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

${\displaystyle z={\frac {{\bar {x}}-{\bar {y}}}{\sqrt {{\frac {\sigma _{x}^{2}}{m}}+{\frac {\sigma _{y}^{2}}{n}}}}}}$
${\displaystyle {\bar {x}}}$ 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,
${\displaystyle \sigma _{x}^{2}}$ and ${\displaystyle \sigma _{y}^{2}}$ are the variances in the two groups,
${\displaystyle p=2(1-\Phi (|z|))}$