This sampling error calculator takes the figures you already have and applies the relationship behind sampling error calculations for you, giving sampling error, degrees of freedom (d) and significance level from confidence level, sample size (n), sample proportion (p̂), population standard deviation (σ), sample standard deviation (s) and one way.
What Is the Sampling Error Calculator?
The sampling error calculator turns a set of measurements into sampling error, degrees of freedom (d) and significance level, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Sampling Error Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with confidence level set to 10, sample size (n) set to 5, sample proportion (p̂) set to 2, the calculator returns degrees of freedom (d) of 4, and significance level of -9, and sampling error of -. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out sampling error?
Enter confidence level, sample size (n), sample proportion (p̂), population standard deviation (σ), sample standard deviation (s) and one way. The calculator then works through the relationship and reports sampling error, degrees of freedom (d) and significance level.
What does the sampling error actually calculate?
It takes confidence level, sample size (n), sample proportion (p̂), population standard deviation (σ), sample standard deviation (s) and one way and converts them into sampling error, degrees of freedom (d) and significance level using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter confidence level?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.