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I have a (to me) complex experimental design I'm working on pre-registering and I want to make sure I'm approaching the model correctly. I've attempted to offer an illustration of the design below.

I have two experimental conditions that are manipulated prior to the administering of the repeated measures, so I think it would be accurate to describe this as a nested design. I'm primarily interested in the main effects at Time 1 and the over time interactions for the groups that change. My question is, since I'm using repeated measures, can I just "lump" the between subjects groups together (so four levels) or is it better to enter two separate between subjects factors (each with two levels) into the model. I've attempted to simulate the data, but that's not helping me clarify.

Is it also appropriate to do planned contrasts here since I have specific comparisons I want to make?

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  • $\begingroup$ Hi, welcome to CV! Can you clarify what "manipulated prior to the administering of the repeated measures" means? Does this mean you have no data prior to any experimental manipulation, but two measures per participant that were both taken after the respective (A or B) manipulations? $\endgroup$
    – Sointu
    Commented Jul 14, 2023 at 13:57
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    $\begingroup$ Thank you! Yes, you are interpreting the design as I have it. The participants come to the lab and are put into an experiment where they are in Condition A (observing someone in conversation) or Condition B (participating in the conversation). Then they receive Time 1 DV measures. Then they either stay in their initial Condition or change to the opposite condition. After this second stimulus exposure they receive the same measures as Time 1 for Time 2 (this is the repeated measure). $\endgroup$
    – Teresa
    Commented Jul 14, 2023 at 15:49

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OK! I admit I'm slightly unsure about this so maybe wait if you get another answer, but since you currently have no answers, I'll have a go.

So you have in some sense 4 different groups: A to A, B to B, A to B and B to A, right? But only 2 different manipulations, A and B.

If you are confident that changing (vs. not changing) condition, and the order or A vs B (for those who changed condition) have no effect on your DV, and that changing and order have no effect on the effect of condition on DV, you can probably just have a 2x2 between (condition) - within (time) ANOVA.

You could check for the potential effect of change by creating a binary variable of change vs. no change (those staying in A or in B would receive value "no" and those changing between conditions receive value "yes") and putting this variable and its interaction with condition into the model. If its main effect and interaction are non-significant, you could remove it and use the 2x2 anova as your main model / the model you report.

Yes you can do planned contrasts after the omnibus ANOVA. Especially if you have pre-registered the contrasts you check - it's great that you're going to pre-register!

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  • $\begingroup$ Thanks!! I think the order of change will matter. So, I think I either have to specify the between subjects variable as one predictor (with four levels) or two predictors (each with two levels). The two predictors with two levels seems the better approach, but the issue I'm running into in my simulated data is that since I don't expect change between Time 1 and Time 2 for A to A, B to B participants, this will produce a nonsignificant omnibus model and it would be inappropriate to interpret the interactions. I thought it might be ok to go this route if I pre-register the planned comparisons? $\endgroup$
    – Teresa
    Commented Jul 14, 2023 at 18:24
  • $\begingroup$ As the order only concerns participants in the change groups, it might be OK to check the possible effect of order for this subgroup (A->B + B->A) only. And I think the 4-level predictor as the between factor would work quite nicely for the main analysis. $\endgroup$
    – Sointu
    Commented Jul 14, 2023 at 19:22
  • $\begingroup$ Re: planned comparisons, it is actually OK to check (theoretically predicted) planned comparisons also in the absence of a significant omnibus interaction, see here and here, so you don't have to worry about the omnibus test :) $\endgroup$
    – Sointu
    Commented Jul 14, 2023 at 19:22
  • $\begingroup$ Sorry for the many comments, but if you edit in "anova" tag you might get more people to see your question and get more advice. $\endgroup$
    – Sointu
    Commented Jul 14, 2023 at 19:26
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    $\begingroup$ Ah, thank you so much! I appreciate your time and feedback and will also add that tag to (hopefully) get some more thoughts, but your feedback follows my speculating. Really appreciate you! $\endgroup$
    – Teresa
    Commented Jul 14, 2023 at 19:31

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