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

${\displaystyle z={\frac {{\bar {x}}-{\bar {y}}}{\sigma {\sqrt {{\frac {1}{m}}+{\frac {1}{m}}}}}}}$
${\displaystyle {\bar {x}}}$ 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,
${\displaystyle \sigma ={\sqrt {\frac {(m-1)\sigma _{x}^{2}+(m-1)\sigma _{y}^{2}}{m+n-2b}}}}$,
${\displaystyle b}$ is 1 if Bessel's correction for Means is selected in Statistical Assumptions and 0 otherwise,
${\displaystyle \sigma _{x}^{2}}$ and ${\displaystyle \sigma _{y}^{2}}$ are the variances in the two groups, and
${\displaystyle p=2(1-\Phi (|z|))}$