SPSS - sum of squares change radically with slight model changes in ANOVA??

Question

I have noticed that the sum of squares in my models can change fairly radically with even the slightest adjustment to my models???? Is this normal???? I'm using SPSS 16, and both models presented below used the same data and variables with only one small change - categorizing one of the variables as either a 2 level or 3 level variable.

Details - using a 2 x 2 x 6 mixed model ANOVA with the 6 being the repeated measure i get the following in the between group analysis

------------------------------------------------------------
Source    | Type III SS |  df  |  MS       |  F      |  Sig
------------------------------------------------------------
intercept | 4086.46     |  1   | 4086.46   | 104.93  |  .000
X         |  224.61     |  1   |  224.61   |   5.77  |  .019
Y         |    2.60     |  1   |    2.60   |    .07  |  .80
X by Y    |   19.25     |  1   |   19.25   |    .49  |  .49
Error     | 2570.40     | 66   |   38.95   | 

Then, when I use the exact same data but a slightly different model in which variable Y has 3 levels instead of 2 levels I get the following

------------------------------------------------------------
Source    | Type III SS |  df  |  MS       |  F      |  Sig
------------------------------------------------------------
intercept | 3603.88     |  1   | 3603.88   |  90.89  |  .000
X         |  171.89     |  1   |  171.89   |   4.34  |  .041
Y         |   19.23     |  2   |    9.62   |    .24  |  .79
X by Y    |   17.90     |  2   |   17.90   |    .80  |  .80
Error     | 2537.76     | 64   |   39.65   | 

I don't understand why variable X would have a different sum of squares simply because variable Y gets devided up into 3 levels instead of 2. This is also the case in the within groups analysis too.

Please help me understand :D

Thank you in advance

Pat

Answer 1

The type III Sum-of-Squares for X tells you how much you gain when you add X to a model including all the other terms. It appears that the 3-level Y variable is a much better predictor than the 2-level one: its SS went from 2.6 to 19.23. (this can happen, for example, if the effect of Y is quadratic: a cut at the vertex is not very predictive, but cutting into three groups would be better). Thus there is less left for X to explain - its SS decreases.

Answer 2

Just adding to what Aniko has said, the reason why variable X has a different sum of squares simply because variable Y gets divided up into 3 levels instead of 2, is that the SS formula for each factor depends on the number of samples in each treatment. When you change the number of levels in one factor, you actually change the number of samples for each treatment and this has an impact on the SS value for all the other factors.