I want to distribute my hospital data into 4 tiers (bins) based on the score. Tier 1 (good hospitals) has the highest score and Tier 4 (not so good hospitals) has the lowest score. The tiers can be of any size and there is no problem with that. Importantly, I want the tiers to be well separated based on the score, so if this makes the tiers unequal in size that is absolutely fine.
In the example below, I created a percentile rank on the score and then used pandas.cut() on the percentile rank to create the 4 tiers. The issue I have is with the tier borders which I think are not well separated. Example (red highlight): DD14 and DD15 have close scores and I don't want them to be in different tiers. Similarly DD24 and DD25 have a similar problem.
Is there a standard statistical approach to address my issue?
- I can round the percentile rank to a whole number to blunt the different and achieve this, but I guess this is not a standard solution, because there could be another scenario where this approach will create different problems in the tier.
- I'm not tiering directly on the score and use percentile rank instead because I want to normalize the values before tiering. I think this is a standard practice.