I'm currently having trouble defining what type of ANOVA I need to run as well as how to run it correctly. This is the following setup:

I have 4 groups of 30 people doing a 2-session task (one after the other), where I record response time. In each of the 4 groups the sessions they do have 2 conditions:

  • AB
  • BA
  • AA
  • BB

My goal is find effects for condition: A or B, as well as ordering effects 1st or second session to explain the shift in means for the response time $Z$. I am currently having trouble on how to correctly run an ANOVA for this problem. My current solution (that I think is incorrect) is to do the following:

To construct a table where I have response time $Z$ in the main column, and for the groups have 2 variables: condition $(0,1)$ for A or B respectively, and session id $(0,1)$ for 1st and 2nd session respectively. It would look something like this:

$Z_{AB}^1$ : 0 0

$Z_{AB}^2$ : 1 1

$Z_{BA}^1$ : 1 0

$Z_{BA}^2$ : 0 1

$Z_{AA}^1$ : 0 0

$Z_{AA}^2$ : 0 1

$Z_{BB}^1$ : 1 0

$Z_{BB}^2$ : 1 1

Sure, I can run this through MATLAB's anovan, and I get a result, but a closer look reveals the problem I think I am doing in my analysis: I am pooling together the results from $Z_{BB}^2$ and $Z_{AB}^2$, as if the second session of both of these groups is independent of the first (which may not be the case -- as they did in fact have different preceding conditions). On the flipside, pooling together the $Z$'s from $Z_{AB}^1$ and $Z_{AA}^1$, should not be a problem as they are both the first session of the within subject experiment. So I am confused: Is this still a correct approach, or under what conditions is my proposed analysis correct/incorrect? Am I being more rigorous by finding a significant result by assuming independence?

  • $\begingroup$ Could you be able to fit general linear model? $\endgroup$ – user158565 Nov 13 '18 at 23:38

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