Editing Sampling distribution (section)

==Standard error==

The [[standard deviation]] of the sampling distribution of a [[statistic]] is referred to as the
[[standard error (statistics)|standard error]] of the statistic. For the case where the statistic is the sample mean, and samples are uncorrelated, the standard error is:
<math display="block">\sigma_{\bar x} = \frac{\sigma}{\sqrt{n}}</math>
where <math>\sigma</math> is the standard deviation of the population distribution of that quantity and <math>n</math> is the sample size (number of items in the sample).

An important implication of this formula is that the sample size must be quadrupled (multiplied by 4) to achieve half (1/2) the measurement error.  When designing statistical studies where cost is a factor, this may have a role in understanding cost–benefit tradeoffs.

For the case where the statistic is the sample total, and samples are uncorrelated, the standard error is:
<math display="block">\sigma_{\Sigma x} = \sigma\sqrt{n}</math>
where, again, <math>\sigma</math> is the standard deviation of the population distribution of that quantity and <math>n</math> is the sample size (number of items in the sample).