To compute Fvalues and degrees of freedom, let p be the rank of . Let q be the rank of , where the L matrix identifies elements of associated with the effect being tested. Let v be the error degrees of freedom and s be the minimum of p and q. Also let and .
Table 5.3, gives the computation of each approximate F from the corresponding test statistic.
Test  Approximate F  Numerator DF
 Denominator DF


Wilks’ Lambda  
Pillai’s Trace  
HotellingLawley Trace  
Roy’s Max Root 