$$\begin{array}{c}t=\frac{\text{Sm}{}_1-{\text{Sm}}_2}{s_p\sqrt{\frac{1}{{\text{S n}}_1}+\frac{1}{{\text{S n}}_2}}}\\ s_p=\sqrt{\frac{\left({\text{Sn}}_1-1\right){\text{Sd}}_1^2+\left({\text{Sn}}_2-1\right){\text{Sd}}_2^2}{{\text{Sn}}_1+{\text{Sn}}_2-2}}\\ \nu ={\text{Sn}}_1+{\text{Sn}}_2-2\end{array}$$