I would like to compare the evolution of scores on a math test between two groups in a longitudinal manner. I have a panel of students that we tested in June, at the end of the year, and then in September, at the beginning of the school year. I am trying to find out if the vacations have a differential effect according to the gender of the student. To do this, I compare the proportion of men who obtained a score defined as "satisfying", to the proportion of women who obtained a satisfying score, in June then in September. How do I know if the evolution of the gap between men and women is significant?
Let me give you a concrete example to make it more clear:
Let's say that in June, 76% of men score well and 81% of women score well. So the gap between men and women is 5 points.
In September, 71% of men score well and 79% of women score well. The gap between men and women is therefore 8 points this time.
How can we test if the school vacations had a different effect by gender? What type of test should be used to determine whether the change from a 5-point gap between men and women in June to an 8-point gap in September is a significant change?
I thought about a Two-Sample McNemar Test. Unfortunately I didn't find any implementation of this test in R.