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Assuming X~B(20,0.5), that gives us a p-value of…
0.00000095367431640625
Time to reject H0!
You’re assuming those 20 were the only ones. Zoom out.
First 20 patients died until the surgeon learned how to do it, next 20 survived. Technically it’s 50% survival rate
Can somebody explain the difference between the mathematician and the scientist parts of this?
The normal person thinks that because the last 20 people survived, the next patient is very likely to die.
The mathematician considers that the probability of success for each surgery is independent, so in the mathematician’s eyes the next patient has a 50% chance of survival.
The scientist thinks that the statistic is probably gathered across a large number of different hospitals. They see that this particular surgeon has an unusually high success rate, so they conclude that their own surgery has a >50% chance of success.
Thanks. I suspect a mathematician would consider the latter point too though.
Normal people too.
“You should know that 9 out of 10 people who undergo this surgery will die. But don’t worry, the last 9 people who took this surgery all died, so you’re in the clear!”
Technically 1 out of 1 people who undergo that procedure die, eventually. Same is true for people who elect not to have the procedure done, eventually.
That’s not confirmed. Only about 93% of people who ever lived died so far.
Death rate is also strongly correlated with when you were born. We’ve gotten much better at not being dead in the last 100 years. For people born in 1925 the death rate is nearly 100%, but for people born in 2025 it has dropped close to zero!
😱😱😱
Does the surgary have personal success rate of 50% or is the number from all the surgeries practiced by all the doctors?
Is the surgery incredibly risky overall but the surgeon only takes patients with the highest chances of survival?
If you were the patient, you’d still be happy about that. If the surgeon is cheating the stats, but has already accepted you as a patient, then you have the highest chance of survival.
Great point, you’re right!
Doctor stabs you. “Oh no! Questioning the surgery claims another…”
How would you scientifically measure a difference between those two definitions?
I mean, say this doctor has a 100% success rate but another doctor has 0%. Those two doctors collectively have a 50% success rate but it you have far better odds with the first doctor than the second
The two doctors would only have a combined 50% success rate if they perform the same number of surgeries
After a certain point, it’s really society’s fault for letting the surgeon batting 0 continue performing surgeries.
That surgeon is bound to get one right one of these days!
@Cenotaph Nope, say the first doctor did 100 successful cases, the other did 2 successful and 2 failed, then the collective would be (100+2)*100/104 = 98.07%
So the number of cases would matter.
Of course. My point was only that there is definitely a difference between an individual doctor’s success rate and the overall success rate of a procedure across all doctors, responding to the commment I replied to.
In a statistical regression model, that would be a variable that encodes a specific individual; although encoding hypothetical (the scientific meaning of that word, not the layperson meaning) attributes of that individual is probably functionally equivalent, more useful, and easier to conduct.
Attributes of the surgeons is not easier, because you need to pick the correct attributes.
Really you just need an indicator variable showing 1 if its data from the surgeon under analysis and zero otherwise.
Then test for that indicator variable being statistically larger than 0.
…How much is the total amount?
Plot twist: 50% of each individual patient survives. Hope you get lucky with which organs make it
The left 50% or the right 50%
Bottom 50%
yes
