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.
Before using the sample size calculator, there are two terms that you need to know. These are: confidence interval and confidence level. If you are not familiar with these terms, click here. To learn more about the factors that affect the size of confidence intervals, click here.
Enter your choices in a calculator below to find the sample size you need or the confidence interval you have. Leave the Population box blank, if the population is very large or unknown.
Sample Size Calculator Terms: Confidence Interval & Confidence Level
The number of observations made by each subject. The sample size calculations are derived from Power Analysis and Sample Size (PASS) software where the alpha and minimum required power is fixed at 0.05 and higher than 0.80 respectively. A discussion on how to use these tables for determining sample sizes required for each of the. PASS provides sample size calculations for over 370 more scenarios than any other sample size software and is the premier software tool for determining the needed sample size or analyzing the power of a study. PASS is used extensively in clinical trial planning, grant proposals, pharmaceutical research, statistical and biostatistical consulting. Your sample will need to include a certain number of people, however, if you want it to accurately reflect the conditions of the overall population it's meant to represent. To calculate your necessary sample size, you'll need to determine several set values and plug them into an appropriate formula.
The confidence interval (also called margin of error) is the plus-or-minus figure usually reported in newspaper or television opinion poll results. For example, if you use a confidence interval of 4 and 47% percent of your sample picks an answer you can be 'sure' that if you had asked the question of the entire relevant population between 43% (47-4) and 51% (47+4) would have picked that answer.
The confidence level tells you how sure you can be. It is expressed as a percentage and represents how often the true percentage of the population who would pick an answer lies within the confidence interval. The 95% confidence level means you can be 95% certain; the 99% confidence level means you can be 99% certain. Most researchers use the 95% confidence level.
When you put the confidence level and the confidence interval together, you can say that you are 95% sure that the true percentage of the population is between 43% and 51%. The wider the confidence interval you are willing to accept, the more certain you can be that the whole population answers would be within that range.
For example, if you asked a sample of 1000 people in a city which brand of cola they preferred, and 60% said Brand A, you can be very certain that between 40 and 80% of all the people in the city actually do prefer that brand, but you cannot be so sure that between 59 and 61% of the people in the city prefer the brand.
Factors that Affect Confidence Intervals
There are three factors that determine the size of the confidence interval for a given confidence level:
- Sample size
- Percentage
- Population size
Sample Size
The larger your sample size, the more sure you can be that their answers truly reflect the population. This indicates that for a given confidence level, the larger your sample size, the smaller your confidence interval. However, the relationship is not linear (i.e., doubling the sample size does not halve the confidence interval).
Percentage
Your accuracy also depends on the percentage of your sample that picks a particular answer. If 99% of your sample said 'Yes' and 1% said 'No,' the chances of error are remote, irrespective of sample size. However, if the percentages are 51% and 49% the chances of error are much greater. It is easier to be sure of extreme answers than of middle-of-the-road ones.
When determining the sample size needed for a given level of accuracy you must use the worst case percentage (50%). You should also use this percentage if you want to determine a general level of accuracy for a sample you already have. To determine the confidence interval for a specific answer your sample has given, you can use the percentage picking that answer and get a smaller interval.
Population Size
How many people are there in the group your sample represents? This may be the number of people in a city you are studying, the number of people who buy new cars, etc. Often you may not know the exact population size. This is not a problem. The mathematics of probability prove that the size of the population is irrelevant unless the size of the sample exceeds a few percent of the total population you are examining. This means that a sample of 500 people is equally useful in examining the opinions of a state of 15,000,000 as it would a city of 100,000. For this reason, The Survey System ignores the population size when it is 'large' or unknown. Population size is only likely to be a factor when you work with a relatively small and known group of people (e.g., the members of an association).
Sample Size Calculation Software Mac Download
The confidence interval calculations assume you have a genuine random sample of the relevant population. If your sample is not truly random, you cannot rely on the intervals. Non-random samples usually result from some flaw or limitation in the sampling procedure. An example of such a flaw is to only call people during the day and miss almost everyone who works. For most purposes, the non-working population cannot be assumed to accurately represent the entire (working and non-working) population. An example of a limitation is using an opt-in online poll, such as one promoted on a website. There is no way to be sure an opt-in poll truly represents the population of interest.
PASS software provides sample size tools for over 1030 statistical test and confidence interval scenarios - more than double the capability of any other sample size software. Each tool has been carefully validated with published articles and/or texts.
Get to know PASS by downloading a free trial, viewing the video to the right, or exploring this website.
PASS comes complete with integrated documentation and PhD statistician support.
PASS has been fine-tuned for over 20 years, and is now the leading sample size software choice for clinical trial, pharmaceutical, and other medical research. It has also become a mainstay in all other fields where sample size calculation or evaluation is needed.
Obtaining A Sample Size In PASS
In PASS, you can estimate the sample size for a statistical test or confidence interval in a few short steps. If you need guidance during any of the steps, PASS has excellent documentation, there are free training videos, and you can contact our team of PhD statisticians.
Choosing A Procedure
Finding the sample size procedure is easy using the drop-down menu, the procedure search, or the category tree. Watch a short video to learn how to select your desired procedure in PASS.
Enter The Values
The sample size procedure tools are easy to use and have built-in help messages for every option.
Sample Size Calculation Software Mac
Enlarge the infographic to see the descriptions of the ways that PASS helps you to enter the proper values in a sample size procedure tool. You can also watch this video to see an example of using a procedure window in PASS.
Ready to Use Output
When a PASS procedure is run, the sample size results and corresponding plots are displayed in the output window. The sample size or power curves can be clicked to be shown in a separate window for viewing or saving.
Navigation of the output is easy with the output navigation tree. The format of the output makes it easy to be viewed, copied and pasted, or saved. Multiple output runs can be sent to the output gallery for saving or for comparing sample size analyses.
To take a video tour of the output window in PASS, click here.