# Independent Samples t-Test - Comparing Two Means with Equal Variances

The test statistic is:

${\displaystyle t={\frac {{\bar {x}}-{\bar {y}}}{s{\sqrt {{\frac {1}{m}}+{\frac {1}{m}}}}}}}$

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,
${\displaystyle s={\sqrt {d_{eff}{\frac {(m-1)s_{x}^{2}+(m-1)s_{y}^{2}}{m+n-2b}}}}}$,
${\displaystyle b}$ is 1 if Bessel's correction for Means is selected in Statistical Assumptions and 0 otherwise,
${\displaystyle s_{x}^{2}}$ and ${\displaystyle s_{y}^{2}}$ are the sample variances in the two groups,
${\displaystyle d_{eff}}$ is Extra Deff.
${\displaystyle p=2\Pr(t_{n+m-2}\geq |t|)}$