Independent Samples T-Test - Pooled Variance

Where ${\bar {x}}_{i}$ is the mean of variable $x$ for the $i$th of $g$ groups, $s_{x_{i}}$ is its Standard Deviation and $n_{i}$ its sample size, the test statistic is for the difference between groups $i$ and $i'$ is given by:

$t={\frac {{\bar {x}}_{i}-{\bar {x}}_{i'}}{\sqrt {s_{x}^{2}(n_{i}^{-1}+n_{i'}^{-1})}}}$,

where:

$p=2\Pr(t_{v}\geq |t|)$,

$v=\sum _{i=1}^{g}n_{i}-g$, and

$s_{x}^{2}=\sum _{i=1}^{g}{(n_{i}-1)s_{x_{i}}^{2}}/v$.