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

The test statistic is:

${\displaystyle t={\frac {{\bar {x}}-{\bar {y}}}{\sqrt {{\frac {s_{x}^{2}}{m}}+{\frac {s_{y}^{2}}{n}}}}}}$

where:

${\displaystyle {\bar {x}}}$ and ${\displaystyle {\bar {x}}}$ are the average values of variables ${\displaystyle x}$ and ${\displaystyle y}$ respectively, where each of these variables represents the data from two independent groups,
the groups have sample sizes of ${\displaystyle m}$ and ${\displaystyle n}$ respectively,
${\displaystyle s_{x}^{2}}$ and ${\displaystyle s_{y}^{2}}$ are the variances in the two groups,
${\displaystyle p=2\Pr(t_{v}\geq |t|)}$,
${\displaystyle v={\frac {({\frac {s_{x}^{2}}{n}}+{\frac {s_{y}^{2}}{m}})^{2}}{{\frac {({\frac {s_{x}^{2}}{n/d_{eff}}})^{2}}{n-b}}+{\frac {({\frac {s_{y}^{2}}{m/d_{eff}}})^{2}}{m-b}}}}}$,
${\displaystyle b}$ is 1 if Bessel's correction is selected for Means in Statistical Assumptions and 0 otherwise,
${\displaystyle d_{eff}}$ is Extra Deff.