3 way interaction in a 4 way ANOVA

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    Dear list,

    I have performed a 4-way repeated measures ANOVA with the factors condition (2 levels), direction (2 levels), location (3 levels) and row (3 levels). The main effects of location and row were significant. Also the following interactions were significant: condition*direction, direction*location, location*row, condition*direction*location. Which is the best way to proceed to understand the 3 way interaction.

    Many thanks



    Unless you have any theoretical motivation, you can really break down the three-way interaction anyway you want. I will do it the way that makes since to me:

    Three-way interaction was significant: condition*direction*location

    Since it was significant, you need to analyze “simple two-way” interactions. I think the best way to do this is by looking at the condition*direction at each level of location. Thus, you will have three two-way simple interactions (a mouth full, I know). Do note that you will be doing this while averaging across your “row” variable (since it was not part of the interaction).

    If any of your three two-way simple interactions are significant, then you will have to break those down as well. For example, if the simple two-way interaction is significant at ONLY level 1 of your location variable, then you can break that down as follows:

    The significant  condition*direction simple interaction at level 1 of location can be examined as a simple simple effect of direction at each level of condition (or the other way around). Meaning, you should look to see if there is a difference between level 1 and level 2 of your direction variable at both levels of condition. NOTE: the last sentence I said is WITHIN level 1 of your location variable (and everything should still be averaged across the row variable).

    I would defintely suggest doing this with a combination of “select data” and SPSS syntax to analyze this. Use Discovering Statistics using SPSS and Levin’s Guide to SPSS for ANOVA.

    I hope that helps. Let me know if you need any clarification.




    Thank you Mike. This was really helpful. I have done followup two-way and one-way ANOVAs to understand the interaction. There was a two way interaction between location and row. The factor row was not a part of the three way interaction I described before. Could I just do a one way ANOVA with the factor location at each levels of row? Or does the presence of three way interaction changes things?

    Many thanks in advance


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