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

The test statistic is:

$z=\frac{\overline{x}-\overline{y}}{\sigma \sqrt{\frac{1}{m}+\frac{1}{m}}}$

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,

$\sigma =\sqrt{\frac{(m-1){\sigma }_x^2+(m-1){\sigma }_y^2}{m+n-2b}}$,

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

${\sigma }_x^2$ and ${\sigma }_y^2$ are the variances in the two groups, and

$p=2(1-\mathrm{\Phi }(|z|))$