Suppose we have 500 students nested in 20 classes (different classrooms), 25 students per class
They all take a test.
The model below would tell you about the average scores and variability among students and classes
Suppose further that a random 10 of the classrooms were painted red the other 10 were painted blue.
Is this a reasonable way to test for the effect of redvblue on test scores? And if it is reasonable, is there a better way?
I'm wondering whether I should be concerned that redvblue was applied at the classroom level rather than the student level.