What happens to the standard error each time you quadruple the sample size?

Mar 27, 2018

Quadrupling the sample size reduces the standard error by half.

Explanation:

The standard error is given by

$S E = \frac{\sigma}{\sqrt{n}}$

If we substitute $4 n$ for $n$, this becomes:

$S E = \frac{\sigma}{\sqrt{4 n}} = \frac{\sigma}{2 \sqrt{n}} = \frac{1}{2} \frac{\sigma}{\sqrt{n}}$

So the standard error has been reduced by half.