Independent Complex Samples Z-Test - Comparing Two Means
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Where [math]\displaystyle{ \bar{x} }[/math] and [math]\displaystyle{ \bar{y} }[/math] are the two means and [math]\displaystyle{ \sigma_\bar{x} }[/math] and [math]\displaystyle{ \sigma_\bar{y} }[/math] are their standard errors:
[math]\displaystyle{ z=\frac{\bar{x}-\bar{y}}{\sqrt{\sigma^2_\bar{x} + \sigma^2_\bar{x}}} }[/math],
where [math]\displaystyle{ p = 2(1-\Phi(|z|)) }[/math] .