To compute F-values 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 
.
. 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 .Approximate F-statistics, gives the computation of each approximate F from the corresponding test statistic.
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