Thread 16774345

How many of you can correctly answer this?

>>16774345 (OP)
None of us, because the question doesn't list the false negative rate.

>>16774345 (OP)
Assuming 0% false negatives...
>1000 people, randomly sampled
>Test them all
>On average, 1 person in your sample actually has the disease, amogus
5% false positive rate means 0.05*999 healthy people test positive on average, or approx 50 false positives
So approx 50 false positives, 1 real positive
So approx 2% chance a given positive has the disease

If you assume it has 0% false negative rate, i think it's 2%
I dont believe that half of the people at harvard med think 95% of people have the disease

>>16774345 (OP)
True positive = 95%
False positive = 5%
20,000 people tested
2,000 actually have it
0.95*2000 = 1900 (true +)
0.05*18000 = 900 (false +)
1900/(1900+900) = 68%

>>16774345 (OP)
1/51 so a little less than 2%.

>>16774362
Correct except only 200 people actually have it kek

>>16774351
Thanks for telling us you've never been enrolled in an ivy league school.

>>16774366
correct except only 20 lol

>>16774362
who said there have been 20000 people tested

>>16774428
Very rude to say that, anon

>>16774468
How so?

>>16774495
Because you're implying someone is stupid. Very mean.

>>16774501
>I don't believe that half of harvard can't do basic math
It's not a dis, you've just never been there if you think that.

>>16774464
Easier to work worth

>>16774509
Idk, man. I think it's easier to assume 1000 people tested:
>1 person has it
>5% of 1000 = 50 false positives
>51 people test positive
>1 of them has it.
>1/51

>>16774517
The correct answer is 20/1019, not 1/51. The difference is that you've assumed the true positive rate is 100%, as opposed to being 95%. Assuming 20k people gets this answer. Yours doesn't.

>>16774518
>The difference is that you've assumed the true positive rate is 100%, as opposed to being 95%.
The question doesn't specify what the true positive rate is, anon. His guess is as good as yours.

>>16774518
>The difference is that you've assumed the true positive rate is 100%, as opposed to being 95%
I am retarded and do not understand what you're communicating here.
At 20,000 should the number of true positives not be 20? Should the number of false positives not be 1020?

>>16774518
the true positive rate is 1/1000 anon
it's literally stated in the problem

true positive = 1/1000
false positive = 50/999 (50 / 1000 for simplicity)

therefore true positive / false positive = 1/51
that anon is right

What does "false positive rate of 5%" mean? Does it mean a) 5% of the time the test says positive it's actually wrong or b) the test says 5% of the population has it?

>>16774576
It means "if you don't have the disease, there is a 5% chance the test returns positive anyway".

There is also the false negative rate: the chance that, if you do have the disease, the test returns negative. This rate is not listed in the question, which makes the question unanswerable.

>>16774585
If you remove iodine, hydrogen peroxide, latex gloves, and the confluence of how basic internal organs work together, the rest of medicine is no better than astrology.

>>16774609
Also splints. How to tie a bone down. Other than that, it's all horse shit.

>>16774612
Splints include tourniquets.

>>16774345 (OP)
nobody ever asks why a perfectly deterministic test would even have a false positive rate in the first place.

>>16774501
Everyone is stupid.
Stop pretending that remarks upon natural human cognition is an insult. Surely you're human and understand that you are frequently stupid.

>>16774708
People ask that all the time, it funnels into "p hacking"

>>16774708
What do you think these tests are? It's not some magic science machine that you stick some blood into and then "beep boop beep. You have diabetes."
There's tolerances of detection rate for various compounds within a sample. There's a magin for what's considered "normal." People outside that margin are sometimes perfectly healthy. People within that margin are sometimes horribly ill.
Biology be like that.

>>16774721
There were no remarks upon cognition, only upon experience.

>>16774728
It would be appreciated if you would cease demonstrating incompetence while whining about someone noting the presence of stupidity in populations of humans.
That you cannot see the way in which a remark upon experience with respect to cognition would be a remark upon cognition is a significant demerit.
The only person being insulted here is anyone forced to deal with you.

>>16774348
When they say <1/5 get it right, it means that FP+FN <= 0.2. The test given to the hypothetical patient is the same test given to the Harvard student is the same as OP's test. Radical semiotics can't wait to hear from you.
>>16774708
You just did.

tom bayes doing backflips in his grave

>>16774761
Tell me that in 8 words.

>>16774771
Shut the fuck up, dumb ass. People dumb.

>>16774783
The same balance of people go to harvard.

>>16774785
You literally said "Tell me that in 8 words."

>>16774828
Why did you break kayfabe by using 9?

>>16774835
>Why did you break my immersion by not continuing the bit you tacitly agreed to only once?
Ah, words.

>>16774840
Harvard peeps are largely daft. Try to disagree.

>>16774724
there shouldn’t ever be a margin if the test is designed correctly.

>>16774585
>tests just magically return positive for no reason other than pure chance
doctors are fucking DUMB

>>16775034
Nigger, have you ever had a real job in your life?
Protip: 1 and 1.0 are two very different numbers. 1.00 is another number entirely.
If you don't know why, then get a job.

>>16774362
So 5% false positive means 5% of people tested is wrongly diagnosed rather than 5% of diagnosed population is wrongly diagnosed. This just reinforces my conviction that all this logic questions is really just a gotcha questions that trap you with semantics rather than test actual reasoning skill. Nobody would fall for this if the definitions are properly spelt out.

>>16774345 (OP)
1/51?

>>16775073
It doesn't matter if you don't understand the question, "false positive" is a term doctors are familiar with, and the question was aimed at doctors

>>16774345 (OP)
Trick question the test is a ruse

>>16774345 (OP)
Think intuitively if the prevalence rate is 1/1000 nigga then 10/1000 is 1% of prevalence

>>16775206
Think nigga if your Iq isn’t the correct level then you’ll be retarded anything below 95 isn’t sentient imo aka the average women PhD

False positive rate is 5% that’s not relevant

False negative rate is 1% 1/1000 (prevalence) that’s all that matters so .1% of all false negatives cause death so 99.9% survival rate

>>16775220
I think my wm is back for intuitive reasoning not actual digit span which fucking sucks I’ll get it taken care of with the spells

>>16774348
Lmfao
>prevalence rate of .1%

>>16775220
Even I fucked up I used raw intuition still right tho I was initially close

>>16774501
Most people are stupid nigga

>>16774351
you used chatgpt retard
>i think muh 2
fucking faggot be decisive you have to use bayes theorum even me the all knowing anti memer got it wrong on the exact prevelance rate

>>16775288
probably some poojeet larping as intelligent lmao when in reality no poojeets are intelligent

I don't know these terms, but If I am understand this correctly:
>only 1 in 1000 people have the disease
>rate of occurrence 0.1% in the natural population
>a false positive rate of 5% means, that if you give it to a RANDOM person, they have a 5% chance to score positive on the test
>So if you gave the test to 1000 people, 51 people would score positive (the 5% false positives and the 0.1% of the population, who actually has it)
>So that's a 1 in 51 chance you are the person with the disease in purely mathematical terms
>that's like 1.9%

>>16776295
lmao great work cheating with my shit

>>16776590
I swear on my prostate, I didn't cheat.

Your stupidity is astounding.

>1/51
it amazes me that people keep quadrupling down on this wrong answer. just google the text of the question. there are dozens of sources with the correct answer online that you can verify none of which give as 1/51

>>16775207
>123test.com
>paying for an online IQ test
The score doesn't matter. You failed the real IQ test here.

>>16776295
>a false positive rate of 5% means, that if you give it to a RANDOM person, they have a 5% chance to score positive on the test
Almost. It means that if you give it to someone who doesn't have the disease, they have a 5% chance to score positive on the test. Which for this particular problem means almost the same thing, but not exactly.

>>16776295
>>So if you gave the test to 1000 people, 51 people would score positive (the 5% false positives and the 0.1% of the population, who actually has it)
Wrong. On expectation, the test would give you 50 positives from the false positives alone, but the true positive might be in that group too. There's a 19/20 chance that he's not. So instead of 50 people, you have 50 + 19/20, and the probability becomes 1 / (50 + 19/20) = 20/1019

>>16776620
>the true positive might be in that group too.
Then it's not a false positive now is it?

>>16776622
For the one truly sick person, there was still a 5 % chance that the test fails and gives a false positive. Or false false positive.

>>16776620
>On expectation, the test would give you 50 positives from the false positives alone, but the true positive might be in that group too.
This is a logically contradictory statement, if
>>16776615
>It means that if you give it to someone who doesn't have the disease, they have a 5% chance to score positive on the test.
is true.

I think you are wrong.

>>16776627
1/1000 chance that you have the disease and a positive result
5/100 * 999/1000 chance that you have a positive result but no disease
1/1000 + 5/100 * 999/1000 that there's a positive result
The chance that you have the disease is (1/1000)/(1/1000 + 5/100 * 999/1000) = 20/1019

>>16776624
We're talking mathematical idealism here. Any question regarding that actual workings of the test are to be ignored.
As such, it is not a false positive if it correctly flags a sick person as sick.

>>16776635
1/1000 chance you have it
50/1000 chance it's a false positive
total number of positives in 1000 is 50 + 1 = 51
only 1 of these is true
therefore 1/51

>>16774345 (OP)
Why weren't they taught how to perform the calculation? They're just supposed to infer the meaning of false positive rate as if they have a 180 IQ?

>>16776651
>50/1000 chance it's a false positive
Wrong. It's 5/100 that it's false positive, and 999/1000 that you don't have the disease. Please stop already.

>>16776656
>50/1000 =/= 5/100
Whatif it's 1/20?

>>16776656
nigga I literally have the book and this is the answer
try to reconsider

>>16776664
what book?

>>16776673
The book.
https://en.wikipedia.org/wiki/The_Book_(short_story)

>>16776656
lol

the amount of answers on this went down

>>16774345 (OP)
On the one hand, anybody who says 95% is retarded, on the other hand, I don't expect a medical student to pull Bayes theorem out of his ass.

>>16774349
whether the test has 100% or 0% false negative the probability is still roughly 2%

>>16776673
Almost every modern probability book has it as an example.
It was a study which perfectly illustrates common probability fallacies, so it is considered a "textbook" case.

The one I was specifically studying was Bertsekas and Tsitsiklis

>>16778231
You were studying a book and still failed to apply Bayes' theorem correctly?

>>16778231
which book and page number? i refuse to believe a standard intro probability book has such wrong info in it

>>16778366
>>16778262
https://pmc.ncbi.nlm.nih.gov/articles/PMC4955674/
here you go you fucking mongoloids
>Assuming a perfectly sensitive test, we calculated that the correct answer is 1.96%
aka 1/51

>>16774345 (OP)
>1/1000 prevalence
>5% false positive
>assume nothing else
>...
>assuming true positive rate of 100% . . .
fuck these retarded questions

>>16778387
The correct answer, 20/1019 ≈ 1.96 %

>>16778387
Washington University psych professor disagrees
https://faculty.washington.edu/llittle/bayestestexample.htm
UCSC Linguistics professor disagrees
https://people.ucsc.edu/~abrsvn/intro_bayes_1.pdf
Those are detailed slides, and maybe now you can finally understand why 1/51 is WRONG and that 20/1019 is CORRECT.

>>16778417
>https://people.ucsc.edu/~abrsvn/intro_bayes_1.pdf
dude did you even read your own links
TOP FUCKING KEK

>>16778417
>>16778423
Literally 1/51
HOW FUCKING DUMB ARE YOU
LMAO

Bless you anon haven't laughed at this big of an idiot for a while now

>>16778417
ah nvm we were arguing for nothing just realized it
you were doing the .999 calculation while most SANE people just simplified it to 1

>>16778423
>>16778425
Are you trolling? I honestly can't tell.

>>16778427
>I was merely sanely wrong

>>16778431
does the 1.96% change you idiot?
congrats you decided to be pedantic and troll everyone who is not as stupid to do an irrelevant 0.999 multiplication which doesnt change the outcome

>>16778438
Oh dear, you're serious. There are so many ways you can be more graceful about this.

>>16778439
you are too fucking dumb
this is probability aka applied math
it's not supposed to be exact you moron
1.96% is too exact anyway
better answer would be 2%

>>16778427
>>16778438
>0.999 multiplication
what are you even on about you mong? 1/51 is NOT equal to 20/1019

>>16778410
>1.96 %
and how much is 1/51?

>>16778443
are you the idiot who thought 50/1000 is different than 5/100?
must be
do the calculations you fucking troll
both are 1.96%

>>16778445
>are you the idiot who thought 50/1000 is different than 5/100?
He's not. It was my post. Also, nobody thought it.
Mine: >>16776635
Yours: >>16776651
Mine: >>16776656

>>16778445
>1/51 = 20/1019
Wheezing over here. By this argument pi = 22/7 and is a rational number
>>16778442
>Math doesn't have to be exact
Please, my sides. Think of my sides anon.

>>16778447
dude you literally thought 5/100 is different than 50/1000
>>16776656

>>16778449
it's not exact when you apply to real world situations like probability

>>16778451
Is that why I said: "5/100 * 999/1000 chance that you have a positive result but no disease"?
And specifically pointed out how that factor of 999/1000 makes your claim of 50/1000 incorrect? Honestly, it's quite funny how not only do you seriously suck at maths, but your verbal IQ is incredibly low too.

>>16778452
Why not 1/50 = 2% instead then?

>>16778455
you just don't understand how probability works
you are literally an autist who gets stuck on technicalities
both are 1.96%
and 1.96% is not even the better anser
https://pmc.ncbi.nlm.nih.gov/articles/PMC4955674/
>Assuming a perfectly sensitive test, we calculated that the correct answer is 1.96% and considered “2%,” “1.96%,” or “<2%” correct.

literally 2% is a better answer than your autism

this isn't imaginary math land
this is a real example from a real world situation where nothing is going to be exact

hence no need to multiply something with .999 when 1 will suffice

>>16778456
yeah this is actually better I agree

>>16778459
So why the rigamarole about arriving at 1/51? You know what I think? You felt like the smart bloke itt. You felt smug. Confident. Intelligent. Then someone proved you wrong with evidence. Your first reaction was to have a meltdown by pretending to laugh at the inadequacy of the person posting the source. Then you realized the source is right and that you just made a fool of yourself. Now you're trying to save face to a bunch of anonymous people who already think you're a retard by pretending you weren't wrong. Keep digging. It's hilarious.

>>16774345 (OP)
Isn't it 95%? The question gives the false positive rate (probability of getting a positive result on a test despite no actual presence of disease), so 95% true positive rate and 5% false positive. It also gives the prevalence, so I'm guessing it wants me to use Bayes theorem of p(actual presence of disease | positive test)
So I guess 2% given those values?
>t. Med student w/ engineering background

>>16778459
>this isn't imaginary math land
>this is a real example from a real world situation
>nothing is going to be exact
*Checks notes*
>Assuming a perfectly sensitive test
Oh

>>16778461
No my mistake was not realizing how dumb you people were and not realizing that 1/50.95 is the same as 1/51 when talking about probability

I admit I never performed the .999 calculation myself so I didn't realize that 20/1019 was the same thing.
Only after this post
>>16778427
did I realize I was talking to literal autists

I just couldn't fathom that someone would be so stupid as to argue over this.

>>16778463
yeah they calculated the perfect answer and then accepted 2% as an answer

>>16778465
>not realizing that 1/50.95 is the same as 1/51
lmao.png

>>16778467
>when talking about probability

>this fucking thread
So, this is the power of /sci/

>>16778470
They're never the same, mouthbreather. Not in probability or anywhere else.

0.095% false positive rate adjusted chance of having the disease

weird that no one else posted the answer, guess I am the smartest

but we all already knew that

>>16778473
You realize math when applied to the real world is not exact right?
Engineers use an approximation of pi
Even fucking NASA does
40 digits of pi are enough to calculate the circumference of the whole universe to an accuracy of 1 hydrogen atom

The point is no science uses perfect math, and probability is one of the most imperfect branches.
Why bother to be precise for something that is not precise by nature, and is just guesswork at best.

But you are just too dumb to realize this.

Have fun begging on the street with your pure Math autism.

Prevalence is 1/1000
False positive is 5%
1000/0.05 = 20,000
Therefore it's 1/20,000 < 1% < 2%
My answer is accepted as correct. Kneel

>>16778481
again with the autism
when will you learn?
in the real world when people say less than 2% it means something close to 2%
https://en.wikipedia.org/wiki/Significant_figures

>>16778483
>when people say less than 2% it means something close to 2%
That is not what sig figs mean, troglodyte

< = ≈
Q.E.D.

what is the answer? i found two difference answers to the same questions from universities
university of santa cruz has 1/50
https://people.ucsc.edu/~abrsvn/intro_bayes_1.pdf
university of washington has .01998
https://faculty.washington.edu/llittle/bayestestexample.htm

>>16778483
lmfao

>>16778487
>https://faculty.washington.edu/llittle/bayestestexample.htm
The 3rd to last line has an error. It says 0.0001, but it should be 0.001. Hence the erroneous final result. Otherwise it'd be the same as in the pdf.

>>16778487
Santa cruz has 20/1019
As does U of W after fixing the typo

>>16778489
i realize i have been interpreting "prevalence of 1/1000" as a rate of 1/1000 instead of 1/(1+1000)....

>>16778485
it means 2 is the significant figure you idiot
so anything from 1.5 - 2 is "less than 2"
but 1.3 would be "more than 1" and not "less than 2"
why am I arguing with an idiot?

I am stopping now.
Goodnight
Stay dumb and ignorant.

>>16775073
>understanding the question is not reasoning skills
midwit detected

Haven't read the thread, but to me this just seems like a badly worded question. It could either mean:
>5% of the positive results are false positives
or
>5% of all tests are false positives
There's really no way to tell from the question which one it means, so the people answering 95% aren't really wrong.

>>16778503
Engineer?

I don't get why its wrong. Does false positive mean something other than "the chance this test returned the wrong result"?

>>16779008
Chance a healthy person taking the test appears sick.

A way of thinking about this problem is "sure, someone testing positive might only have a 5% chance of being healthy. But he only has a 0.1% chance of being sick. Take both probabilities into account to get the real chance."

>>16779077
>He has a 5% of being healthy but only a 0.1% chance of being sick

So what is the other 94.9% chance?

>>16778524
I feel like that information is contained in the medical definition of false positive, which you would hope Harvard Med Students would know.

>>16776295
>51 people would score positive
You can't conclude that. You only know the average prevelance rates. It is conceivable that you can sample 1000 people and more than 1 actually have the disease, even if the disease rate is 1/1000.

>>16779081
The chance of not testing positive.
Excluded from the sample space because we know he did, indeed, test positive.

Kinda like that troll question about chance of having two heads up coins given you know one is heads up. The chance of landing two tails "exists" but you exclude it from the sample.

>>16779088
You are right of course. I was just talking in the context of averages.

95.005% if we're assuming the 5% false positive rate means the patient could still have it

idk man, seems to me like a disease test should have a 0% false positive rate

>>16774345 (OP)
what does "rate of false positives" mean?
p(~disease & positive result) or p(~disease | positive result)? if it's the later then 95% is correct