Independent Samples T-Test - Pooled Variance

Where ${\overline{x}}_i$ 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 $i^{\prime }$ is given by:

$t=\frac{{\overline{x}}_i-{\overline{x}}_{i^{\prime }}}{\sqrt{s_x^2(n_i^{-1}+n_{i^{\prime }}^{-1})}}$,

where:

$p=2\mathrm{Pr}(t_v\ge |t|)$,

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

$s_x^2=\sum _{i=1}^g(n_i-1)s_{x_i}^2/v$.