# Simplified 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:
${\displaystyle t={\frac {{\bar {x}}-{\bar {y}}}{\sqrt {s_{\bar {x}}^{2}+s_{\bar {x}}^{2}}}}}$,
${\displaystyle p=2\Pr(t_{v}\geq |t|)}$,
${\displaystyle v={\frac {(s_{\bar {x}}^{2}+s_{\bar {x}}^{2})^{2}}{{\frac {(s_{\bar {x}}^{2})^{2}}{n-1}}+{\frac {s_{\bar {y}}^{2})^{2}}{m-1}}}}}$
the groups have sample sizes of ${\displaystyle m}$ and ${\displaystyle n}$ respectively.