Calculation.
Sample size calculator for your research
With this calculator, you’ll be able to quickly and effectively measure the sample size of your next research. Surely, using it will allow you to save a lot of time. Take the most advantage out of it and use it whenever needed.
Confidence Level : Indicates the degree of confidence that the data is representative of the entire population. Margin of Error : It is the percentage of error that may exist in your sample . The larger the margin of error, the lower the confidence level of the results. Population : Total number of people your universe represents. How to use our sample calculator?Using our calculator is fairly easy. However, we’d like to share the following tips and notes for you to fully understand the entire process behind this useful, nearly magical tool.  Steps to use our sample size calculator
Remember that the sample will be representative because it will have the right margin and confidence level, so follow the following suggestions:
If you set the sample calculator to a confidence level of 95%, an error margin of 5%, and a total population of 7743955, the sample size would be 385. Now let’s break these concepts down a bit more: The margin of error or confidence intervalThe margin of error , also called confidence interval , is the negative or positive number that is generally reported in the outcome of a survey. For example, if you set the margin of error to 4 and 47% of your sample picks an answer, you can be certain that if you had formulated the question to the entire population, from 43% (47% - 4) to 51% (47% + 4) would have chosen that answer. To facilitate this process, you can too use our margin of error calculator. Confidence levelThe confidence level is how frequently the real percentage of the population would choose a specific answer. A confidence level of 95% means you can be 95% certain; a confidence level of 99% means you can be 99% certain. Most researchers use a 95% confidence level. For instance, if you ask a sample of 1000 people in a city what are their preferences in terms of soda, and 60% claim it’s Brand A, you can be certain that 40% - 80% of people in the city prefer that brand, but you can’t be that certain that 59% - 61% of the people in the city prefer that brand. Three factors help determine the confidence of your research: Sample sizePercentage or variability, total population. The greater the sample size, the more certain one can be that the responses represent the population. This means that for a determined confidence level, the bigger the sample, the smaller the margin of error (or confidence interval). Nonetheless, this relationship is not linear. In other words, doubling the sample size, will not reduce at half the margin of error. The accuracy also depends on the percentage of the sample that picks a response in particular. If 99% of your sample said “Yes” and 1% “No”, the probability of an error is remote, regardless of the sample size. However, if percentages are 51% and 49% respectively, the likelihood of an error is broader. Determining the sample size for a determined accuracy level, you must use the worst possible percentage (50%). Also, you must use this percentage when determining a general level of accuracy for a given sample. To determine the margin of error for a specific response in your sample, you can use the percentage by picking that answer and obtaining a narrower interval. In research, it’s common to go for the maximum variability option, especially when there are no backgrounds for a subject. For these cases a standard value of p=q=0.5 or 50%. It’s unlikely to know the exact size of a specific population. However, it is not an issue. The mathematical probabilities show us that the total population is irrelevant unless the sample size exceeds a small percentage of the total population you’re researching. This means that a sample of 500 people is just as useful to research a state of 15,000,000 or a city of 100,000. The calculation of the confidence interval infers that you have a random and confident population sample. If your sample is not truly random, you cannot trust those intervals. Samples that are not random are usually a result of an error or limitation in the sampling procedure. An example of this error would be calling people to their homes during the day, and put aside anyone who’s not at home (like most workers in the world). You cannot assume that non-workers (or home-workers) represent accurately an entire population. To learn more on sample size calculation, check our guide on: How to calculate sample size ? Sample calculator formulaAlthough it may seem like magic, behind our sample size calculator there is a methodology that validates the sample calculation. For this one, we rely on the following formula: Sample size = Z2 * (p) * (1-p) / c2
Tips for a proper calculation of the sample sizeHere you can find a few suggestions to determine the sample size in your next research:  Best practices when calculating the sample size
Importance of calculating the sample sizeSamples can offer data that allow inferring over the entire population. It’s through compiled data that researchers may get findings of a population. Other reasons why it’s important to calculate the sample size, are the following:
In summary, the sample size calculation is a very important process within any research project. It must be run during the planning phase of the study, based on the question types and the research design. It’s also advisable to count with a sample size calculator such as QuestionPro’s for help, to avoid errors when trying to determine the percentage of the population to be researched. We hope this sample size calculator comes in handy to collect the necessary data that assures success for your research project. What to do with your sample?There! Now you know the exact number of surveys to run for your study to be within a valid range, thanks to the sample size calculated. Do you need an automatic tool for the collection and analysis of your data? At QuestionPro, we can help. What are you waiting for?
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 Sample Size CalculatorPublished: March 1, 2010 by Jessica Harper Not sure what sample size you need? Try out this calculator from Creative Research Systems. About the Author Jessica Harper Using Sample Size Calculators: Step-by-Step Tutorials IntroductionA sample size calculator is a useful tool that helps researchers and statisticians determine the appropriate sample size for their study. It takes into account various factors such as the desired level of confidence, margin of error, and population size to calculate the optimal sample size. In this blog post, we will explore how to use a sample size calculator and provide step-by-step tutorials to help you get started. Step 1: Define Your Study ParametersThe first step in using a sample size calculator is to define the parameters of your study. This includes determining the desired level of confidence, margin of error, and population size. The level of confidence refers to the degree of certainty you want to have in your results, typically expressed as a percentage (e.g., 95% confidence level). The margin of error is the maximum amount of error you are willing to tolerate in your results, usually expressed as a percentage (e.g., ±5% margin of error). Finally, the population size refers to the total number of individuals in the population you are studying. Step 2: Choose a Sample Size CalculatorThere are several sample size calculators available online, each with its own interface and features. Some popular options include G*Power, Raosoft, and Sample Size Calculator by Creative Research Systems. Choose a calculator that best suits your needs and preferences. Step 3: Enter Your Study ParametersOnce you have chosen a sample size calculator, it’s time to enter your study parameters. Most calculators will have input fields where you can enter the level of confidence, margin of error, and population size. Some calculators may also allow you to specify additional parameters such as the expected proportion or standard deviation. Step 4: Calculate the Sample SizeAfter entering your study parameters, click on the “Calculate” or “Calculate Sample Size” button to obtain the recommended sample size. The calculator will perform the necessary calculations based on the input parameters and provide you with the optimal sample size for your study. Now that you understand the basic steps involved in using a sample size calculator, let’s dive into some tutorials to help you apply this knowledge. Tutorial 1: Using G*PowerG*Power is a popular sample size calculator used by researchers in various fields. To use G*Power, follow these steps:
Tutorial 2: Using RaosoftRaosoft is another widely used sample size calculator that offers a user-friendly interface. Here’s how you can use Raosoft:
Tutorial 3: Using Sample Size Calculator by Creative Research SystemsSample Size Calculator by Creative Research Systems is a comprehensive tool that allows you to calculate sample sizes for different study designs. Here’s how you can use it:
A sample size calculator is an invaluable tool for researchers and statisticians. By following the steps outlined in this blog post and using the provided tutorials, you can easily determine the optimal sample size for your study. Remember to choose a calculator that suits your needs and always enter accurate study parameters to obtain reliable results. About the Authorapp-samplesize.com Learn more about [your subject]. Start Now!Session expired Please log in again. The login page will open in a new tab. After logging in you can close it and return to this page.  Sample Calculator How many people do you need to talk to to get a margin of error you are comfortable with? Consult our handy calculator and find out! Listed below are few terms you will need to understand before using the sample size calculator: Confidence Level: The percentage value that tells how confident a researcher can be about being correct. A 95% confidence level is a generally acceptable level of confidence and is most typically used and accepted within the research industry. Which means that if a study were conducted 100 times, answers would be within the margin of error 95 out of 100 times. Margin of Error / Confidence Interval: Assumes that you have a random sample. The margin of error for a typical survey is +/- 5%. This means that results may vary as much as five percent in either direction. The margin of error for sub-samples (i.e. men versus women), is based on the number in that sub-sample. Population Size: The population size is the universe from which you are taking your sample. If the population size is very large or unknown, leave this field blank. DIRECTIONS:
CAUTION: Sampling error is only one source of bias. Contact us to discuss other possible sources of bias (i.e. question bias). ***************
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Sample Size Calculator - Confidence Level, ...
Sample Size Calculator. This Sample Size Calculator is presented as a public service of Creative Research Systems. You can use it to determine how many people you need to interview in order to get results that reflect the target population as precisely as needed. You can also find the level of precision you have in an existing sample.
View our sample size formulas for our sample size calculator from Creative Research Systems. Go to Navigation Go to Content. Creative Research Systems. Client Login. Your Complete Survey Software Solution . Call Today for Your FREE Consulations (707) 765 - 1001. Home; About.
Sample Size Calculator
This Sample Size Calculator is presented as a public service of Creative Research Systems survey software. You can use it to determine how many people you need to interview in order to get results that reflect the target population as precisely as needed. You can also find the level of precision you have in an existing sample. ©2019 Centre of ...
Creative Research Systems offers a free sample size calculator online. Learn more about our sample size calculator, and request a free quote on our survey systems and software for your business.
Creative Research Systems Sample Size Calculator. This free interactive web-based sample size calculator can be used to understand the relationship between number of samples, variation in indicators and confidence in survey results. The Conservation Gateway is for the conservation practitioner, scientist and decision-maker.
(For more advanced students with an interest in statistics, the Creative Research Systems website (Creative Research Systems, 2003) has a more exact formula, along with a sample size calculator that you can use.
With this calculator, you'll be able to quickly and effectively measure the sample size of your next research. Surely, using it will allow you to save a lot of time. Take the most advantage out of it and use it whenever needed. Sample Size Calculator. Confidence Level: 95% 99%.
Sample Size Calculator. Published: March 1, 2010 by Jessica Harper. Not sure what sample size you need? Try out this calculator from Creative Research Systems.
Step 2: Choose a Sample Size Calculator. There are several sample size calculators available online, each with its own interface and features. Some popular options include G*Power, Raosoft, and Sample Size Calculator by Creative Research Systems. Choose a calculator that best suits your needs and preferences. Step 3: Enter Your Study Parameters
Riley Research Survey Poll Brand Market Focus Testing Position Political Public Relations Advertising Web Consumer Portland Oregon PR Strategic. ... (This sample size calculator was created by Creative Research Systems.) Sample Size: n= 50 . 100 . 200 . 300 . 400 . 600 . 800 . 1,000 :
Survey Research Aids. Creative Research Systems offers a series of free aids for survey researchers. The first is an online sample size calculator. It can tell you how many people to interview to get a desired accuracy level for your surveys. It can also tell you the plus or minus figure for a sample you already have.
Survey Sample Size Calculator - IdSurvey
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.
The sample size of 307 students is based on research carried out by Saadatian et al. [10] who also used Roasoft.inc [11] a freely available online tool to determine the sample size. ...
What is a good sample size for a qualitative research study? Our sample size calculator will work out the answer based on your project's scope, participant characteristics, researcher expertise, and methodology. Just answer 4 quick questions to get a super actionable, data-backed recommendation for your next study.
Sample Size Calculator. This Sample Size Calculator is presented as a public service of Creative Research Systems. You can use it to determine how many people you need to interview in order to get results that reflect the target population as precisely as needed. You can also find the level of precision you have in an existing sample.
Download scientific diagram | 4: Sample size calculator (Creative Research Systems, 2012) from publication: Waste Composition and Students' Acceptance of Waste Segregation in West Lake Student ...
The Survey System: Sample Size Calculator. "Want to take a survey but not sure how many responses to collect? This calculator gives you the number for any given population size and desired confidence level. A reverse caulculator lets you enter characteristics of an existing survey and gives the confidence interval (plus-or-minus number) to ...
Creative Research Systems. Client Login. Your Complete Survey Software Solution . Call Today for Your FREE Consulations (707) 765 - 1001. Home; About. Reviews/Comments; ... (and this Web site) includes a sample size calculator that can help you decide on the sample size (jump to the calculator page for a general discussion of sample size ...
Calculadora de Tamaño de Muestras. Esta Calculadora de Tamaño de Muestras es un servicio público de Creative Research Systems. Se utiliza para determinar cuántas personas se deben entrevistar para obtener resultados representativos de la población objetivo con la precisión necesaria. Además permite determinar el nivel de confianza de una ...
The research follows a qualitative and quantitative approach, through questionnaires and face-to-face interviews with IT executives and propose a structural equation model to measure the main ...
About Creative Research Systems. Creative Research Systems was founded in 1982 to provide software for market researchers, political pollsters, human resource professionals, social scientists, and others who use questionnaires. Over the past 36 years, Creative Research Systems has established a reputation for developing leading edge survey ...