Which design to use and how to analyze my results?

Hi everyone,

I am taking a DoE class and I'm going crazy. I can't seem to figure this one out, although I know it's fairly simple. I hope I can get some input from you guys!

There’s a new teaching method that’s being applied to test if academic performance is improved in elementary school students. The method is applied to children in 2^{nd} and 5^{th} grade. Within a city, 20 schools are chosen from 5 different districts (4 schools per district). In each school, two 2^{nd} grade and two 5^{th} grade classes are chosen to test the new method and the old method in each grade (each class has anywhere from 18 to 32 students). At the end of the year, all the students, regardless of the method they got, get the same test to evaluate their knowledge to find out which method is better.

So, there’s 5 districts > 4 schools per district > two 2^{nd} and 5^{th} grade classes per school > 18-32 students per class > same test for everyone at the end of the year.

What I need to do is decide which design I will be using, how I will evaluate the final result to decide which method works best, and evaluate the possible factors that affect the academic result. I was hoping you guys could point me in the right direction here, although I have a few ideas:

1. I was thinking of using a Simple Factorial design. Would that be ideal in this case?

2. I thought of using a t (Student’s) test to see which method is better, since there’s only 2 methods to compare and I can’t do any other post hoc tests if I don’t have more than 3 groups to compare.

3. I have no clue about analyzing the factors that might affect academic performance. Can that be done with the Simple Factorial design as well?

Thank you very much!

-Daniel