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I'm running a 2x2 factorial ANCOVA, where the factors are either being in condition A or B and either being part of a certain group or not, with two covariates being age and gender. When I run the full factorial model, one of the main effects is significant but the interaction is not.

However, when I build the model and only include the interaction and covariate, and do not include main effects, the interaction is significant.

If I am only interested in the interaction, can I interpret it as significant, or must I include the main effects too?

Thanks for your help!

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    $\begingroup$ The question of type "specify interaction but omit the main effects" was asked many times here. Search by tags "main-effect" and "interaction". A short answer is that is a silly action because without the main effects in the model the interaction is no longer an "interaction" term, rather, it is a factor on its own. $\endgroup$ – ttnphns Mar 28 '19 at 0:51
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If you're using GLM or UNIANOVA (Analyze>General Linear Model in the SPSS menus), then including an interaction among two factors where the main effects are not also specified does not actually fit a different model, but only changes the meaning of what you're getting for the "interaction" effect. In a 2x2 factorial, there's one degree of freedom for each "main effect" and one for the interaction. Since these procedures don't reparameterize to full rank to handle the overparameterized nature of the model, if you remove the main effect specifications, all three degrees of freedom will be taken up by the interaction term. It turns into a pooled omnibus test of those three effects.

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