Hotelling test of linear hypotheses
= Hotelling test of linear hypotheses
{c}
{title2=$T_B^2=n(B\bar X)^T(BSB^T)^{-1}B\bar X$}
For a fixed rank-$m$ constraint matrix $B$, apply <Hotelling's T-squared statistic> to the transformed observations $BX_j$. Under $B\mu=0$, $(n-m)T_B^2/(m(n-1))\sim F_{m,n-m}$ for $n>m$. If the displayed contrasts are dependent, use a basis of their row space and replace $m$ by the <rank>.