Easily Calculate Sample Size with this Tool
Sample Size Calculator Guide
Provide the population size for the target population that your survey results will be representing
This is not your sample size but the entire population size you want to represent. Examples would be:
- The state of California (39.51 million)
- Pacific Gas & Electic (PG&E) Customers (16 million)
- Active members of the California Bar Association (190 thousand)
Enter your target population size.
The margin of error (also known as the confidence interval) represents how precise your results will be + or – the population statistic.
The margin of error represents the difference of proportion from the true proportion that is acceptable to the researcher for a given population statistic.
In the social sciences, 5 percent is an acceptable margin of error. You can change the margin of error depending on your precision needs. If you have no preference, choose a 5 percent default.
Sample size increases as the margin of error decreases.
Trying to figure out how sample size affects the margin of error? Learn more about the margin of error here.
Select the reliability level
In statistics, this a measure of the reliability of a result and should not be confused with the confidence interval.
A confidence level of 95 percent means there is a probability of at least 95 percent the result accurately represents the population.
Increasing the confidence level will increase the sample size.
This is your estimated sample size based on the inputs provided
The calculator uses a p-value of 0.50 which is the standard distribution or deviation recommend for most research where you don’t know the previous or actual deviation.
All other inputs are controllable with the calculator. However, 95% confidence levels and 5% margin of error are generally accepted settings for research.
Please refer to best practices for sample size calculator later in this article for how to calculate sample size and use sample size estimates.
How to Calculate Sample Size for Your Survey
If you are searching for a sample size calculator you know the goal of a survey is to acquire conclusions from a representative sample of a target population. But one problem of designing a survey is figuring out just how many participants to include to have a sample that can truly represent the population. Statistics solves this problem, giving survey designers a clear-cut way of calculating the minimum sample needed for the survey to be “valid” in science’s eyes.
This method of calculating the required sample size for your survey is easy enough for even the first-time survey-creator or an experienced research expert to estimate probability sampling needs.
Choose the alpha level and corresponding confidence level
The alpha level is the probability of rejecting the null hypothesis of the survey (usually that there is no difference between the groups you wish to investigate) assuming that the null hypothesis is actually true.
In most sciences, 0.05 is the standard alpha level. However, alpha levels 0.01 and 0.1 are not uncommon. If you do not know which alpha level to choose, set alpha = 0.05. The confidence level will be 100 minus the alpha value. If the alpha is 0.05 the confidence level is 0.95 or 95%.
Choose the margin of error (confidence interval)
The margin of error represents how precise your results will be + or – a given population statistic. Technically, the margin of error represents the difference in proportion from the true proportion acceptable to the researcher for the population statistic. If you want the difference of the absolute value of the range, run a confidence interval test.
The margin of error also referred to as the confidence interval, is often expressed as a range ± the population parameter σ. In the social sciences, 0.05 is an acceptable margin of error. You can change the margin of error depending on your precision needs. If you have no preference, choose e = 0.05 as the default.
Use our margin of error calculator to check to see if the sample size relative to the population size is within an acceptable parameter. Anything above five percent, you may want to increase your sample size.
Estimate the standard deviation
It’s best to use standard-deviation data from previous or similar studies for your current. Often it is the case there is no prior research for your topic of interest. In these circumstances, for the sake of being conservative, set the standard deviation, p = 0.5.
Please note, if you are planning to use a distribution value other than 0.5, you have the replace p2 with p(1-p) in the initial sample size calculator equation below.
Find the z-score for the confidence level
You can find this value by using any t-table, which will be available in most introductory statistics books. The bottom two rows include the most frequently used confidence levels, along with their z-scores.
Use the alpha value or the confidence level to look up the corresponding value while assuming the degrees of freedom value in the table is large (this way your estimate will still be conservative).
For example, you will find for an alpha level of 0.05, the corresponding z-score in the table assuming a large degree of freedom value is 1.96. So, z value = 1.96.
We have included a simplified z-score lookup table with the most common survey research confidence intervals used below:
T-Table with Z Scores
Calculate the initial sample size estimate
Simply calculate N = ( z 2× p 2 ) / e 2
Calculate the final sample size estimate
Divide N by 1 + (N / population), where “population” is the size of the total population you are targeting.
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