Independent Complex Samples Z-Test - Comparing Two Means

Where $\bar{x}$ and $\bar{y}$ are the two means and $\sigma_\bar{x}$ and $\sigma_\bar{y}$ are their standard errors:

$z=\frac{\bar{x}-\bar{y}}{\sqrt{\sigma^2_\bar{x} + \sigma^2_\bar{x}}}$,

where $p = 2(1-\Phi(|z|))$ .