Three-way mixed ANOVA - Post-hoc-analysis (Scheffé-test?)


New Member
Hello everybody,

I hope someone is able to help me here, because I'm desperate and can't find help anywhere :-(. English is not my first language, so please excuse any errors.

For my final thesis, I conducted a 2x2x3 mixed ANOVA in SPSS, mixed meaning that the first factor was a between-subjects factor and the other two are within-subject factors. My sample size is n = 472, but the two groups resulting from the between-subject factor are unequal, namely n = 209 and n = 263.

As a result of the ANOVA, I get
- two significant main effects (for the between-subject factor and for the second of the two within-subject factors),
- two significant two-way interactions between the between-subject factor and the two within-subject factors respectively,
- and finally a significant three-way-interaction between all three factors.

Now I have a lack of understanding/several problems:

1. Am I correct in thinking that I don't need to conduct a post-hoc-analysis for the significant main effect for the between-subject factor because it only has two levels? If so, is an interpretation of this effect by simply looking at the means reasonable?

2. For the remaining effects, I somehow need to conduct post-hoc-tests to find out which groups actually differ, correct?
My professor wants me to calculate Scheffé-tests, but SPSS offers them only for between-subject factors (I'm thinking there must be a reason for that?). He gave me a Scheffé-formula for a 2x2-ANOVA with one between- and one within-subject factor, but even he was unsure how to adapt this formula for my design. Besides, if I understood it correctly, this formula is only helping with one of the interactions (I think the three-way-interaction possibly) and needs to be rearranged for the other analysis.

Now I'm thinking that my design is not so unusual that there is no "standard" procedure to further analyse the global ANOVA-results. Isn't there a approved post-hoc-procedure for a mixed design in SPSS? In one book I have, the results are broken down by contrasts, but I think with them, you can't compare all conditions and that is what I need to do. But what about the "compare main effects" with Bonferroni-correction? I read that this is not really a post-hoc-test, but what is it then?

And if I really need to calculate all those Scheffé-tests by hand, is there someone here who is proficient enough to help me step by step with the correct formulae and who can check my results?

Thank you very much in advance for reading and hopefully for helping!!