Comparing frequencies of outcomes within a 2x2 (game theoretic) decision matrix across treatment and control group

[matteomilani]

I collected data where two players interacted with two choices each, where a 2x2 table resulted when representing the game in strategic form. The 4 outcomes are (A, A) ; (A, B) ; (B, A) ; (B, B). My null hypothesis is that the outcome (B, B) is more likely in the treatment group (Treat==1) than in the control group (Treat==0). The control group has 14 subjects and the treatment 16. How could I test my null? I could perform the test both manually or on STATA.

 

[hlsmith]

Rate difference with confidence interval. If interval excludes "0" the rates are different. Please don't post the same question under multiple topic areas - it can result in redundant posts and take up people's time. Welcome to the forum.

 

[matteomilani]

Rate difference with confidence interval. If interval excludes "0" the rates are different. Please don't post the same question under multiple topic areas - it can result in redundant posts and take up people's time. Welcome to the forum.

Sorry about that I did not know under which precise category to post the question. One last follow-up question, what if I cannot assume a normal distribution?

 

[hlsmith]

I assumed that if you have a 2x2 table, you had a binary outcome. If not, please describe.

 

[matteomilani]

Yes I have a 2x2 table but I have 14 subjects in the control group and 16 in the treatment group. So I cannot meet the assumption necessary to assume a normal distribution, am I right? Otherwise I thought about the Fisher's exact test but using that I can only draw conclusions about the depence of the two variables and not the difference in their proportions.

 

[hlsmith]

If you have two binary variables, there is no continuous assumption since you have no continuous variable/associations, right

Rate difference with confidence intervals.