[Note: I updated the question after getting comments, thanks!]
I am currently trying to find out if there is a significant difference in performance for different kinds of questions in a subject, but I have trouble finding the right way to analyze the data.
I have exams for about 10 years, with two different kinds of questions (type A and B), and wonder whether students perform better on type A than type B. The students get between 0 and 100 points on each question, so the mean score for each type of question is my response variable. All students answer all questions on each exam. The problem is further complicated by the fact that two different tutors make the questions. Thus difference in score might be due to one tutor making harder questions than the other. One tutor makes questions as type A more often than the other, so this might affect the result.
So for each question, I know the score all students got, which tutor made it, and which category (type A or B) it belongs to. Whether there is a difference between performance on type A and B is the interest here.
Example: Question 1 on the 2013 exam was type A and made by tutor 1. I know the scores from 30 students, so I can calculate the mean score and variance.
At first I thought I might just put all questions of type A in one group, and all questions of type B in the other group and perform a paired t-test, but that does not take into account that there are different groups of students over the years, and the questions have different variances (some questions are answered almost correctly by everyone, but most are not). In addition, there is the possibility that one tutor makes harder questions than the other, regardless of type.
EDIT: I think using a generalized mixed model might work, if I use tutor and type as covariates, and student as random intercept, and see if the coefficient for type is significant. Perhaps I should also included year as covariate? As the score is between 0 and 100, I am not quite sure which model I should fit though. A beta model would have been nice (just letting the score be between 0 and 1 instead), but is that possible?
Any thoughts on how I might approach this? I am very grateful for all help!