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There are similar questions on this topic. I have checked them, but I haven't found a specific answer to my (simplistic) questions. There are 3 explanatory variables: A(3 levels, between), B(2 levels, within), C (4 levels, within). The 3-way interaction AxBxC is not significant. Of the 2-way interactions, only AxB is significant. My first question is whether it is even legitimate to interpret two-way interactions if the three-way is not significant.

My second question is whether it is legitimate to decompose the significant two-way term by looking at each level of the third variable (C).

My final question is whether this discussion is modified if the main effect of C is found to be significant. Thanks!

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It is quite legitimate to interpret 2-way interactios in the absence of 3-way interaction. The converse (interpreting a 3-way interaction in the absence of lower order effects) is what would be debatable.

Not quite sure what you mean by "decompose the significant 2-way term by looking at it at each level of the third variable". You mean performing different ANOVA analysis, splitting the sample by levels of C? I guess if C matters for the AxB effect, this would show up in a significant 3-way interaction, see no advantage in doing what you propose.

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  • $\begingroup$ Thanks a lot for the response. Just to be clear I understood the implications, I can attempt to interpret the significant AxB term output from the model. I am using the output of a statistical package to get this term (SPSS) - Is it calculated by the equivalent of averaging over the third factor (C)? $\endgroup$
    – Gaby
    Jul 22, 2018 at 10:20
  • $\begingroup$ If your design is balanced (=equal number of observations per cell), yes, the AxB effect fitted to the whole sample would be equivalent to the average of AxB effects fitted to each of the subsamples corresponding to a single C level. $\endgroup$
    – F. Tusell
    Jul 22, 2018 at 10:33

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