Sampling Error Calculator

What Is Sampling Error?

Sampling error is the expected difference between a sample statistic and the true population parameter caused by random sampling variation. Here it is estimated as a margin of error using a critical value times standard error. Related tools: Sample Size Calculator and Confidence Interval Calculator.

Proportion Margin of Error

$$e_{\hat{p}} = z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Mean Margin of Error

With known population standard deviation:

$$e_{\bar{x}} = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$$

With sample standard deviation, replace $z_{\alpha/2}$ with $t_{\alpha/2}$ and use $s$ instead of $\sigma$.

Example

In a sample of 500 with $\hat{p} = 0.80$ at 95% confidence, sampling error is about $\pm 3.51\%$, so the true proportion likely falls between 76.5% and 83.5%.