$$\nu =\frac{{\left(\frac{{\text{Sd}}_1^2}{{\text{Sn}}_1}+\frac{{\text{Sd}}_2^2}{{\text{Sn}}_2}\right)}^2}{\frac{{\left(\frac{{\text{Sd}}_1^2}{{\text{Sn}}_1}\right)}^2}{\left({\text{Sn}}_1-1\right)}+\frac{{\left(\frac{{\text{Sd}}_2^2}{{\text{Sn}}_2}\right)}^2}{\left({\text{Sn}}_2-1\right)}}$$