# Independent Complex Samples t-Test - Comparing Two Means

Where $\displaystyle{ \bar{x} }$ and $\displaystyle{ \bar{y} }$ are the two means and $\displaystyle{ s_\bar{x} }$ and $\displaystyle{ s_\bar{y} }$ are their Standard Errors, the test statistic is:
$\displaystyle{ t=\frac{\bar{x}-\bar{y}}{\sqrt{s^2_\bar{x} + s^2_\bar{y}}} }$,
$\displaystyle{ p = 2\Pr(t_v \ge |t|) }$,
$\displaystyle{ v = \frac{(s^2_\bar{x} +s^2_\bar{y})^2}{\frac{s^4_\bar{x}}{n-b}+\frac{s^4_\bar{y}}{m-b} } }$
the groups have sample sizes of $\displaystyle{ m }$ and $\displaystyle{ n }$ respectively (or effective sample sizes if a design effect has been specified),
$\displaystyle{ b }$ is 1 if Bessel's correction is selected for Means in Statistical Assumptions and 0 otherwise.