Mixed ANOVA: p-Value of within factor increases by adding a between factor...?


I thought I'm good in math and statistics but this one is giving me a real headache...hope one of the pros here can explain/solve it...

I ran a mixed ANOVA with one within and one between factor, both variables have 2 outcomes - pretty easy. Accidentally when I first did it, I forgot to add the between factor, so I just had the F and p-Value for the within-factor, which is the same as running a t-Test for dependent samples.

Then I added the between factor and in the SPSS output it changed the F and p Values for just the within factor. I am not talking about the between factor effect or the interaction of both factors... This output changed both for univariate and multivariate tests and contrasts.

Of course every added factor has an influence for the entire GLM, but to the within factor itself...? The F value drops and the p Value for the within factor increases if you add more and more between factors...

Can anybody explain? Any help would be much appreciated!

Thanks, Marc

I finally figured it out myself. There are 2 reasons:

1. Interaction effect. The interaction within x between decreases the residual sum of squares and the residual variance, so the F and p-Values change.

2. Unequal group-sizes. If both groups defined by the between factor are not of the same size, the sum of squares of the within factor changes. And so does F and p-Value.

Hope this might help anybody who faces the same problem...