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I'm running a 2x2 ANOVA analysis in R - the model is linear. The maximal model (containing a continuous DV, one 5-level categorical IV, one continuous IV and the interaction term) yields an output showing the interaction term and main effects to be non-significant.

Simplifying the model by removing the interaction causes one of the main effects to become highly significant (moving from a p-value of 0.07 to < .001). I am wondering if anyone can give a (lay!) description of why this might be the case?

This is a well powered analysis and centring the IV and continuous DV makes no difference to the output of the maximal nor the simplified model.

Forgive that I cannot share the raw data due to ethical reasons. Please let me know if there is anything else I can do to improve the question however!

Thank you!

Sarah
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    1) When you have an interaction term, one generally does not pay attention to the significance of the main effects (they can be interpreted but have a different meaning than in models without an interaction). 2) Removing *any* term from the model can alter the p-values of the remaining terms. 3) A related thread: Related: https://stats.stackexchange.com/questions/424272/why-does-a-positively-correlated-variable-have-a-negative-coefficient-in-a-multi/424273#424273 – mkt Sep 24 '19 at 19:11
  • Thank you for you comment! Is this even the case where the interaction is non-significant though? – Sarah Sep 24 '19 at 19:15
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    You mean altering the p-values? Yes, removing any term, significant or not, can alter the coefficient values and the p-values of the remaining terms in the model. Another possibly useful thread: https://stats.stackexchange.com/questions/31027/how-to-interpret-main-effects-when-the-interaction-effect-is-not-significant – mkt Sep 24 '19 at 19:22
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    Thank you again! I suppose the shift was so substantial (from a p value of 0.07 to one of < .001 that I wondered how that was possible! – Sarah Sep 24 '19 at 19:23

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