Rank correlation - Comparing multiple sets of ranked metric values

JKru

New Member
#1
Rank correlation - Comparing multiple sets of ranked metric values
First, I would like to thank the mods and experts who maintain and answer questions on this forum.
Second, I really appreciate the fact that you reply to people who place "Please Help ME!!" in the subject line despite the fact "Forum Guidelines: How To Post" mentions how stupid that is.
Third, I did my best to search for an answer to my question, but I kept running into poorly worded questions and ranks that had the same members.
With those things in mind, I am sure that since I at least tried to follow the guidelines, I will get the help I need. So here goes...
I am looking to study the ranking systems of top high schools. I would like to compare three systems where each system bases the ranking on a different formula and each formula uses different data.
Since the data goes into the formula which produces a score, I don't see any reason to test the correlation of data to the score in each system (would most of you agree?); however, what I am interested in testing, is if there is a correlation between the score and the rank. For this I could go back five years, record the score and rank for the top 25 schools and get something that would look like this for one system, which I would repeat for the others:
Rank, Year 1, Year 2, Year 3, Year 4, Year 5
1, 1200, 1100, 1325, 1111, 1445
2, 1120, 1022, 1220, 900, 1234
3, 1050, 900, 1190, 888, 1055
etc for the top 25 schools.
So this is where I need help.
What test should I use to determine if there is a correlation between the score and rank?
I think the Kruskal-Wallis test is appropriate for this, and I'd use this as the null hypothesis: The median scores of the top 25 schools over 5 years are the "same".
I hope that I have explained the situation well enough, and someone is able to confirm and/or offer suggestions to my solution.
To summarize, here are my three questions:
1) If a formula is used to calculate a score from a given set of data, is there any reason to test the correlation of data to the score? [The most accurate regression formula is a formula.]
2) Given multiple sets of scores that are ranked, is a Kruskal-Wallis test appropriate for testing the correlation of the score to the rank?
3) Is the proposed null hypothesis appropriate?
Here are two additional questions I have:
2B) Would the same test that compares scores to rank (Question 2 above) be appropriate to also test the correlation of the rank to an individual item that is in the score? For instance, average GPA is used in the formula to calculate the score. Is the Kruskal-Wallis test (or other test) still valid even though the GPA may not be in the same order now as the rank?
3B) What would be an appropriate null hypothesis for this new scenario?
Thank you so much for your time and consideration.