I did a pre-education and post-education quiz for a group of anonymous individuals. Individuals took a 2-3 question quiz, viewed an educational video, and then took another 2-3 question quiz. The quiz questions were different in the pre-quiz and post-quiz. This was repeated on 8 different occasions, each module was about a different topic. The individuals were allowed to stop participating in the process, so quite often the number of individuals that took each post-quiz was less than the number that took the pre-quiz (i.e. 10 took the pre-quiz, but only 8 took the post-quiz). Thus I can't directly compare the number of correct answers.
Normally, I would do a McNemars if I was interested in individual questions and I could actually match the two samples. However, I am interested in the aggregate of all 8 educational modules. I am interested in comparing the amount of correct answers on the pre-quizzes versus the post-quizzes. Since the amount of questions attempted was different pre and post each time: (1) is it OK to do a paired t-test on the correct proportions? (2) what test do I use if I want to look at each module individually?