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I have the following situation. A subject comes to the clinic at day 1 and is evaluated using a 10 item checklist. The sum of those 10 items is the subjects score. A intervention is performed. The subject then comes back to the clinic at day 10 and is evaluated with the same 10 item checklist. Each of the questions on the checklist is Yes/No with probability p, so I know that the sum of the 10 Bernoulli(p) is Binomial(10,p). I perform this experiment on 30 people and my objective is to determine if there is any difference before and after intervention. My sample data table looks like:

id day score
1    1     3
2    1     6
3    1     1
4    1     2
5    1     0
1   10     5
2   10     2
3   10    10
4   10     7
5   10     4

A naive method that comes to mind is to do a paired t-test on the scores but I'm not so sure that comparing the means of Binomial rv's is valid in this case.

Does anyone have any other suggestions on how to analyze this data? One idea that comes to mind is to do a GEE with binomial family see here but I'm not sure how to implement that in R. My best guess would be:

geeglm(cbind(score,10-score)~factor(day), family=binomial(link="logit"),
       id=id, corstr = "independence", std.err="san.se") 

Is this a valid analysis or are their other ways as well?

Thanks

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I would actually suggest serious reconsideration of whether you want to consider this to be binomial data. In particular, you are making the assumption that for an individual, the probability responding "yes" is equal for all questions, and that all the answers are independent from each other. That seems like a very unlikely scenario.

If you have a large dataset, I would actually recommend the paired t-test as a more reasonable analysis. You are right to be concerned because your data is not normally distributed. However, with large samples this is of little consequence.

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