# Paired Z-Test of Means

Where $\bar x_1$ and $\bar x_2$ are the two means, the test statistic is:

$z=\frac{\bar x_1-\bar x_2}{s_{{\bar x_1} - {\bar x_2}}}$

where:

$p \approx 2(1-\Phi(|z|))$,
$s_{{\bar x_1} - {\bar x_2}}$ is computed as the Standard Error of $d$,
the value for the $i$th observation is computed as $d_i = x_{i1} - x_{i2}$, and
$x_1,x_2$ are the observed values on the two variables.