Similar (and follow up questions) to my last posts. Calculating a composite index in PCA using several principal components
I have created a composite index to rank counties in Colorado based on cancer registry, hospitalization and ER visit, community health survey data, and poverty/race ethnicity data at the county level. The variables underwent descriptive stats, were tested for normality, standardized, and underwent PCA in SAS including varimax rotation. Relevant components (by way of Cattell plot "elbow" and Kaiser criteria) were retained and combined to make an index score. These new components could be thought of as "disease" and "demographics" respectively.
Outputs of one of these indices is as follows:
COUNTY NSI Adams 1.81 Alamosa -0.87 Arapahoe 3.18 Archuleta -0.12 Baca -2.1 Bent -2.22
These aren't the easiest for me or my audience to understand, so I've ranked them 1st to 64th (1st being the best) based on what I know of the underlying variables within the components retained for the index:
COUNTY Rank Adams 2 Alamosa 4 Arapahoe 1 Archuleta 3 Baca 5 Bent 6
My question is, what inferences can I make from this index? It was my understanding that I could only make inferences into relative differences (e.g. county ranked 15th is better than county ranked 30th) but that I can't quantify those differences (e.g. county ranked 15th is #% better than county ranked 16th). Would I be able to make more inferences if I standardized the scores to fall between 0-100? My gut says no but I wanted to check. Even if I could then say something like "the county with a score of 100 is 2 points better than the county with a score of 98". that still doesn't define what the magnitude of a difference of 2 means.
Many thanks in advance!