# Interpreting Interactions: When the F test and the Simple Effects disagree.

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The way to follow up on a significant two-way interaction between two categorical variables is to check the simple effects.  Most of the time the simple effects tests give a very clear picture about the interaction.  Every so often, however, you have a significant interaction, but no significant simple effects.  It is not a logical impossibility. They are testing two different, but related hypotheses.

Assume your two independent variables are A and B.  Each has two values: 1 and 2.  The interaction is testing if A1 – B1 = A2 – B2 (the null hypothesis). The simple effects are testing whether A1-B1=0 and A2-B2=0 (null) or not.

If you have a crossover interaction, you can have A1-B1 slightly positive and A2-B2 slightly negative. While neither is significantly different from 0, they are significantly different from each other.

And it is highly useful for answering many research questions to know if the differences in the means in one condition equal the differences in the means for the other. It might be true that it’s not testing a hypothesis you’re interested in, but in many studies, all the interesting effects are in the interactions.

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Saranea August 15, 2017 at 6:38 am

Hi Karen,
Could you please help me with this question. I have run a 3*3 ANOVA. I have also chosen a simple planned contrast within SPSS to compare each variable to the first variable. I am not too sure if this is the results i should be reporting after looking at the main effects and interactions. Please help.

Sophie December 28, 2016 at 6:27 am

How do I interpret my results, when the interaction is significant and the means show the effect I want, but testing the simple effects only reveals a p = .80? Can I draw conclusions from my significant interaction or the ‘marginal significant’ p value (I don’t know if it is allowed to say that)?

Emil June 28, 2015 at 5:43 pm

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