Where \(\bar{x} \) and \(\bar{y} \) are the two means and \(\sigma_\bar{x} \) and \(\sigma_\bar{y} \) are their standard errors:
\[\begin{align} z=\frac{\bar{x}-\bar{y}}{\sqrt{\sigma^2_\bar{x} + \sigma^2_\bar{x}}} \end{align},\]
where \(p = 2(1-\Phi(|z|))\).