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!

P.S. apologies if this is an obvious or stupid question!

  • $\begingroup$ 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 at 0:51

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