Four-Way ANOVA with mixed design

[Gang Chen]

I am trying to work out some four-way ANOVA with mixed design on my own 
instead of relying on some software packge, and have successfully 
contructed the F statistics for all the terms based on the general rules 
of thumb for writing the ANOVA table. In the first design, among the 
four factors, A, B, and C are fixed while D is random and nested within 
A. As usual, all the F statistics for the terms are in the form of the 
ratio of two MS's.

Now I am doing the same for a slightly different design of four-way 
ANOVA: factors A and B are fixed, while C and D are random with D nested 
within A. It turns out that most of the F statistics are the same as the 
previous design. However, the ones I came out with for the only three 
fixed terms are in the following format:

Factor A: [MSA+MSCD(A)]/[MSD(A)+MSAC]
Factor B: [MSB+MSBCD(A)]/[MSBC+MSBD(A)]
Interaction of A and B: [MSAB+MSBCD(A)]/[MSABC+MSBD(A)]
This is the first time that I encounter F statistics in ANOVA in the 
form of the ratio of some combinations of MS terms. Could someone verify 
whether I am on the right track about this design? Any comments would be 
highly appreciated.

Thanks from,
Gang Chen

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