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# Within-subject repeated counterbalanced caffine experiment

Dear all,

Not sure if this is the right place to ask for statistics help, but I love the JASP software and I guess there is no harm in trying:)

Anyway, I was wondering if anyone could give me some pointers about how to analyze my thesis experiment.
We had 12 participants, each performed something called "Random dot motion" cognitive tests with coffee
and decaffinated coffee (randomly counterbalanced) on two separate days.
This test gives response times and correct wrong data. (Each block of trials were about 200 choice tasks)
There was also a speed-accuracy trade off condition. One where they had to answer quickly within 1 second
(forced deadline speed) and another one where accuracy was the point and there was no deadline. (I am also struggling with how our experiment actually could show that caffine has an effect on the speed-accuracy trade off but I think I have some ideas about that...)

Now I am wondering which analysis to perform.
In similar studies some have done paired t-tests, and other studies seem to be doing repeated measures ANOVA, and looking at interactions.
The main problem is that there was a lot of learning, so the differences from one day to the other is mainly learning.
From what I can understand it seems I have two options, one is the repeated measures ANOVA,
and seeing if there is an interaction effect treatment*time, the other is to group all caffine
and all non-caffine trials together and doing one way paired t-test? Since the counterbalancing was done randomly is this possible?

Also not sure which assumtions I need to check for the tests to be valid, in the ANOVA I guess it is normality of the residuals and sphericity.

Sorry if this is a stupid question, any help would be greatly appreciated.

• Dear Supermario,

Sorry for my tardy reply. Here are my thoughts:
1. With "randomly counterbalanced" do you mean "counterbalanced" or "randomly determined"? Even if it was counterbalanced, you may get a more diagnostic test by adding time as a covariate.
2. These data definitely need to be analyzed with the diffusion model. Not with ANOVA. Not with a t-test. Easiest is to use the EZ diffusion model, extract the parameters of interest, and do a test on those. You have hundreds of trials, a speed-accuracy manipulation (so sufficient errors, at least in one of the conditions). The conditions seem right for a diffusion model analysis.

Cheers,
E.J.

• Dear EJ,

1. We randomly assigned half of the participants to get coffee on the first trials (day one) and decaffinated on the second trials and vice versa, I thought this was called counterbalanced, perhaps I am confused with the terms.

2. Unfortunately our test was made using four choices, not the two that is usual for the DDM (A person in my group insisted on it since she had programmed the task in python etc. Long story). I found a paper concerning multiple choices with the DDM “http://www.pnas.org/content/108/33/13852.short”, but I am not sure as to how I could use the model with my four choices. (We had up down left right as choices). A friend of mine (engineering PHD student) suggested discarding half of the choices and then doing the DDM but I doubt this would make much sense.

How would the EZ diffusion model be used, is it a function where you put in the relevant data (means, SD etc)? I read about it, how this is a good model to use, but concluded it would not be possible with my four choice experiment.