I am trying to determine how to calculate the factors that have the most significant impact on a weighted average. For example, let's say I am reviewing the number of patients that responded to a survey saying that they had a positive experience. The overall percentage of patients that had this response was 80%. When reviewing the data by doctor, it is broken down as follows:
- Doctor 1: 30 / 40 = 75%
- Doctor 2: 20 / 25 = 80%
- Doctor 3: 5 / 5 = 100%
- Doctor 4: 5 / 8 = 62.5%
- Doctor 5: 20 / 22 = 91%
How could I rank the 5 doctors in terms of having the most significant positive impact on the overall percentage? Since this is a weighted average, there are 2 factors at play: each doctor's percentage, and the size of their denominator ("weight"). For example, Doctor 3 has the highest percentage, but Doctor 5 probably had the most significant positive impact on the overall percentage because he has a weight that is over 4x larger than doctor 3. Is there a formula to calculate overall impact while taking both factors into account?
I found the following post on this site that has a (somewhat) similar problem: Contribution (weighted average) of change in rate over time
but I don't see a solution. And, this post is wanting to calculate the impact to a change in rate/percentage over time; I'm taking that complexity out and just want to know the impact on a rate/percentage at one point in time. As a side note, to solve this other post's problem, I think you could use a price index approximation technique, such as the Marshall Edgeworth price index. However, I don't think that is a solution to my problem.
Thanks for any help/insight you can provide!