Hi I'm trying to analzye some data, and I want to be sure that I am doing it correctly. Here is the situation. I have a 3 way interaction that is not significant, for ease of discussion let's say the factors are A, B, C Each of which has 2 levels. Of the 3 possible 2 way interactions only A*C is significant, A*B is not and B*C is not, in the output of the 3 way ANOVA. My primary interest in the data however is looking at the A*B interaction. Is it statistically correct to collapse across levels of factor C to arrive at a 2 Way ANOVA analysis to look at this question. If I collapse across C the A*B interaction becomes significant which is the main point of our study.
I'm thinking perhaps incorrectly, that if the three way is not significant then this should mean that the two way interactions of each set of two Factors should not act significantly differently between levels of the third factor. If this is right, you should be able to correctly collapse across any factor to perform and analyze the resulting two way ANOVA. Some of my friends have suggested that it would not be legal to collapse across C since the A*C interaction is siginificant, but rather you could do this in special cases only with specific types of interactions.
Can anyone shed light on this?
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