]> $$\begin{array}{c}t=\frac{\text{Sm}{}_1-{\text{Sm}}_2}{s_p\sqrt{\frac{1}{{\text{S n}}_1}+\frac{1}{{\text{S n}}_2}}}\\ s_p=\sqrt{\frac{\left({\text{Sn}}_1-1\right){\text{Sd}}_1^2+\left({\text{Sn}}_2-1\right){\text{Sd}}_2^2}{{\text{Sn}}_1+{\text{Sn}}_2-2}}\\ \nu ={\text{Sn}}_1+{\text{Sn}}_2-2\end{array}$$ $$t=\frac{{\text{Sm}}_1-{\text{Sm}}_2}{\sqrt{\frac{{\text{Sd}}_1^2}{{\text{Sn}}_1}+\frac{{\text{Sd}}_2^2}{{\text{Sn}}_2}}}$$ $$\nu =\frac{{\left(\frac{{\text{Sd}}_1^2}{{\text{Sn}}_1}+\frac{{\text{Sd}}_2^2}{{\text{Sn}}_2}\right)}^2}{\frac{{\left(\frac{{\text{Sd}}_1^2}{{\text{Sn}}_1}\right)}^2}{\left({\text{Sn}}_1-1\right)}+\frac{{\left(\frac{{\text{Sd}}_2^2}{{\text{Sn}}_2}\right)}^2}{\left({\text{Sn}}_2-1\right)}}$$ $$Y_s\pm t_{\left(\frac{\alpha }{\mathrm{2,}}N-1\right)}\frac{s}{\sqrt{N}}$$