Independent Samples t-Test - Comparing Two Means with Unequal Variances

The test statistic is:

$t=\frac{\overline{x}-\overline{y}}{\sqrt{\frac{s_x^2}{m}+\frac{s_y^2}{n}}}$

where:

$\overline{x}$ and $\overline{x}$ are the average values of variables $x$ and $y$ respectively, where each of these variables represents the data from two independent groups,

the groups have sample sizes of $m$ and $n$ respectively,

$s_x^2$ and $s_y^2$ are the variances in the two groups,

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

$v=\frac{(\frac{s_x^2}{n}+\frac{s_y^2}{m}{)}^2}{\frac{(\frac{s_x^2}{n/d_{eff}}{)}^2}{n-b}+\frac{(\frac{s_y^2}{m/d_{eff}}{)}^2}{m-b}}$,

$b$ is 1 if Bessel's correction is selected for Means in Statistical Assumptions and 0 otherwise,

$d_{eff}$ is Extra Deff.