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 