# Independent Complex Samples Z-Test - Comparing Two Means

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

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

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