                                         
<p>Difference of variances: Here, the null hypothesis is of the form \(H_0: \sigma^2(P)-\sigma^2(Q)=0\), and the corresponding test statistic is given by 
$$T_{m,n}=\frac{N^{1/2}(\hat{\sigma}_m^2(X_1,\dots,X_,)-\hat{\sigma}_n^2(Y_1,\dots,Y_n))}{\sqrt{\frac{N}{m}(\hat{\mu}_{4,x}-\frac{(m-3)}{(m-1)}(\hat{\sigma}_m^2)^2)+\frac{N}{n}(\hat{\mu}_{4,y}-\frac{(n-3)}{(n-1)}(\hat{\sigma}_y^2)^2)}}$$ 
where \(\hat{\mu}_{4,m}\) the sample analog of \(E(X-\mu)^4\) based on an ii