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Bayesian Repeated Measures ANOVA - averaging across repeated measures factor levels

Hello Bayesian Statistics Enthusiasts!

I am planning an analysis for data that is structured as follows:

Dependent variable: stimulation strength in mV

Repeated measures factor:

  • Level 1: Sham stimulation
  • Level 2: Verum stimulation type 1
  • Level 3: Verum stimulation type 2
  • Level 4: Verum stimulation type 3

Participants came to the lab 4 times, visits were counterbalanced across participants.

For this particular analysis I am not interested in the differences between the different Verum stimulation levels, in fact, I am not expecting any systematic differences there. If levels 2 to 4 would influence the dependent variable differently, then I'd have to assume that there is some weird confound there.

So, what I could do is average across the verum levels and set up the repeated measures model like this:

Dependent variable: stimulation strength in mV

Repeated measures factor:

  • Level 1: mV in sham stimulation
  • Level 2: average mV across verum stimulation types

As far as I see it, this should not violate any of the assumptions of the Bayesian RM ANOVA model but I am not 100% sure. I guess I may lose information in level 2 here, right? But then again if use all 4 levels, I am not sure if it will be straight forward to interpret the results. I am having difficulties making an informed decision whether this is a good idea or if it brings with it any problems that I dont forsee at the moment.

Could you help me out with this? Is it a good idea to specify the ANOVA with these 2 levels?

Or would it be better to specify all 4 levels as stated above?

Thank you all for helping me with this!


  • Hi KV,

    In these kind of situations I always wonder: if levels 2-4 are not supposed to differ, why was the experiment set up this way? Anyway, yes, a rough method is just to average within levels 2-4. There are more elegant (multi-level) procedures available, but this has the advantage of simplicity. Also, you are then effectively conducting a t-test, right?



  • Hi E.J.<

    Yes, it sounds like bad experiment planning, I know :p.

    This is because the experiment has two parts. For the first part of the experiment (which the question here relates to), the verum visits won't differ. In the second part the difference in verum visits takes effect.

    The analysis here only relates to the tasks in the first part of the experiment.

    Re t-test: You're right, basically a paired t-test. I was so in the RM ANOVA mind-set that this completely passed me.

    Thank you for your comment. So, I assume you also do not see any problem with averaging over the visits? Also not in the Bayesian scheme?

  • well, it is always more elegant to account for the entire hierarchical structure instead of averaging, but averaging does give you some robustness, so I'm fine with averaging here

  • I agree... that's why I was in two minds about this in the first place. Thank you for your help (and stamp of approval ;) :) )

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