Bessel's Statistical Formula

$\begin{displaymath} t={\bar w-\omega\over \sigma_w/\sqrt{N}} = {{\bar w-\omega} \over {\sqrt{\sum_{i=1}^n (w_i-\bar w)^2\over N(N-1)}}}, \end{displaymath}$

(1)

where

$\displaystyle \bar w$	$\textstyle \equiv$	$\displaystyle \hat x_1-\bar x_2$	(2)
$\displaystyle \omega$	$\textstyle \equiv$	$\displaystyle \mu_{(1)}-\mu_{(2)}$	(3)
$\displaystyle N$	$\textstyle \equiv$	$\displaystyle N_1+N_2.$	(4)