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So…
- normal people are scared because they fall for the gambler’s fallacy,
- mathematician is feeling fine because a 50% chance is a 50% chance,
- and the scientist is feeling extra fine because the experimental data shows that the surgery is actually safer than 50%
Did I get it right?
10 points to Gryffindor
Yay!
Gamblers fallacy or law of large numbers…
Being taught Statistics at University was a real eye opener on this…
So mathematicians and scientists cannot be normal people?
No, never.
Until vastly larger numbers of people get trained in Advanced Mathematics and Degree Level Scientific disciplines, the human norm will never be anywhere near Mathematicians and Scientists.
It’s quite literally abnormal to be a Scientist or Mathematician.
Then again, so is being Homeless or an Olympic-level Athlete.
no.
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.
I was thinking more a binomial proportion test with the available data ;)
Also, yep, “assuming” was a key part of the statement!
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?
Mathematician sees each individual outcome as independent 50% chance.
Scientist realises that the distribution of failures and successes puts him in a favorable position. e.g. for the 20 in a row to be a success in a 50% fail rate that means the previous 20 were all failures or some similar circumstances where the success rate rose over time or similar polarization of outcomes in the sample data which places them above average odds.
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.
Anyone with a good high school education should understand this.
Normal people too.
The popularity of casinos and lotteries say otherwise.
Someone who goes to casinos would come to the same conclusion, thinking that the surgeon is ‘running hot’.
And me mate paul
My aunt Nancy would surely be in the 50% who die
Would be or do you want her to be? Sound like aunt Nancy isn’t very nice.
“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!
Being alive has both a 100% morbidity rate and a 100% mortality rate.
The Main cause of divorces are marriages.
😱😱😱
Does the surgary have personal success rate of 50% or is the number from all the surgeries practiced by all the doctors?
I mean even then the stats can change with so many variables. It’s kind of like how you have a 50% chance of surviving by splitting up with Sam. You both knew it had to be done- the forest was thick and you knew it could only stalk one of you. You wish you had more time with him, but someone had to survive to tell the tale.
As you get some distance and pray to God that you are alone, you crouch low and look for any sign of a trail or a building to get to. The fog is beginning to thicken as you decide to move downhill. Water flows downward, so this is the best chance you have to find a river.
You keep running as quietly as you can as the last glow of sunlight dissipates from above the trees. You begin to panic as you realize there’s no hope for navigation in pure darkness. But then hope. The bubbling of water on rocks tells you that the river is just below. You cautiously move through the brush, heart pumping- were you being followed? It could have been waiting for the perfect moment- who knows how quietly it can move.
You get down to the river when you see a light on the other side. You focus on the shining and see it’s a flashlight. Sam had taken the flashlight with him, is it possible your paths reconnected? You wade across the shallow current- the water is cold but maybe this means you two lost whatever it was miles ago. Your shoes press down on the pebble shores as you scrape your way up the bank. “SAM” you whisper “SAM HEY”. No response. You slow down as you approach the flashlight laying on the ground. It was Sam’s, but Sam was nowhere to be seen. You reach down as you feel rain drops slowly fall on you. As you grab the light you notice something- the raindrop on your hand is dark.
As you realize what you are seeing, you begin to shake, mouth agape. You feel another drop on your shoulder. You knew you shouldn’t. You knew you should have accepted it and just moved on. You shouldn’t have looked up.
There he was. The top half of Sam was dangling from the branches, his pale face looking down at you with blood streaking across his face and dripping off his nose. How could this happen? What could do this to Sam, especially since you knew he was the fastest man in your platoon. He was able to get to you with the ammunition you needed when you’re whole unit was under fire in Kuwait. He saved your life, but you couldn’t do the same for him.
The shock is broken when you hear heavy boots stepping in front of you. It was over. There was nothing you could do. Nothing you ever could do. It- he- whatever you would call the figure in front of you just stated back into your soul. You felt the rattling of your lungs as you took the last few breaths you ever would. The blood soaked hands that reached out through the darkness led up to the man of your nightmares. Bits of Sam falling out of his mouth, he is fully revealed. It was him. It was always him. It was always
But yea in order to answer this we should define our parameters a bit more.
I’m so glad I decided to read this without skipping to the end first. What a great little journey, thanks for this.
My only suggestion is to spoiler the last bit for those with wandering eyes.
Is the surgery incredibly risky overall but the surgeon only takes patients with the highest chances of survival?
Irrelevant, still good news if he’s gonna be operating on me!
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.
98.07 for the surgery in general but not if you have decided to go to the first doctor. Then the 50% chance of the second doctor doesn’t not come into the equation, assuming surgery is done by the first doctor who is independent of second doctor. Hope that makes more sense.
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.
Plot twist: 50% of each individual patient survives. Hope you get lucky with which organs make it
…How much is the total amount?
WIth or without tax?
