# Looking for suggestions on how to distinguish between two different distributions in my data when no labels are available

My data consists of medical claims from thousands of providers across the country. The data contains how much they were paid for each service they performed and how many units of each service they provided. Imagine the data has been subset to just providers who provide drug infusions to keep it simple.

Provider type 1 infuses drug X and they are paid 1000 dollars for 10 units of the drug (i.e. 100 dollars per unit) and Provider type 2 infuses the same drug X and they are paid 1000 dollars for 100 units of the drug (i.e. 10 dollars per unit).

It turns out that there's two different unit types to bill for each drug, provider type 1 is paid using method A and provider type 2 is paid using method B. 10 units of type A is the same as 100 units of type B.

This is analogous to two cab drivers both being paid 100 dollars where the first cab driver has driven 100km and the second driver has driven 62.13 miles. It's the same fare for the same distance but two different units of measure. 100/100 km = 1 dollar per unit Vs. 100/62.13 miles = 1.61 dollars per unit.

In the absence of any labels in my data, how can I analytically distinguish between the two methods to say provider 1 is paid using method A Vs. method B?

Any approaches would be greatly appreciated.

• Did you try to simply plot the distribution of price per unit for drug X? May 12, 2023 at 7:06