this post was submitted on 09 Oct 2024
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Science Memes

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50% survival rate (sh.itjust.works)
submitted 1 week ago by [email protected] to c/[email protected]
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[–] [email protected] 50 points 1 week ago (2 children)

Can somebody explain the difference between the mathematician and the scientist parts of this?

[–] [email protected] 15 points 1 week ago* (last edited 1 week ago)

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.

[–] [email protected] 206 points 1 week ago* (last edited 1 week ago) (2 children)

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.

[–] [email protected] -2 points 1 week ago (1 children)

The scientist is making a possibly incorrect assumption based on incomplete data. All we know is that the last 20 were successful.

It's the same as seeing someone flip tails 20 times in a row. Do you think it's just a coincidence and the chance of heads or tails is still 50/50 or do think there's something special about the person that makes them flip tails more often?

[–] [email protected] 4 points 1 week ago (1 children)

Or do think there's something special about the person that makes them flip tails more often?

Yes, that’s the conclusion that the scientist has come to. The chance of getting 20 in a row is so extraordinarily unlikely that it’s reasonable to conclude that the chance is not 50/50 for that particular surgeon.

[–] [email protected] 0 points 1 week ago* (last edited 1 week ago)

I think that's a misunderstanding of statistics and the scientist is making a faulty generalization. You're only looking at the last 20 and not all of the the surgeries. Imagine the surgeon has had 10020 surgeries and the first 10000 are an even 50/50 split, but the last 20 are all successful. Would you really think you have a higher chance because the last 20 were successful?

And just for fun you can throw 10000 coin flips into libreoffice or excel and see how many in a row can be heads (1) or tails (0). I didn't get 20 in a row but I did get 19 in a row, and the statistical probability of 50.1/49.9. Something extraordinarily unlikely can still fall within the statistical average.

[–] [email protected] 60 points 1 week ago (2 children)

Thanks. I suspect a mathematician would consider the latter point too though.

[–] [email protected] 6 points 1 week ago* (last edited 1 week ago) (1 children)

Anyone with a good high school education should understand this.

[–] [email protected] 1 points 1 week ago

That's sort of why I asked. I thought I was missing something but no, the meme is apparently assuming academic professionals are dummies. Not to say that we should expect nuance and robust portrayals from a meme.