Independent Complex Samples Z-Test - Comparing Two Means

Where $\overline{x}$ and $\overline{y}$ are the two means and ${\sigma }_{\overline{x}}$ and ${\sigma }_{\overline{y}}$ are their standard errors:

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

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