Publication date: 04/21/2023
Statistical Details for Approximate F-Tests
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 
.
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 |
|
|
|
|
Hotelling-Lawley Trace |
|
|
|
|
Roy’s Max Root |
|
|
|
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