SPSS - Does the sum of squares change radically with small model changes in ANOVA?
I've noticed that the sum of squares in my models can change quite drastically with even the slightest tweak to my models ???? This is normal???? I am using SPSS 16 and both models below used the same data and variables with only one small change - classifying one of the variables as a level 2 or 3 variable.
Details - Using a mixed 2 x 2 x 6 ANOVA model with 6 being a repeated measure, I get the following in the analysis between groups
-------------------------------------------------- ---------- 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 same data, but a slightly different model, where the Y variable 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 the X variable will have a different sum of squares simply because the Y variable is divisible by 3 levels instead of 2. This is also the case in intra-group analysis.
Please help me understand: D
Thank you in advance
Pat
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Type III Sum-of-Squares for X tells you how much you get by adding X to the model, including all other terms. It looks like the 3-level Y variable is a much better predictor than the 2-level one: its SS is from 2.6 to 19.23. (this can happen, for example, if the Y effect is quadratic: the cut at the vertex is not very predictive, but it is best to cut into three groups). Thus, there is less left to explain X - its SS is decreasing.
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Just adding to what Aniko said, the reason the X variable has a different sum of squares simply because the Y variable is divisible by 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 are actually changing the number of samples for each treatment, and this affects the SS for all other factors.
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