I have a question about something that my statistics teacher said about the following problem:
There are two hospitals named Mercy and Hope in your town. You must choose one of these in which to undergo an operation. You decide to base your decision on the success of their surgical teams. Fortunately, under the new health plan, the hospitals give data on the success of their operations, broken down into five broad categories of operations. Suppose you get the following data for the two hospitals:
Type A B C D E All
Operations 359 1836 299 2086 149 4729
Successful 292 1449 179 434 13 2366
Type A B C D E All
Operations 88 514 222 86 45 955
Successful 70 391 113 12 2 588
You notice that, in all types of operations, Mercy has a higher success rate than Hope, yet Hope has the highest overall success rate. Which hospital would you choose and why (choose two answers)?
A) Mercy; since I would go in for a specific operation, I want the hospital that has the best success rate for that operation.
B) Hope; since they do fewer operations in all categories, they are not "operation-happy" like Mercy.
C) Hope; this is an example of Simpson's paradox and we should always chose the "obvious" conclusion.
D) Mercy; looking at column E, Mercy clearly does more difficult surgeries and so is probably a better hospital.
E) Hope; it has the better overall success rate.
F) Mercy; this is an example of Simpson's paradox and we should always chose the opposite of the "obvious" conclusion.
My question isn't even about the occurrence of Simpson's paradox in this situation. My question is simply about the fact that my professor insists that A) and D) are the right answers instead of A) and F). He says,
"Because the success rate is so low for Type E surgeries,we can conclude that they are difficult and not just uncommon. Hence, Mercy probably has better equipment/doctors when compared to Hope."
I don't understand how he could imply on a statistical basis that he can tell that Mercy does "more difficult surgeries". It is obvious that Mercy has better success rate at type E surgeries, but why does that mean they do "more difficult surgeries". I think I am being screwed over by the wording of this problem and the professor isn't budging. Can someone please explain why I am wrong or how I can explain this to the professor?