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Satterthwaite [10] degrees of freedom

For a $t-test$ or an $F-test$ 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}  

where $dl_s$ are the degree of freedom for the $MS_s$.

Didier Leibovici 2001-03-01