I am investigating how students score on a test, based on their experience on the subject. My outcome, test_answer, is binary (0 for a wrong answer, 1 for a correct answer). Experience is a categorical variabel: group 0-3 (0 is no experience, and 3 is the group with the most experience). I have investigated this using a logistic regression model (I’m using Stata):
logit test_answer i.experience, or
Thus, I’ve got ORs incl. 95% CIs and p-values for all experience-group compared to no experience (group 0 = ref):
- Experience-group 0: ref.
- Experience-group 1: 4.5 (4.1-4.9)
- Experience-group 2: 9.1 (7.4-11.0)
- Experience-group 3: 8.0 (7.1-8.9)
- All p<0.001
I would like to also compare the groups with each other, and not just with the reference group. I could use chi^2 Test of Independence to determine whether there is a significant association between reader experience and test-score, and this way see if there is pairwise differences between them.
However, I was wondering if there is a more elegant way to do it. I already have ORs incl 95% CIs for the groups, so I think, that I somehow could make use of these to get 95%CIs for the pairwise differences, and from these calculate p-values. But I am not sure how I would do this. Can any of you guys help me? Or maybe you have an even better/more elegant way?
Additional info: My data format is long, i.e. like this:
student_id experience test_answer
1 0 1
1 0 0
1 0 1
... ... ...
2 2 0
2 2 1
... ... ...
