Standard error

Standard Error for Mean

S E_{\bar{x}} = \frac{s}{\sqrt{n}}

where:

$s$ is the sample standard deviation
$n$ is the sample size

Standard Error for Proportion

S E_{\hat{p}} = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}

where:

$\hat{p}$ is the sample proportion
$n$ is the sample size

Standard Error for Difference in Means

S E_{{\bar{x}}_{1} - {\bar{x}}_{2}} = \sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}}

where:

$s_{1}$ , $s_{2}$ are the sample standard deviations
$n_{1}$ , $n_{2}$ are the sample sizes

Standard Error for Difference in Proportions

S E_{{\hat{p}}_{1} - {\hat{p}}_{2}} = \sqrt{\frac{{\hat{p}}_{1} (1 - {\hat{p}}_{1})}{n_{1}} + \frac{{\hat{p}}_{2} (1 - {\hat{p}}_{2})}{n_{2}}}

where:

${\hat{p}}_{1}$ , ${\hat{p}}_{2}$ are the sample proportions
$n_{1}$ , $n_{2}$ are the sample sizes