Publication date: 03/23/2021

Approximate F-Tests

To compute F-values and degrees of freedom, let p be the rank of Equation shown here. Let q be the rank of Equation shown here, where the L matrix identifies elements of Equation shown here 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 Equation shown here and Equation shown here.

Table 5.3, gives the computation of each approximate F from the corresponding test statistic.

Table 5.3 Approximate F-statistics

Test

Approximate F

Numerator DF

Denominator DF

Wilks’ Lambda

Equation shown here

Equation shown here

Equation shown here

Pillai’s Trace

Equation shown here

Equation shown here

Equation shown here

Hotelling-Lawley Trace

Equation shown here

Equation shown here

Equation shown here

Roy’s Max Root

Equation shown here

Equation shown here

Equation shown here

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