# Correct group of factorial and repeated-measure ANOVA

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?

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