I did a linear mixed model full factorial with 2x2. I use the linear mixed model like an ANOVA and I have one significant main effect and a significant interaction effect.To solve the interaction I split my data by one variable and analyze the main effect by the other variable (just like pairwise comparisons) but both my to analyze don't show a significant effect. So why is there a significant interaction then? In the Graph I see that it is nearly a crossed interaction but as no comparison becomes significant I would not expect a significant interaction. Any help would be very much appreciated.