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Deriving distributions
Satterthwaite [
10
] degrees of freedom
For a
or an
and the denominator is a linear combination of Mean sum of Squares (MS), the Satterthwaite formula to approximate the degrees of freedom for the denominator is:
where
are the degree of freedom for the
.
Didier Leibovici 2001-03-01
or an 
and the denominator is a linear combination
of Mean sum of Squares (MS), the Satterthwaite formula to approximate
the degrees of freedom for the denominator is:
![\begin{displaymath}
\frac{[\sum_sc_sMS_s]^2} {\sum_s(c_sMS_s)^2/dl_s } \nonumber
\end{displaymath}](img439.gif){kind=small}
are the degree of freedom for the
.