What test to use for checking the association between a percentile and a sensitivity test

[orchid_sugar]

I have a percentile score of how good a hospital is (could be continuous variable, but I categorized it into 5. 0-20%, 21-40%, 41-60%...) and a sensitivity result of how accurately a hospital reports an event (0 to 1, which can also be a percent if x100). I was told since it is not uniformly distributed, we have to use nonparametric analysis, which my graduate program did not go over much. What test would you do for above analysis (for if percentile score of how good a hospital is continuous and categorical)?

Can the Wilcoxon rank sum test be used when a variable has 5 categories and another variable continuous?

If yes, how can I interpret it? So far the internet is mainly showing 2x2.

Can Spearman be used with the above variables?

[StatDave · Accepted solution]

If you are only interested in testing for a linear association between the two continuous variable (on the percent  or proportion scale), then yes, you could use the Pearson or Spearman correlation in PROC CORR to get that test. Do not categorize either variable as that just wastes information. If you think the association might be important, but not necessarily linear, then you could fit a fractional logit model as described in this note. With that model you could even use a spline on the predictor (accuracy measure) to allow for an indeterminate shape on the association. That is done by specifying the SPLINE effect in the EFFECT statement in PROC GLIMMIX or PROC LOGISTIC.