Paired t-Test of Means

Where ${\overline{x}}_1$ and ${\overline{x}}_2$ are the two means, and $s_{{\overline{x}}_1-{\overline{x}}_2}$ is an estimate of the Standard Error of the difference between the means:

$t=\frac{{\overline{x}}_1-{\overline{x}}_2}{s_{{\overline{x}}_1-{\overline{x}}_2}}$

where

$p\approx 2\mathrm{Pr}(t_{n-1}\ge |t|)$,

$n$ is the sample size,

$s_{{\overline{x}}_1-{\overline{x}}_2}$ is computed as the Standard Error of $d$,

the value for the $i$th observation is computed as $d_i=x_{i1}-x_{i2}$ where $x_1,x_2$ are the observed values on the two variables.