I am using school-level data to compare mean scores for two groups (Group A schools and Group B schools), as measured by a series of indicators: 1) grade-level exam percentile, 2) percent of male students who meet standards on exam, 3) percent of male students who exceed standards on exam, 4) percent of female students who meet standards on exam, 5) percent of female students who exceed standards on exam.
I know these indicators are correlated as they all are based upon upon exam score. A fellow grad student suggested a series of t-tests between school types A and B for each indicator, but I am concerned about an increase in Type 1 error. Then another student suggested I use z-test, but because I am dealing with school-level data this did not make sense to me as it doesn't matter how many students are in each group because I am comparing schools, not student-level data. I think I should be running a MANOVA, but am genuinely not sure if that is the right way to go about this.
EDIT --- extra info from comment
I have a sample size of 60 schools, only school-level data (no student-level data). I have 20 schools in group A and 40 comparison schools in group B.
Best Answer
I would suggest using Principal Components Analysis (PCA). Given a set of highly correlated features, it may work to use PCA to output a orthogonal (uncorrelated) set of transformed features.