I am trying to build a linear model where X1 = Time and X2 = Treatment. When I use the Fit Model tool, I am seeing a discrepancy in the ANOVA table and the Effects table (screenshot below). The Sum of Squares columns should add to the same total (in this case, 6277.9477), correct? The SS under Effects Tests does not sum to this value. Why would this be? Am I misunderstanding the calculations here? Or is this a bug in JMP?
This is not a JMP bug. The Sums of Squares will add up if you are using what is called Type I Sum of Squares (Type I SS). The problem with Type I SS is that it is order dependent. That means that the model A, B, and A*B would give different results than the model B, A, B*A. Therefore, Type I SS are not usually used except in "by hand" calculations.
What JMP is using is the Type III Sum of Squares (Type III SS). That removes the order dependency by only calculating the SS for a term AFTER all other terms have been put in the model. This provides stable estimates, but they are not additive to the model SS.
Thanks Dan. If I can ask a follow-up...
This experiment is a full factorial with 7 time points, 4 treatments, and 2 replicates. My understanding is that, in a balanced design (which this is), the factors are orthogonal, so Type I, Type II, and Type III Sums of Squares should all be identical. So why would they be different?
That is not what orthogonal means. Orthogonal means that the SS would stay the same when removing terms (regardless of which type of SS are being used). Orthogonal has nothing to do with the order that terms are entered into the model.