In calculating the variance of a mean or in constructing an approximateF-test, it is frequently necessary, particularly with unbalanced data, to form a linear function of mean squares,MS= Σai, where theaiare known constants. Satterthwaite [1] suggests that MS is approximately distributed asx2fE(MS)/ftwhere the degrees of freedom is estimated by,f= (MS)2/Σ[(aiMSi)2/fi], wherefiis the degrees of freedom associated withMSi. Satterthwaite remarks that caution should be used in applying this formula where some of theaiare negative. The primary purpose of this paper is to investigate the validity of Satterthwaite's procedure when someMSiare subtracted. Due to the mathematical complexity of the distribution ofMS, the problem is studied by a computer simulation.