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In my liner mixed effect model, there are two independent variables location (2 factors: E, word) and cond_aud (3 factors:CA,EA,NoA). As I used sliding contrast which means that the model summary only gave me the interactions of location: CA-EA, location: EA-NoA. To test the interaction of location: NoA-CA, I used emmeans function without adjustment:

contrast(emmeans(lmerwp2,~location*cond_aud),interaction=c("pairwise","pairwise"),adjust="none")

And results show a significant interaction between E-words and CA -NoAas below:

enter image description here

However, follow-up pairwise comparisons show that there is no simple effect of location(i.e., E-words) in CA or NoA (see below), although the direction of effects are opposite. How could the interaction be significant when no simple effects are significant? Or should I just report the different directions of simple effects?

enter image description here

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    $\begingroup$ Could you please include more details on the original linear mixed model, not just the abstraction from it done via emmeans? The outputs you show say "results are averaged over the levels of: cond_vd," a predictor not in your calls to emmeans. I'm not sure that will matter for an answer to your question, but it might be informative in providing a context. $\endgroup$
    – EdM
    Commented Jun 8, 2021 at 15:43
  • $\begingroup$ Yes, it is possible for that to happen. Try to remember that the goal of statistical analysis is to explain the patterns in the data, not to obtain asterisks. $\endgroup$
    – Russ Lenth
    Commented Jun 9, 2021 at 0:03
  • $\begingroup$ @Russ Lenth,just to clarify, the summary of my lmer model (dv ~ location * cond_vd * cond_aud + (cond_vd + cond_aud | pp) + (1 | worditem) showed that there is no significant interaction of location:cond_vd:cond_aud (CA-NoA), which means that the interaction of location: cond_aud (CA-NoA) is not modulated by the variable of cond_vd. So in this case, based on the reports I put in the post, I should just report that the effect of location was in different directions in CA and NoA. Did I understood it accurately? $\endgroup$
    – Chloe
    Commented Jun 9, 2021 at 0:14
  • $\begingroup$ That is not a correct interpretation. Being unable to prove there is an effect is not the same as proving that there is no effect. $\endgroup$
    – Russ Lenth
    Commented Jun 9, 2021 at 0:51
  • $\begingroup$ @Russ Lenth, I get your point. But in this case why would you suggest as the best way to report such interaction? $\endgroup$
    – Chloe
    Commented Jun 9, 2021 at 1:18

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