## Model Type III Sum of Squares [General Sta­tis­tics]

Hello Obi,

» I also want to use the Venn Diagram when looking at the method of calculating the SSs. I am imagining a Venn Diagram with Factors A, B and C pictured as spheres that sometimes overlap.
»
» For Type I, if I want to determine the SS for factor A first then we have SS(A). Then if the next is factor B, we have to remove the component of A in B which gives SS(B∩A'). And finally for C, we have SS(C∩A'∩B').
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» For Type III, we just do SS(A), SS(B) and SS(C). or something in that light. I don't know if it's the right way to imagine it.

I can't follow what you are saying here. Type III SS for a factor A is essentially the SS for A given B and C in the model. I guess you might refer to that as SS(A|B∩C), but check it with someone who understands statistics. I don't.

»
» However I want to confirm the statement that "SS results for Type I and III are the same for a balanced design". Is that true?
»

Correct, but note the meaning of balance may differ for other designs; traditionally in BE balance is when you have an equal number of evaluable completers in RT and TR and when the analysis only involves those evaluable completers.

» I read it somewhere. Though I noticed they mentioned orthogonality as well.
»

Orthogonality is a quite abstract term and entire books are written about it. In this context it means you can partition the variability onto the factors of the design. FDA used the term in a presentation some years ago about in vivo and in vitro factors that affect bioequivalence testing for OIPs and suddenly everybody was talking about orthogonality in a grandiose hodgepodge of confusion.
The community has not recovered yet. If you mention something that could hypothetically affect the outcome of a BE trial or treatment success (like inhaler training, or lactose grade, or an image of mickey mouse printed on the side of the inhaler to make it appealing to children) people will unhesitatingly ask if that's an orthogonal factor.

I could be wrong, but...

Best regards,
ElMaestro

"Pass or fail" (D. Potvin et al., 2008)