When I run repeated measures ANOVAs with JMP (RMS, with Subject as a random factor), I have noticed that when a certain factor is crossed with Subject, the corresponding DF Den stays independent while the DF Dens for the other factors are put together as “Residual”. Please see Images 1-3 of the attached file on how “DF Den” under “Test Denominator Synthesis” change across images. But if I use SPSS (General Linear Model > Repeated Measures > Custom, Type III), DF Dens stay always independent even when Subject is not crossed with other factors. I have been wondering why that would be the case.
I have looked at the JMP book “Fitting Linear Models Version 14” and found the following on pp. 197-198 of Chapter 3:
“Test Denominator Synthesis
For each effect to be tested, an F statistic is constructed. The denominator for this statistic is the mean square whose expectation is that of the numerator mean square under the null hypothesis. This denominator is constructed, or synthesized, from variance components and values associated with fixed effects.
Source Shows the effect to be tested.
MS Den Gives the estimated mean square for the denominator of the F test.
DF Den Gives the degrees of freedom for the synthesized denominator. These are constructed using Satterthwaite’s method (Satterthwaite 1946).
Denom MS Synthesis Gives the variance components used in the denominator synthesis. The residual error variance is always part of this synthesis.”
I also looked at Satterthwaite (1946), but it was too technical for me to follow.
Could you kindly explain why my example turns out to be this way?