- Thread starter Poppy1
- Start date
- Tags post hoc tests repeated measures anova spss three-way anova

Sorry, yes, each factor is on two levels, all repeated measures (every subject in every cell). If factors are A, B, C, then A*C interacted. A, B, C were main effects. So I guessed the next step is to do either post hoc tests or simple main effects in SPSS to describe the interaction? I just read that the post hoc tests could be paired-sample t-tests with the alpha adjusted (bonferroni) and I could just report the p values. But somewhere else I read that I should be using the Estimated Marginal Means and use the Simple Main Effects syntax in SPSS, and again just report the p values? I just tried both and in the t-test result one of the comparisons had a p value of .08 so I concluded it was not significant. But when I ran the simple effects syntax the p value for that same comparison was .026. Is alpha still .05 in this latter case, and therefore that comparison now significant? So sorry if these are silly questions!!

I gather you already understand that no followup is needed for the main effects. With only two levels, the p-value for them *is* your comparison of the two levels they represent.

If you had 3 non-repeated factors, the issue would be a bit more complicated, because you would not want to compare all the subjects in A1C1 to A2C1 with a regular unpaired t-test while some of each were in B1 and others in B2. Given a main effect of B, you would be greatly increasing the variability of subjects within the two groups. To avoid that, you would use the error term from within the individual cells in an appropriate way.

Manipulating repeated measures error terms is more difficult, but I think you have an easy solution. For every subject, get the average of his or her value in A1B1C1 abd A1B2C1 etc.. In other words, average across the two levels of B for each subject. Then do the analysis on just A and C.

I'd guess that the main effects of A and C and the interaction will have the same F and P as they did overall. For terms that don't directly involve B the analysis averages over it anyway.

So now you can do paired t-tests to compare your cells of interest. Using a pooled error term from the whole design could give you more degrees of freedom, and perhaps a smaller p value, but the value is small unless your n is tiny. Plus doing that makes assumptions. I don't know that I could guide you on *exactly* how to do that without digging upsome research or trying some examples.

I'm not sure what exactly it does with the compare means Bonferroni when there are only 2 means. Check to see if the F from that is the square of the t value from the paired t-test. And if the df are the same. If both are the same, then it didn't adjust the p value in either case.

Do we need an adjustment? Not sure. I usually adjust when I have multiple levels of one independent variable. When following up to interpret an interaction, I don't adjust for the number of simple effect comparisons -- the point there is to pull apart the interaction, not to agonize over whether a given simple effect is significant. If one is significant and the other is not, you can say that, because the interaction itself is supporting the idea that there are differences between the simple effects.

Of course, if it is critically important theoretically to show that the A effect is significant specifically in C1 and you're going to be writing, "Future studies can restrict to C1, because that's where the effect is" then I WOULD Bonferroni correct. Some of this is judgment.

You know, in truth, sometimes I don't do simple effects at all, depending on what I want to show. If the A difference is 11 for C1 and -2 for C2, and the interaction is significant, you can state that the effect of A (in the direction A1-A2) was significantly more positive in C1 than C2. Just based on the interaction. That may answer the question.

This approach becomes essential is the A effect is 6 for C1 (p = 0.2) and -6 for C2 (p = 0.2). Neither is significant. But you can still interpret the interaction!