Standard error

The standard error plays the same role for a statistic that the standard deviation plays for raw data, and it gets smaller as the sample size grows. For example, the standard error of a sample proportion is $\sqrt{\frac{p(1-p)}{n}}$ (the square root of p times one minus p, divided by n). For a sample mean it is $\frac{\sigma}{\sqrt{n}}$ (sigma, the population standard deviation, over the square root of n). A smaller standard error means the estimate is more precise, which narrows a confidence interval.