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Significant interaction no significant comparision

Dear community,

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.

 

Re: Significant interaction no significant comparision

Two things. First, splitting the data by one variable reduces the power of the test for significant effects of the other variable. Second, when a significant interaction effect is present in the response but not accounted for in the model, the main effect may not be significant because the effect of the insteraction is now in the error sum of squares instead of the model sum of squares.

Re: Significant interaction no significant comparision

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