I found this and i understand why D is the correct answer, but people were saying that the correct answer is actually 1.87% Why is that? (Also we are ignoring the small things like usually only people with symptoms are tested, lets assume everyone gets tested.)

File: 13 KB, 551x433, Corona.png [View same] [iqdb] [saucenao] [google]

Anonymous Sat May 2 16:53:28 2020 No.11629529 [Reply] [Original]

I found this and i understand why D is the correct answer, but people were saying that the correct answer is actually 1.87%

Why is that?

(Also we are ignoring the small things like usually only people with symptoms are tested, lets assume everyone gets tested.)

Anonymous Sat May 2 17:06:05 2020 No.11629581

>>11629529
I hope this is a joke, but the first sentences is pointless- not being "affect"ed doesn't mean you don't have it. And regardless, this isn't a question of if someone was sampled randomly from the population.

Based solely on the test percentage, 95%. It means that the probability of having it and testing negative combines with the probability of not having it and testing positive as the inverse probability, however looking at the answers that was not considered so B is the correct answer.

>>	Anonymous Sat May 2 17:07:55 2020 No.11629588 >>11629581 Not OP, glad it wasn't me being retarded that the "right" answer wasn't there.

Anonymous Sat May 2 17:09:42 2020 No.11629594

>>11629529
[math]P(A|B) = \frac{P(B|A)P(A)}{P(B)}[/math]

We want P(Has Corona | Tested Positive), so P(A) will be probability of having coronavirus and P(B) is the probability of testing positive.

P(A) is 0.001, as given in the problem.
P(B|A) is 0.95, as given in the problem.

P(B) should be the overall probability of testing positive, but we don't know that from the given information. However, we can rewrite P(B) like this:

[math]P(B) = P(B|A)P(A) + P(B|\neg A)P(\neg A)[/math]

We know:
[math]P(B|\neg A) = 0.05[/math]
and
[math]P(\neg A) = 0.999[/math]

So in summary:
[math]P(A|B) = \frac{0.95*0.001}{0.95*0.001 + 0.05*0.999} = 0.01866[/math]

So yeah, the correct answer is 1.86% and my guess is that the answer key is just rounded up.

>>	Anonymous Sat May 2 17:09:47 2020 No.11629596 >>11629581 was not expecting someone on /sci/ be this unfamiliar with conditional probability and Bayes's Theorem. i didnt come here to argue wether its 95% or 2%, im asking if it really is 1.87% and if it, why?

Anonymous Sat May 2 17:14:22 2020 No.11629618

>>11629596
>im asking if it really is 1.87% and if it, why?

It is because of Bayes' Theorem. But intuitively, the reason why the chance of really having the virus is so low is because the low rate of the virus in the population vastly outweighs the relative accuracy of the test.

Another way to think of it:
You take a DNA paternity test that is 99% accurate and it says that your father is Tupac Shakur. But you live in a Hasidic Jewish neighborhood in New York and your mother has been in a wheelchair since birth.

P(B|A) might be really high, but the fact that P(A) is so stupidly low is the reason why the probably of the test's result being correct is basically zero.

>>	Anonymous Sat May 2 17:15:35 2020 No.11629623 File: 330 KB, 468x602, disgust.png [View same] [iqdb] [saucenao] [google] who tests positive? 0.05 of .999 and .95 of 0.001 anyway im not gonna write it out but the answer is 0.018664047

>>	Anonymous Sat May 2 17:19:17 2020 No.11629638 >>11629594 but why is it 0.999 and not 1?

Anonymous Sat May 2 17:23:20 2020 No.11629651

>>11629638
Because the probability of something happening and the probability of something not happening have to add up to 1.

It's given in the problem that P(A), the probability of having coronavirus without any other prior information, is 0.001. So it must necessarily be true that the probability of not having coronavirus, without any other prior information, is 0.999.

>>	Anonymous Sat May 2 17:24:56 2020 No.11629655 retards: * it says 0.1% are AFFECTED with coronavirus, many more can have it and test positive but not be AFFECTED * You are not sampling randomly from the population. YOU TEST POSITIVE- the isolated chance is the sole probability given by the test

>>	Anonymous Sat May 2 17:26:03 2020 No.11629660 >>11629655 who are you even replying to?

>>	Anonymous Sat May 2 17:29:21 2020 No.11629663 >>11629529 Baye's theorem, look it up

>>	Anonymous Sat May 2 17:29:32 2020 No.11629664 >>11629529 Presumably you've cut off >E. 50% as some kind of joke?

>>	Anonymous Sat May 2 17:32:26 2020 No.11629673 >>11629664 The right answer. You either have it or you don't.

Anonymous Sat May 2 17:35:50 2020 No.11629690

>>11629529
Depends what it means by 95% accurate.
If it means that 95% of the time it says yes, the answer is actually yes, then it is 95% chance you have it.
If it means that if you take a million people with the virus, test them all, you'll get 950k positives, then it is a 2% chance you have it.
Under no circumstance is it 1.87%
Regardless it doesn't matter, it is an overhyped meme. The coronavirus is no more dangerous than a regular virus/flu/cold

Anonymous Sat May 2 17:37:41 2020 No.11629695

>>11629623
The question doesn't say there will be any false positives, it only suggests the existence of false negatives.
This >>11629690 is me and I will stand corrected that there is *A* circumstance where it is 1.87%. But that is only if there's also false positives.
So there are 3 potentially correct answers, the question is worded poorly

Anonymous Sat May 2 17:38:00 2020 No.11629696

>>11629690
You don't know what the word accuracy means.

https://en.wikipedia.org/wiki/Accuracy_and_precision#Common_technical_definition

95% accuracy means that if you test a person with the virus, 95% of the time it will result in a positive reading.

Anonymous Sat May 2 17:39:02 2020 No.11629699

>>11629690
this guy >>11629594
disagrees with you.

im just wondering why the more simple method of calculating it doesnt work.
if on average 50 out of 1000 people get a false positive and you are one of them, it means you have a 2% chance of having it, even if we inlcude the 1 true positive its still just 1 out of 51 which is 1.96%

>>	Anonymous Sat May 2 17:49:44 2020 No.11629753 wtf is this shit itt? If you took the test and tested positive it's right 95% of the time, then you have a 95% chance of having it... B How many people affected is irrelevant.

>>	Anonymous Sat May 2 17:51:25 2020 No.11629762 wtf is this shit itt? If you took the test and tested positive and it's right 95% of the time, then you have a 95% chance of having it... B How many people affected is irrelevant.

Anonymous Sat May 2 17:51:56 2020 No.11629763

>>11629753
Let's suppose that you get a genotyping test done and it tells you that you're Abraham Lincoln. Genotyping is highly accurate but also has errors, so this is really possible in real life.

Would you still say there's a 99.9% chance that you're actually Abraham Lincoln? Or is there some relevant information that might make a true positive less likely, even though the test is generally accurate?

>>	Anonymous Sat May 2 17:52:14 2020 No.11629764 >>11629762 its conditional probability bitch.

>>	Anonymous Sat May 2 17:52:58 2020 No.11629766 >>11629763 >>11629762 linking to new post since >>11629753 deleted

>>	Anonymous Sat May 2 17:53:27 2020 No.11629769 >>11629764 What's your point you idiot?

>>	Anonymous Sat May 2 17:54:49 2020 No.11629775 >>11629696 okay but that doesn't say whether it is 95% or 100% of the time that you get a negative when testing someone without it >>11629699 see >>11629623 for their logic. Depends on the meaning of a poorly worded question

>>	Anonymous Sat May 2 17:55:47 2020 No.11629782 >>11629766 The new post says the same thing with a fixed typo, idiot.

>>	Anonymous Sat May 2 17:56:21 2020 No.11629783 >>11629775 the probability of getting a negative when you dont have it is not only the same 95% but also IRRELEVANT because the condition is that you tested positive.

Anonymous Sat May 2 17:57:20 2020 No.11629788

>>11629762
Question is worded dumb but they are saying this:
>pretty much everyone does not have it, but 5% of them get false positives
>if you get a positive, it is more likely to be one of the 95% that have false positives than to be one of the .1% (or .095%) that have actual positives

Anonymous Sat May 2 17:57:41 2020 No.11629791

>>11629775
>okay but that doesn't say whether it is 95% or 100% of the time that you get a negative when testing someone without it

If the 95% refers to the false negative rate, then the problem is unsolvable because the question doesn't ask about someone who tested negative.

Positive/negative predictive values can factor in both false negatives and false positives, but PPV/NPV are not 'accuracy'.

>>	Anonymous Sat May 2 17:58:56 2020 No.11629798 >>11629782 well you fixed your spelling but your logic is still wrong if you know how to program, write up a Monte Carlo simulation for the problem. It'll give you 1.86% after a large number of trials.

Anonymous Sat May 2 18:00:02 2020 No.11629808

>>11629699
.1% of people have it
95% of them test positive
therefore .095% of people test positive and are positive
95% of people don't have it
5% of them test positive
4.75% of people test positive and don't have it
>therefore 4.75%+.095% of people test positive
>so 4.845% of people test positive
>.095%/4.845%=1.9607843%
so this is the actual answer

>>	Anonymous Sat May 2 18:01:06 2020 No.11629812 >>11629808 P(A\|B) is not equal to P(A)*P(B). Your answer is wrong.

Anonymous Sat May 2 18:02:11 2020 No.11629818

>>11629808
>>11629699
oh sorry I mean 99.9% of people don't have it
I wrongly said 95% of people don't have it
so let's start over
.1% of people have it
95% of them test positive
therefore .095% of people test positive and are positive
99.9% of people don't have it
5% of them test positive
4.995% of people test positive and don't have it
>therefore 4.995%+.095% of people test positive
>so 5.09% of people test positive
>.095%/5.09%=1.8664047%
so this is the actual answer

>>	Anonymous Sat May 2 18:02:58 2020 No.11629821 >>11629594 P(B\|A) is not the same as 1 - P(B\|not A).

Chillfill >paypal.com/chillfil(...) Sat May 2 18:03:06 2020 No.11629822 [DELETED]

>>11629529
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Anonymous Sat May 2 18:03:25 2020 No.11629824

>>11629812
Not wrong method, just accidentally put 95% instead of 99.9% because I forgot that 99.9% of people were not infected kek
idk what your meme-tier notation of P(A|B) means though but if you mean my method is wrong then you're wrong, see >>11629818, I get the right answer when I don't enter a data piece wrong like a champ

>>	Anonymous Sat May 2 18:04:23 2020 No.11629829 >>11629822 sorry pal but i've been done with school for quite a while now, i just like math and should have studied more of it.

>>	Anonymous Sat May 2 18:05:29 2020 No.11629832 >>11629822 >grades joke's on you, I don't have grades dumb chink

>>	Chillfill >paypal.com/chillfil(...) Sat May 2 18:05:37 2020 No.11629835 >>11629829 You're really gonna trust 4chan with this? You've got to be trolling

Anonymous Sat May 2 18:05:47 2020 No.11629836

>>11629798
Let's pretend the OP pic doesn't say anything irrelevant as not to confuse your tiny mind:

A test for coronavirus is 95% accurate.
You take the test and test positive.
What is the chance you have corona?

No one is going to say "b-but this isn't enough information. how many people get this virus?"

The answer is B. There are four fucking lights. Anyone saying otherwise is a troll or stupid enough to believe the trolls. Go back to discord, you infuriatingly stupid kid.

This is not the same as the monte hall problem, if that's to what you refer. I care not to look it up.

Anonymous Sat May 2 18:10:30 2020 No.11629859

>>11629836
It depends on what the question means retard
does it mean
>95% of people that test positive are positive
or does it mean
>95% of people that are positive test positive
in the first scenario it's 95%
in the second senario it depends if there are also false positives or only false negatives. If there are also false positives then it's ~1.86%, if there are no false positives then it's 100%
so the question is ambiguous and can either be 100%, 95%, or ~1.86%
RETARD

Anonymous Sat May 2 18:11:22 2020 No.11629863

>>11629821
You are correct, but if a test is 95% accurate, the probability of testing positive given that you don't have coronavirus is 5%. You can do this because there's only two outcomes for the test.

subtracting 0.95 from 1 wouldn't give you the right answer if 'inconclusive' was also a possibility.

>>	Anonymous Sat May 2 18:12:35 2020 No.11629867 >>11629859 oh and if there's false positives but not false negatives, then it's around 1.96%

Anonymous Sat May 2 18:12:37 2020 No.11629868

>>11629836
not gonna teach you intro statistics

if you really believe you're right - then program a simple 20 line monte carlo simulation and tell me what the final probability is. you're arguing for an alternative answer to a question template used in every statistics class across the world.

your answer is wrong and you're doubling down because of the Dunning-Kruger effect

>>	Anonymous Sat May 2 18:14:13 2020 No.11629875 >>11629836 >This is not the same as the monte hall problem LOL https://en.wikipedia.org/wiki/Monte_Carlo_method imagine being lectured about statistics from someone who doesn't know what a monte carlo simulation is

>>	Anonymous Sat May 2 18:15:33 2020 No.11629882 >>11629867 but how does the existance of false negatives affect your chances of having corona when you tested positive?

>>	Anonymous Sat May 2 18:18:32 2020 No.11629891 >>11629529 >lets assume everyone gets tested.) In NYC , the answer turned out to be 25% of the population got the disease, and 0.7% of them died. Why do you hate America?

Anonymous Sat May 2 18:21:13 2020 No.11629911

>>11629882
Because false negatives means less true positives than no false negatives. Forgive the subsequent redd*t spacing, trying to make it easy to follow.

If there's false positives and false negatives:
95%(99.9%): true negative
5%(99.9%): false positive
95%(.1%): true positive
5%(.1%): false negative
true positive÷(true positive+false positive)=95%(.1%)÷[95%(.1%)+5%(99.9%)]≈1.87%

If there's false positives and not false negatives:
95%(99.9%): true negative
5%(99.9%): false positive
100%(.1%): true positive
0%(.1%): false negative
true positive÷(true positive+false positive)=100%(.1%)÷[100%(.1%)+5%(99.9%)]≈1.96%

t. college dropout

Anonymous Sat May 2 18:32:47 2020 No.11629962

>>11629529
This thread is dumb

What does 95% mean? that 95 percent of people with corona tested postiive? that 95 percent of people without corona tested negative?

Anyone who got 1.87% or 9% or 9.5% is a retard who needs to stop and think. If you have an accurate test, then if you test positive, that means you are more likely than not to have corona. I don't care what math anyone did. You can eliminate anything below 50% with basic reasoning and you can eliminate 100%. 95% may not be exactly correct, but it definitely the most reasonable answer here.

Anonymous Sat May 2 18:36:09 2020 No.11629974

>>11629962
It's because retards think they're sampling the entire population and calculating the chance that any given person has both the virus and the result.

The question is just looking at one person, and so the probability is based purely on the results of the test.

Anonymous Sat May 2 18:37:13 2020 No.11629983
File: 62 KB, 552x419, Amerifat.jpg [View same] [iqdb] [saucenao] [google]

>>11629962
100% and 1.87% can both be correct you fucking moron tard.
>95% of people that test positive have it
>95% of people that have it test positive, and 95% of people that don't have it test negative
>95% of people have have it test positive, and 100% of people that don't have it test negative
>100% of people that have it test postive, and 95% of people that don't have it test negative
can be any of those 4 interpretations and by those, 100% and 95% and 1.87% and 1.96% are all accurate
YOU need to stop and think mr brainlet with clogged arteries. probably an amaerican pic rleated it's you

Chillfill >paypal.com/chillfil(...) Sat May 2 18:38:16 2020 No.11629989 [DELETED]

>>11629974
>>11629962
>>11629911
>>11629875
>>11629836
Heh, guys, why don't you settle this the smart way and ask an expert? I have expertise in statistics with analysis and statistical methods. 10% discount if you order within the next 10 minutes!

Anonymous Sat May 2 18:45:49 2020 No.11630016

>>11629618
>it says that your father is Tupac Shakur. But you live in a Hasidic Jewish neighborhood in New York and your mother has been in a wheelchair since birth.
That's a really specific sexual fantasy. But you masturbate to this?
Maybe if my dad was Shaq and my mom was Emilia Clarke?

>>	Anonymous Sat May 2 18:45:58 2020 No.11630018 >>11629962 >What does 95% mean? It means when you do the test on a verified known sample of patients the test gets the correct answer 95% of the time.

>>	Anonymous Sat May 2 18:46:59 2020 No.11630022 >>11629618 In the real world though, if you took a cvirus test with 95% accuracy, and it was positive, you would conclude that you do indeed have cvirus.

Anonymous Sat May 2 18:49:03 2020 No.11630032

>>11629651
>probability of having coronavirus without any other prior information, is 0.001
With a million known cases in a nation of 328 million, the odds of any randomly selected American already knowing they have the 'Rona is about 0.3%. The odds of having it with or without knowing is obviously higher.

>>	Anonymous Sat May 2 18:54:07 2020 No.11630057 >>11630022 which is why OP said (Also we are ignoring the small things like usually only people with symptoms are tested, lets assume everyone gets tested.)

Anonymous Sat May 2 18:54:38 2020 No.11630060

>>11629529
I cant believe the amount of unadulterated retardation in this thread.

Listen kids, the first bit that says "corona affects 0.1% of the population" is completely irrelevant. Its a red herring. What the question asking is the chance you have of having Corona. Since the test is 95% accurate and you tested positive then your chance is 95%
The answer is clearly B.

Jesus Christ. This is the same level as 1+1=2 and still you monkeys manage to fuck it up.

>>	Anonymous Sat May 2 19:04:28 2020 No.11630095 >>11630060 What.

>>	Anonymous Sat May 2 19:18:22 2020 No.11630121 File: 96 KB, 559x451, dunning-kruger.png [View same] [iqdb] [saucenao] [google] >>11630060 This post is a great example of Dunning Kruger.

Anonymous Sat May 2 19:23:46 2020 No.11630143

>>11629529
I can't believe the amount of unadulterated retardation in this thread.

Listen kids, the second bit that says "A test for it is 95% accurate." is completely irrelevant. It is a red herring. What the question is asking is the chance you have of having Corona. Since Corona affects 0.1% of the population then your chance is 0.1%
The answer is clearly E. 0.1%

Jesus Christ. This is the same level as 1+1=2 and still you monkeys manage to fuck it up.

>>	Anonymous Sat May 2 19:37:16 2020 No.11630181 It's not bayes theorems idiots. Just do P(accurate)×P(accurate\|positive) + P(innacurate)xP(inaccurate\|negative)

>>	Anonymous Sat May 2 19:38:47 2020 No.11630188 >>11629808 Wrong. That's the probability that you'll test positive, not that you have it. They are different

>>	Anonymous Sat May 2 19:40:05 2020 No.11630193 I got 0.190 recurring why am I such a brainlet

Anonymous Sat May 2 19:47:10 2020 No.11630212

>>11630143
The percentage of the country's population that gets huge tumors is. 1%
You get an x ray done and they find a huge ass tumor inside your body. Multiple doctors see it and confirm that you have a huge ass cancerous tumor in your body. It looks like a tumor and behaves like a tumor. The likehood that you have a huge ass tumor in your body is 99.9%

Whats the likehood you have huge cancerous tumor?

>>	Anonymous Sat May 2 19:47:43 2020 No.11630214 >>11630143 >What the question is asking is the chance you have of having Corona You mean what is the chance of you having Corona given you test postive which is quite different

>>	Anonymous Sat May 2 19:55:44 2020 No.11630233 its B if the word if was before "you test positive," then it would be D

>>	Anonymous Sat May 2 19:57:15 2020 No.11630236 >>11630193 nevermind I got 1.87%

>>	Anonymous Sat May 2 19:58:19 2020 No.11630239 >>11629529 what is the uncertainty of the measurements?

>>	Anonymous Sat May 2 19:59:48 2020 No.11630242 >>11630239 95%

>>	Anonymous Sat May 2 20:03:10 2020 No.11630249 >>11630242 sorry 5%

Anonymous Sat May 2 20:37:12 2020 No.11630323

>>11629974
>>11629962
Say 0.00000000000000000000000000000000001% of people have corona and you test positive. If 95% accuracy means 95% of people who have it test positive and 5% of people who don't have it test positive, what is the probability you have it?

>>	Anonymous Sat May 2 20:44:05 2020 No.11630341 >>11630323 >95% means whatever I want it to mean

Anonymous Sat May 2 20:50:01 2020 No.11630355

>>11630341
95% of the time it gives a correct answer, 5% gives the opposite. But there is more than one way to interpret it. I give you two more difficult.

Corona affects 0% of the population
A test for it is 95% accurate
YOU TEST POSITIVE
What is the chance you have Corona?

Corona affects 100% of the population
A test for it is 95% accurate
YOU TEST POSITIVE
What is the chance you have Corona?

Anonymous Sat May 2 20:51:04 2020 No.11630358

>>11630323
>Sorry sir, but even though I tested positive for coronavirus there's only a 0.0000000001% chance I have sir, time to go coofing over everyone

Retard, we're not sampling the population at random. Sure if we rattled around the entire country and picked one faggot out of a faggot raffle, SURE then the probability would be <2%. But we are GIVEN a test that will give a false positive 5% of the time. The chance of us getting a false positive is 5%.

>>	Anonymous Sat May 2 20:53:14 2020 No.11630370 >>11630358 Do you see any difference between the two situations >>11630355

Anonymous Sat May 2 21:13:04 2020 No.11630414

>>11629529
https://en.wikipedia.org/wiki/False_positive_paradox

the problem is "95% accuracy" doesn't really mean anything. its not using the right language to describe the situation, so it sounds like it means 95% chance you have corona but it doesn't.

>>	Anonymous Sat May 2 21:52:02 2020 No.11630557 >>11629638 0.999 = 1

>>	Anonymous Sat May 2 21:53:00 2020 No.11630563 >>11630557 0.999...=1 0.999 and 1 have a 0,001 difference.

>>	Anonymous Sat May 2 22:59:39 2020 No.11630797 >>11629529 Positive predictive value is shit since prevalence is low so who cares

>>	Anonymous Sat May 2 23:28:43 2020 No.11630853 >>11629594 Would the answer be different if you didn't know the % of population having the virus?

>>	Anonymous Sun May 3 00:02:37 2020 No.11630943 >>11630212 How many States are there in the 50 States of the USA?

>>	Anonymous Sun May 3 00:25:28 2020 No.11630999 File: 19 KB, 640x726, 1588276967421.jpg [View same] [iqdb] [saucenao] [google] >>11629529 D is not the correct answer. The correct answer is indeed 1.87% and this anon >>11629818 did a good job explaining why. >>11629690 Bruh you're way off base.

>>	Anonymous Sun May 3 00:30:04 2020 No.11631007 >>11630557 Nice meme friend. I like it.

>>	Anonymous Sun May 3 00:37:28 2020 No.11631021 The answers in this thread makes /pol/ look intelligent

>>	Anonymous Sun May 3 00:38:55 2020 No.11631025 >>11631021 And you make /pol/ look verbose.

Anonymous Sun May 3 00:47:05 2020 No.11631045

>>11630018
So then it's actually only 90% accurate? Because if it only fails to get the right answer on solid grounds 5% of the time, then that remaining 5% will just randomly go to positive or negative. So then it has the right answer 97.5% of the time.
but if it's only right 95% of the time then it's
>90%: actually knows what it's talking about
>5%: "lol idk" and gets lucky guess
>5%: "lol idk" and gets unlucky guess

>>	Anonymous Sun May 3 00:48:41 2020 No.11631049 >>11630188 Method is correct, I had just accidentally plugged in 95 instead of 99.9 because I wasn't paying attention. See >>11629818

>>	Anonymous Sun May 3 01:31:51 2020 No.11631170 >>11629594 >but we don't know that from the given information It either happens or it doesn't, 50%

>>	Anonymous Sun May 3 01:35:53 2020 No.11631174 >>11629594 >However, we can rewrite P(B) like this: >[math]P(B) = P(B\|A)P(A) + P(B\|\neg A)P(\neg A)[/math Why?

>>	Anonymous Sun May 3 01:49:24 2020 No.11631201 >>11631021 /pol/ is honestly average 143 IQ

>>	Anonymous Sun May 3 01:53:19 2020 No.11631214 File: 13 KB, 768x269, conditional-56edf9de5f9b5867a1c1924c.jpg [View same] [iqdb] [saucenao] [google] >>11631174 Because of pic related. We get P(B∩A) + P(B∩¬A).

Anonymous Sun May 3 02:00:16 2020 No.11631225

>>11629594
P(B|A) is not known. Test accuracy is the percentage of true positives AND true negatives. P(B|A) is only the percentage of true positives.

There is not enough information given to get the exact answer, but the answer is closest to 2% since the percentage of true positives must be less than or equal to the percentage of the population with coronavirus.

TP = x < 0.001
TN = 0.95-x
FN = 0.001-x
FP = 0.05-(0.001-x) = 0.049+x

P(A|B) = TP/(TP+FP) = x/(0.049+2x) = 1/(0.049/x+2) =< 1/(0.049/0.001+2) = 1/51 ~ 1.961%

So the answer is 1/(0.049/x+2) which is between 0 and 1/51.

No Bayes theorem needed.

>>11629581
>>11629596
>>11629618
>>11629623
>>11629690
>>11629696
>>11629699
>>11629762
>>11629983
>>11630060
>>11630143
>>11630999
Wrong.

>>	Anonymous Sun May 3 02:09:39 2020 No.11631243 It’s 95% because it could be a false positive

>>	Anonymous Sun May 3 02:10:00 2020 No.11631244 https://youtu.be/JZ31Dj5t4uk?t=131 ,,

>>	Anonymous Sun May 3 02:13:53 2020 No.11631251 >>11631244 Ex bush official is a fucking liberal What else is new

Anonymous Sun May 3 02:15:03 2020 No.11631255

>>11629529
>Corona affects 0.1% of the population
Are we talking about reality here because that's clearly wrong. If we're talking a theoretical mathematical situation question than sure the outcome is crazy low because 0.1% is given.

The question should be rewritten 'Corona has infected 0.1% of the population' to be more accurate to reality since the R factor for Covid is estimated as high as 6.

Shit travels by goddamned air conditioning for hell's sake.
https://wwwnc.cdc.gov/eid/article/26/7/20-0764_article

>>	Anonymous Sun May 3 02:22:27 2020 No.11631276 >>11631255 At most you have an x/(0.05+x) chance of having the virus given you got a positive test result, where x is the infection rate. So even if 10% of the population has it, that's only a 2/3 chance you have it.

>>	Anonymous Sun May 3 02:26:09 2020 No.11631286 >>11630121 the irony the post

Anonymous Sun May 3 02:31:09 2020 No.11631291

>>11631225
x is 0.00095 bro. Everyone itt has been working on the basis that "95% accurate" means that 95% of the time the test will be positive for someone with the disease and negative for someone without it. If you want to argue semantics instead of mathematics just so you can say everyone else is wrong then that's up to you.

>>11631255
>Are we talking about reality here

No, it's just a topical example of a counter-intuitive probability problem.

Anonymous Sun May 3 02:33:01 2020 No.11631295

>>11629529
Out of everyone with corona, 95% of them test positive.
Out of everyone without corona, 5% of them test positive.

0.9% have corona, 0.1% do not.

Out of 0.1%, 95% test positive, and 5% test negative.
Have & pos = 0.095%
Have & neg = 0.005%
Out of 0.9%, 95% test negative and 5% test positive.
Don't have & pos = 0.045%
Don't have & neg = 0.855%

So 0.095% out of 0.095% + 0.045%, right?

I don't know the Bayesian theorem, so I'd like to know if I'm making an error.

>>	Anonymous Sun May 3 02:34:48 2020 No.11631296 >>11631295 >0.9% have corona, 0.1% do not. switched those around

Anonymous Sun May 3 02:34:48 2020 No.11631297

>>11629529
>.1% of people have it
We want P(Has Corona | Tested Positive), so P(A) will be probability of having coronavirus and P(B) is the probability of testing positive.
>95% of them test positive
P(A) is 0.001, as given in the problem.
>therefore .095% of people test positive and are positive
Motherfucker
>95% of people don't have it
P(A) is 0.001, as given in the problem.
We know:
P(B|¬A)=0.05
and
P(¬A)=0.999
>5% of them test positive
Suck my balls retard
>4.75% of people test positive and don't have it
It is because of Bayes' Theorem. But intuitively, the reason why the chance of really having the virus is so low is because the low rate of the virus in the population vastly outweighs the relative accuracy of the test.
It's given in the problem that P(A), the probability of having coronavirus without any other prior information, is 0.001. So it must necessarily be true that the probability of not having coronavirus, without any other prior information, is 0.999.
Fuck your mother
If it means that if you take a million people with the virus, test them all, you'll get 950k positives, then it is a 2% chance you have it.
Under no circumstance is it 1.87%
0.999...
Therefore the answer is A
QED dumbfucks

>>	Anonymous Sun May 3 02:35:49 2020 No.11631302 >>11631295 >0.9% have corona, 0.1% do not. You're working with percentages, my man. Those need to sum to 100, not 1.

>>	Anonymous Sun May 3 02:41:00 2020 No.11631312 Gentlemen, ever wondered why spaceships sometimes blow up? Well, here is why >>11631295 >>11631291 >>11631276 >>11631255 >>11631225 >>11631214 >>11631174 >>11631045

>>	Anonymous Sun May 3 02:49:30 2020 No.11631325 >>11629764 It's literally not. What proportion of the population has no effect on the test's accuracy. In the real world you run multiple tests. This is why 1 kit =/= 1 test =/= 1 person tested.

>>	Anonymous Sun May 3 02:53:33 2020 No.11631335 File: 19 KB, 657x527, apu unimpressed.png [View same] [iqdb] [saucenao] [google] >it's a '/sci/ argues over a poorly worded question' thread

>>	Anonymous Sun May 3 02:53:50 2020 No.11631336 >>11631312 In the real world: Shifting the wings back causes the whole fucking plane to tilt up. Software is installed to adjust for it. Something goes wrong. Planes falling out of sky

>>	Anonymous Sun May 3 02:55:11 2020 No.11631339 >>11631335 >Imagine learning LaTeX just to make the frog look better.

Anonymous Sun May 3 03:07:25 2020 No.11631359

>>11631295
The big problem with your thinking is that it doesn't take into account the rate of Coronavirus among the general population. If you're testing 1 million random people with a uniform .1% Coronavirus distribution (1000 people with COVID19, 999,000 without), your 95% positive rate for Coronavirus patients who test positive is going to be a smaller overall population than the 5% of the false positives.

(49,500 false positives vs 950 true positives)

This would make your overall likelihood of having the disease the number of true positives divided by the total number of test positives (950/(49500+950)) ~ 1.8%.

The actual population size tested is totally arbitrary and as the population size grows larger and larger you approach a limit "true positive" rate of about 1.87% chance that a positive test result is indicative of actually having the Coronavirus.

>>	Anonymous Sun May 3 03:20:55 2020 No.11631393 >>11631302 Ah, that was it! Thank you.

Anonymous Sun May 3 03:29:33 2020 No.11631410

0.1% have
99.9%, therefore, do not.
95% of the tests are right
and 5% are not.
So,
have&positive = 0.1%*95% = .095%
have&negative = 0.1%*5% = .005%
not have&positive = 99.9%*5% = 4.995%
not have&negative = 99.9%*95% = 94.905%

you know that you tested positive, so the chance that you have it is equal to the chance that you're in the "have&positive" category rather than "not have&positive".

That is, %.095/(.095% + 4.995%) = 1.866%

>>	Anonymous Sun May 3 03:39:47 2020 No.11631434 >>11629699 >50 out of 1000 people get a false positive and you are one of them, it means you have a 2% chance of having it What about false negatives?

>>	Anonymous Sun May 3 03:41:38 2020 No.11631436 File: 27 KB, 590x444, ffs.jpg [View same] [iqdb] [saucenao] [google] >>11629594 >mfw I give the correct explanation in the 3rd post and come back to 107 replies

>>	Anonymous Sun May 3 03:44:18 2020 No.11631443 Question has four possible answers 5% of people answer question 10% answer correctly 80% are lawn mower mechanics 17% of lawn mower mechanics are aliens How many answered the question correctly? Let the games begin.

>>	Anonymous Sun May 3 03:45:28 2020 No.11631445 >>11631443 37% of lawnmower aliens

>>	Anonymous Sun May 3 03:47:06 2020 No.11631446 >>11629529 My issue with the problem is deciphering what a "95% accurate" test means when you need to factor in both false positives and negatives

>>	Anonymous Sun May 3 03:48:38 2020 No.11631447 >>11629762 assume nobody has the virus the test is 95% accurate 5% of those tested will be positive even though nobody is infected

Anonymous Sun May 3 03:53:52 2020 No.11631454

>>11631436
>be lawn mower mechanic from planet Buttplug
>Given childishly simple problem
>Make a mountain out of a molehill
>Still gets the wrong answer
>"hurr I am so smart"
>goes back to fixing lawn mower
>try to fit sparkplug into carburetor because "muh superior reasoning skills!"

I guess it must be sort of blissful, being so stupid.

>>	Anonymous Sun May 3 03:59:03 2020 No.11631461 >>11630212 >he likehood that you have a huge ass tumor in your body is 99.9% more like 99.99999 from what you describe your test is not shit

Anonymous Sun May 3 04:10:58 2020 No.11631482

>>11631454
it's literally a template problem for Bayes' Theorem. the problem is the same but the wording is changed to coronavirus for muh relevance

you get this kind of problem in literally every intro statistics course taught in literally every college in the world. the answer is 1.86%. if you don't believe me, write up a monte carlo experiment in R or MATLAB or Python or whatever and see what rate you get.

>>	Anonymous Sun May 3 04:15:59 2020 No.11631486 >>11631297 please rewrite your schizo post and redo your calculations

Anonymous Sun May 3 09:06:56 2020 No.11632102

>>11631291
>x is 0.00095 bro. Everyone itt has been working on the basis that "95% accurate" means that 95% of the time the test will be positive for someone with the disease and negative for someone without it.
Yes, so that means

P(true positive or true negative) = 0.95

Now how do you get from there to

P(true positive|true positive or false negative) = 0.001*0.95?

Anonymous Sun May 3 09:11:41 2020 No.11632110 [DELETED]

>>11629529
Imagine we have a sample of 10 million people. 0.1% have the disease, so 10 000 000 * 0.001 = 10 000, so 10 000 people have the disease.
5% of people test positive, so 10 000 000 * 0.05 = 500 000 people test positive. Of those 500 000, 10 000 will have the disease.
So if you test positive, your chance of having the disease is 10 000 / 500 000 = 1 / 50 = 2%

Anonymous Sun May 3 09:20:12 2020 No.11632125

>>11631295
>Out of everyone with corona, 95% of them test positive.
incorrect. Accuracy is the percentage of true positives and true negatives among the tests.

Let's say the population has 1000 people. This means 1 person has coronavirus. This person either got a true positive or false negative and is the only person who could get these results.

If they got a TP then TP = 1 and FN = 0. Since accuracy = TP+TN and 950 tests have these results, TN = 949. The rest of the population must have FP = 50. This means someone who got a TP or FP has a 1/(1+50) chance of being a TP.

If they got a FN then TP = 0 and FN = 1. Since accuracy = TP+TN and 950 tests have these results, TN = 950. The rest of the population must have FP = 49. This means someone who got a TP or FP has a 0/(0+50) chance of being a TP.

So we see the answer can range from 0 to 1/51, depending on whether the test is more likely to give false negatives or false positives.

>>	Anonymous Sun May 3 09:21:32 2020 No.11632129 >>11631312 Please explain what was wrong with >>11631225 >>11631276

>>	Anonymous Sun May 3 09:24:58 2020 No.11632134 >>11629529 >For how smart /sci/ is, they still refuse to use a calculator https://qz.com/1848674/how-to-interpret-the-specificity-sensitivity-of-antibody-tests/?

>>	Anonymous Sun May 3 09:26:47 2020 No.11632138 File: 27 KB, 573x311, p.png [View same] [iqdb] [saucenao] [google] >>11629529

>>	Anonymous Sun May 3 09:29:32 2020 No.11632143 >>11631286 hurr durr

Anonymous Sun May 3 09:31:27 2020 No.11632145

>>11631359
>your 95% positive rate for Coronavirus patients who test positive
Incorrect. See >>11632125

>>11631410
>have&positive = 0.1%*95% = .095%
How can you assume that the proportion of true positives among positives is equal to the proportion of true negatives among negatives? What if the test produces no true positives and the 95% of test results that are accurate are all true negatives? Then your chance of having the disease after getting a positive test is 0. There is not enough info to answer the question.

>>	Anonymous Sun May 3 09:32:10 2020 No.11632147 >>11632125 >ctrl+f >range >1 result That's your answer

>>	Anonymous Sun May 3 09:32:29 2020 No.11632148 >>11631436 Then please explain how you know P(B\|A) = 0.95

>>	Anonymous Sun May 3 09:34:23 2020 No.11632153 >>11631251 >i have no self-awareness

Anonymous Sun May 3 09:35:21 2020 No.11632156

>>11631312
There is a group of coronavirus 'truthers' who think the whole thing is overblown by the media. These dumb fuck right wing inbred morons are doing shit like
https://www.bbc.com/news/world-us-canada-52496514
Some of those dumbasses are probably in this thread or others like it.

I made a reasonable point that the question does not reflect reality because 'corona' does not in fact only affect .1% of the population. I don't see how pointing that out makes me someone who will cause spaceships to explode.

Anonymous Sun May 3 09:36:45 2020 No.11632159

>>11629529
The chance of testing positive while being positive is 0.1% * 95%, the chance of testing positive while being negative is 99.9% * 5%. The chance of being positive while testing positive is the ratio between testing positive and being positive, and the sum of the two probabilities.
In this case, [math]\frac{0.095\%}{5.09\%} = 1.866\%[/math]

Anonymous Sun May 3 09:38:32 2020 No.11632162

>>11631482
>it's literally a template problem for Bayes' Theorem.
It literally isn't since you can't determine P(positive test|coronavirus) from the information given.

The problem is much more easily understood by dividing the population into true positives, true negatives, false positive and false negatives.

The information given is the following:

TP+FN = 0.001
TP+TN = 0.95
TP+TN+FP+FN = 1

We want to find TP/(TP+FP) but all we can determine is that this ranges between 0 and 1/51.

>>	Anonymous Sun May 3 09:40:33 2020 No.11632165 >>11632156 >'corona' does not in fact only affect .1% o 0.1 * 1/100 * 327M = 0.327M ok so it's about 0.5%, now what?

>>	Anonymous Sun May 3 09:41:49 2020 No.11632170 >>11632162 This seems right to me, but what's the formal name for this kind of math?

>>	Anonymous Sun May 3 09:43:33 2020 No.11632177 >>11632110 >5% of people test positive How do you get this from the information in the problem? The percentage of positive tests ranges between 4.9% and 5.1%, depending on whether the test is biased towards false positives or false negatives.

>>	Anonymous Sun May 3 09:44:51 2020 No.11632179 >>11632138 P(sick and positive) = 95% Incorrect. See >>11632125

>>	Anonymous Sun May 3 09:47:30 2020 No.11632187 >>11632179 >P(sick and positive) = 95% is correct prompt gives "A test for it is 95% accurate."

>>	Anonymous Sun May 3 09:49:39 2020 No.11632192 >>11632147 You should have looked for between as well: >>11631225

>>	Anonymous Sun May 3 09:51:56 2020 No.11632199 >>11632159 >The chance of testing positive while being positive is 0.1% * 95% Incorrect, see >>11632125

>>	Anonymous Sun May 3 09:52:59 2020 No.11632202 >>11632170 Statistics? https://en.wikipedia.org/wiki/Positive_and_negative_predictive_values

>>	Anonymous Sun May 3 09:54:21 2020 No.11632206 >>11632187 That means 95% of tests are true positives or true negatives. How do you get to a statement only about true positives?

>>	Anonymous Sun May 3 10:00:43 2020 No.11632218 >>11632199 out of 1000 people, with an accuracy of 95% and a rate of 0.1% of infection, your expected positive rate is in the range of 51-49 people

>>	Anonymous Sun May 3 10:01:34 2020 No.11632221 >>11632202 What I was looking for was calculated risks, which is a proper subset of statistics

>>	Anonymous Sun May 3 10:01:43 2020 No.11632222 >>11632206 95% accurate for healthy = 95 neg + 5 pos 95 % accurate for sick = 5 neg + 95 pos

>>	Anonymous Sun May 3 10:05:40 2020 No.11632228 ITT. Get a load of these retards unable to answer a simple question

>>	Anonymous Sun May 3 10:06:39 2020 No.11632229 >>11632228 Not having the correct answer up on a list of multiple choice really fucks with people Just look at all the troll IQ threads

Anonymous Sun May 3 10:09:25 2020 No.11632234

>>11632222
How do you know the test is equally accurate for healthy and sick people? Accuracy of the test are these results combined. The test could be 0% accurate for sick people and 95.1% accurate for healthy people and still have a total accuracy of 95%. You're assuming information not given.

>>	Anonymous Sun May 3 10:10:38 2020 No.11632236 >>11632234 >Accuracy of the test are these results combined [citation needed]

>>	Anonymous Sun May 3 10:14:05 2020 No.11632247 >>11632236 From the OP: >A test for it is 95% accurate Is that 5% false positive? If so, what about false negatives? You physically can't decouple that into two figures without more information, and as such only a range will be correct

>>	Anonymous Sun May 3 10:15:14 2020 No.11632252 >>11629529 >Why is that? because you get a shitload of false positives from the 99.9% part, the healthy ones

>>	Anonymous Sun May 3 10:15:55 2020 No.11632255 >>11632218 Yes. So the chance of testing positive while being positive is TP/(TP+FN) which ranges from 0 to 1.

>>	Anonymous Sun May 3 10:16:57 2020 No.11632258 >>11632236 Here you go: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4614595/

>>	Anonymous Sun May 3 10:17:37 2020 No.11632261 >>11632247 yes, assuming the 95% is about "you" no matter if "you" are healthy or sick

>>	Anonymous Sun May 3 10:19:36 2020 No.11632265 >>11632258 well, not the prompt, so idgaf

>>	Anonymous Sun May 3 10:23:55 2020 No.11632282 >>11632265 It's basic terminology for statistics and diagnostic testing: https://en.wikipedia.org/wiki/Sensitivity_and_specificity If you aren't willing to interpret the prompt correctly then don't attempt to answer the problem.

>>	Anonymous Sun May 3 10:25:10 2020 No.11632286 >>11632125 >et's say the population has 1000 people. Wouldn't the probability change as you scaled this up? Wouldn't you get a different answer if you had a population of 10,000 with 10 CV?

>>	Anonymous Sun May 3 10:25:45 2020 No.11632291 >>11632282 >interpret the prompt lol, another day another schizo

Anonymous Sun May 3 10:29:23 2020 No.11632299

>>11632286
>Wouldn't the probability change as you scaled this up?
The probability will always be between 0 and 1/51. Just divide the population numbers by 1000 to get proportions.

>Wouldn't you get a different answer if you had a population of 10,000 with 10 CV?
Then TP is between 0 and 10 instead of 0 and 1. Everything scales and you get the same answer.

>>	Anonymous Sun May 3 10:30:24 2020 No.11632305 >>11632291 How does knowing basic statistical terminology make me "schizo?"

>>	Anonymous Sun May 3 10:31:05 2020 No.11632307 >>11632299 Ahh I see my issue. I was trying to solve it with a decimal which gets more accurate as you scale it up

>>	Anonymous Sun May 3 10:35:59 2020 No.11632314 >>11632255 if you have 1 positive in a range of 51-49 that tested positive, the chance of testing positive and being positive is 1.866%

Anonymous Sun May 3 10:45:12 2020 No.11632334

>>11632314
No, the chance of testing positive and being positive is simply the chance of a true positive, which must be less than or equal to the 0.1% chance of being positive.

The question is asking for the chance you are positive *given* you tested positive, which is the precision of the test = TP/(TP+FP).

Anonymous Sun May 3 10:50:53 2020 No.11632346

>>11632102
>so that means P(true positive or true negative) = 0.95

I meant that, whether you have the disease or you don't, if you take the test you have a 95% chance of getting a correct result back. That is:

>if you have coronavirus, then P(test positive) = 0.95
>if you don't have coronavirus, then P(test negative) = 0.95

This is a pretty well-known statistics problem that has just been made topical by making it about the coronavirus and so I'm pretty certain this is how the question is meant to be interpreted. I'm not a biochem/medicine guy though so idk if your interpretation is what "accurate" means in terms of real-world testing.

Anonymous Sun May 3 11:00:34 2020 No.11632374

>>11632346
>meant that, whether you have the disease or you don't, if you take the test you have a 95% chance of getting a correct result back.
Yes, and I'm asking you how you determined that, when the question only tells you that the proportion of correct results is 95%, not the proportion of correct positive results is 95%

If the test never gives true positives to sick people and gives true negatives to 950/999 of healthy people, then the proportion of correct results is 95% but the chance of getting a correct result if you're sick is 0%.

>This is a pretty well-known statistics problem that has just been made topical by making it about the coronavirus and so I'm pretty certain this is how the question is meant to be interpreted.
Yes, it is well known. But you don't seem familiar with it. See https://en.wikipedia.org/wiki/Sensitivity_and_specificity

Anonymous Sun May 3 11:04:56 2020 No.11632386

>>11632374
>the question only tells you that the proportion of correct results is 95%

I'm saying that the test being 95% accurate means that 95% of positives are true positives and 95% of negatives are true negatives. Again, idk if that's the correct terminology used in medicine, but I'm pretty sure that's what the question means.

>>	Anonymous Sun May 3 11:05:28 2020 No.11632390 >>11632334 Of the 49-51 that tested positive, each and every one of them, with the given data, would have a 1.866% chance of being actually positive after testing positive

Anonymous Sun May 3 11:06:24 2020 No.11632394

>>11632386
>I'm saying that the test being 95% accurate means that 95% of positives are true positives and 95% of negatives are true negatives.
It doesn't. Read https://en.wikipedia.org/wiki/Sensitivity_and_specificity or https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4614595/

>>	Anonymous Sun May 3 11:10:00 2020 No.11632402 >>11629529 95.1%

>>	Anonymous Sun May 3 11:10:15 2020 No.11632403 >>11632390 That's impossible. If there are 49 that tested positive then there are 0 that are actually positive. 0 =/= 1.866%. If there are 51 that are positive then there is 1 that is positive. 1/51 =/= 1.866%.

>>	Anonymous Sun May 3 11:11:46 2020 No.11632406 >>11629529 I know this is stupid but: 0.1%

>>	Anonymous Sun May 3 11:12:40 2020 No.11632410 >>11632403 >If there are 49 that tested positive then there are 0 that are actually positive. there's a 95% of having 1 positive testing positive, and 5% of having 1 positive testing negative. The actual range is slightly wider than that

Anonymous Sun May 3 11:12:48 2020 No.11632411

>>11632346
>if you have coronavirus, then P(test positive) = 0.95
>if you don't have coronavirus, then P(test negative) = 0.95
The issue I think many are having is that the false positive and false negative rates are almost never the same, to the point where they are always distinct figures

>>	Anonymous Sun May 3 11:13:53 2020 No.11632413 >>11632394 Bruh read my second sentence. If you want to be a stickler for definitions and say the answer is "yuo can't know!!1", then that's fine, but everyone else seems to be content with the other interpretation.

>>	Anonymous Sun May 3 11:15:11 2020 No.11632418 >>11629529 >all these brainlets The chance is still 0.1% >muh P(A\|B) Thats only about how certain you are you have it, not the chance you actually have it.

>>	Anonymous Sun May 3 11:17:56 2020 No.11632425 >>11632410 >there's a 95% of having 1 positive testing positive No, there's a 95% chance of having a test be true. The chance of a positive testing positive is completely unknown and between 0 and 100%.

>>	Anonymous Sun May 3 11:19:08 2020 No.11632429 >>11632413 Everyone else is wrong. Their being content is irrelevant. If you can't accept fundamental statistical definitions then don't attempt statistics.

>>	Anonymous Sun May 3 11:24:48 2020 No.11632454 >>11629529 So 5% of the 0.1% is actually free of covid? or is the 0.1% the 100% fact?

Anonymous Sun May 3 11:25:51 2020 No.11632460

>>11632429

Get over yourself m8. Your interpretation is wrong because it gives uncountably many solutions to a *multiple choice* question. D was definitely meant to be the correct answer and I know that because I was in the /b/ thread where this image was first posted (the OP made an error in his calculations to get 2%, but definitely intended for that to be the answer). Your interpretation cannot give an exact answer.

Anonymous Sun May 3 11:37:53 2020 No.11632500

>>11629529
If you test positive and the accuracy of the test is 95% then the chance you having it is 95%. Which is answer B.

Since it affects 0.1% of the population then the chance of it affecting you is 0.1% of 95% chance that you actually have it, which is 0.95% ( an answer not provided in the multi-choice selection ). But this is entirely irrelevant, since the question concerns the chance you have it, not the chance you are affected by it.

I really dont see what is so difficult about this problem and why some people are making it seem so complicated.

Anonymous Sun May 3 11:51:57 2020 No.11632550

>>11632162
>It literally isn't since you can't determine P(positive test|coronavirus) from the information given.
95%
>NOOOO BUT W-WE DON'T KNOW P(positive|not corona)
5% because the test is 95% likely to give you a true result, 5% is a false result.
You are just mad that you couldn't figure it out at first and will argue nonstop about wording.
>TP+FN = 0.001
>TP+TN = 0.95
Ok so you are just retarded and passed statistics with a pity score, if not that you have never taken statistics

Anonymous Sun May 3 11:56:42 2020 No.11632565

>>11632425
>The chance of a positive testing positive is completely unknown and between 0 and 100%.
From the given data in the problem
>A test for it is 95% accurate.
with 95% accuracy, you have 95% chance of a positive testing positive, or a negative testing negative, and a 5% chance of a positive testing negative or a negative testing positive as the base definition of the problem's parameters.

Anonymous Sun May 3 12:01:30 2020 No.11632580

>>11632460
>Your interpretation is wrong because it gives uncountably many solutions to a *multiple choice* question.
All the multiple choice answers are incorrect, what is your point?

>Your interpretation cannot give an exact answer.
LOL and your (wrong by definition) interpretation gives an exact answer that is not any of the choices.

Anonymous Sun May 3 12:20:56 2020 No.11632638
File: 27 KB, 640x359, 626.jpg [View same] [iqdb] [saucenao] [google]

>>11632580

Dude do you ever read the entirety of the post you're replying to before you start typing your rant? I acknowledged that D is incorrect, but it was INTENDED to be the correct answer. The OP of the thread miscalculated the probability and the anons in that thread explained why D should be 1.87% instead. Your interpretation literally cannot give an exact answer and I can't believe you're still pathetically trying to insist it's the right one.

Anonymous Sun May 3 12:21:03 2020 No.11632640

>>11629529
when you start using words in a formal mathematical meaning, you are no longer at liberty to employ grammatical flexibility. in particular, "being 95% accurate" has no defined meaning, and if you mean "has an accuracy of 95%", then you should state this in *exactly* those words, unless you are trolling.

>>	Anonymous Sun May 3 12:21:12 2020 No.11632642 >>11629529 the chance is 0% because I don't have coronavirus

Anonymous Sun May 3 12:25:31 2020 No.11632665

>>11632500
>If you test positive and the accuracy of the test is 95% then the chance you having it is 95%. Which is answer B.
>I really dont see what is so difficult about this problem and why some people are making it seem so complicated.
Peak midwit. Learn Baye's theorem, retard.
>affected
>have it
You are right about this one, it's different data, exercise worded wrong. But you demonstrated you don't know statistics already.
>>11632394
>>11632638
>95% of positives are true positives and 95% of negatives are true negatives.
Yeah, that's what the exercise means, but usually measuring IRL like https://en.wikipedia.org/wiki/Sensitivity_and_specificity will give you different sensitivity and specifity. If they are different then the problem is unsolvable.
But Mr. Sperglord is so far up his ass to know what you mean

Anonymous Sun May 3 12:51:12 2020 No.11632719

>>11632638
>Dude do you ever read the entirety of the post you're replying to before you start typing your rant? I acknowledged that D is incorrect, but it was INTENDED to be the correct answer.
Then why are you referring to the question being multiple choice as if it has any bearing on my answer? This is as irrelevant as saying D is 2% not 1.87%

>Your interpretation literally cannot give an exact answer
Because the question has no exact answer. I'm sorry you thought you had the correct interpretation because you got an exact answer, but it's wrong. Instead of getting mad about it just accept it or counterargue. Instead you just spout irrelevancies.

>>	Anonymous Sun May 3 12:52:14 2020 No.11632722 >>11632640 >"being 95% accurate" has no defined meaning Wrong: see either link in >>11632394

>>	Anonymous Sun May 3 12:53:42 2020 No.11632726 >>11632550 >95% No that's P(true positive or true negative) >Ok so you are just retarded and passed statistics with a pity score, if not that you have never taken statistics Not an argument, try again.

>>	Anonymous Sun May 3 12:54:44 2020 No.11632729 >>11632565 >with 95% accuracy, you have 95% chance of a positive testing positive Wrong. Look up the definition of test accuracy.

Anonymous Sun May 3 13:06:41 2020 No.11632760

>>11632719
>multiple choice as if it has any bearing on my answer?

Because a multiple choice question is obviously meant to have just one answer. Your interpretation gives uncountably many solutions. I can promise you that the OP who created the question meant "accurate" to mean the interpretation I (and everyone else except you) have used. You are WRONG. It's not a matter of opinion, the OP straight up explained his meaning in the /b/ thread. Your arrogance does not change that.

Anonymous Sun May 3 13:09:20 2020 No.11632768

>>11632760
>Because a multiple choice question is obviously meant to have just one answer.
Are you completely illiterate? The question was also meant to have 2% as its answer but you seem fine contradicting that.

You are WRONG by definition. No amount of projection, special pleading, or appeal to majority will change that.

>>	Anonymous Sun May 3 13:15:31 2020 No.11632787 >>11632729 Right. Look up the definition of autism.

>>	Anonymous Sun May 3 13:16:19 2020 No.11632793 >>11632665 You confused sensitivity with accuracy. Get over it, it's not my fault you can't read.

>>	Anonymous Sun May 3 13:18:01 2020 No.11632799 >>11632787 >he proved me wrong, I better call him autistic to save face Stay mad.

>>	Anonymous Sun May 3 13:20:03 2020 No.11632806 >>11629529 I'm kinda retarded but I don't see how it's anything but 0.1%. It says it right there.

>>	Anonymous Sun May 3 13:20:59 2020 No.11632810 >>11632799 >he proved me wrong lol, ok sweetie

>>	Anonymous Sun May 3 13:21:20 2020 No.11632813 >>11632793 >>11632729 Wrong, it means 95% of the times it is true. Which is the same thing as >>11632565 said. Shut up autistic kid

>>	Anonymous Sun May 3 13:32:18 2020 No.11632848 >>11632768 >The question was also meant to have 2% as its answer No it wasn't. The OP messed up his calculations and even accepted in the /b/ thread that it should have been 1.87%.

Anonymous Sun May 3 13:42:57 2020 No.11632884

>>11632806

It changes because if you have the disease you have a higher chance (95%) of testing positive than if you don't have it (5%). You are then in a position when you have to calculate the probability of a true positive vs a false positive and this is not the same as the 0.1% chance you had before taking the test.

>>	Anonymous Sun May 3 13:54:52 2020 No.11632919 >>11632806 >>11632884 I'm extremely retarded and somehow missed the text that says you test positive.

Anonymous Sun May 3 13:55:55 2020 No.11632922

>>11632665
Seriously, why are you introducing Baye's theorem to a problem which is elementary, childish even? I think you have had an overdose of Dunning Kruger. Try reading the question again. What is it asking you? What relevant information are you given?

Look, I will even rephrase the problem for you. Exact same problem, just different words.

You are playing a single game of chance.
If you win there is 0.1% chance you will die.
There is a 95% chance of winning
You win.
What was the chance of you winning?

Gee, its like asking how many apples are there in a box containing ten apples.

Maybe it will make more sense to you now. Or perhaps it will once you start taking your meds again, lol, you stupid motherfucker.

>>	Anonymous Sun May 3 14:09:51 2020 No.11632967 >>11632922 >trying this hard

Anonymous Sun May 3 14:23:26 2020 No.11633009

>>11629529
You take a test, it confirms you as postive. This is untrue 5% of the time. Thusly, irrespective of any population of infected people less than 95%, there is a ~95% chance you are infected. However, in a population with 100% infection, obviously, you have a 100% chance. At certain rates it is more likely the test is wrong than you are actually uninfected. This seems like a far more complex problem than it immediately appears.
HOWEVER, irrespective of any possibilities, if you test positive, there is a minimum 95% chance you are infected, no ifs ands or buts, its directly stated and any other way of looking at it is brain dead retarded.

>>	Anonymous Sun May 3 14:27:45 2020 No.11633019 >>11632162 finally someone who knows what they are talking about. /sci/ is a shitshow when it comes to any sort of real math or science.

>>	Anonymous Sun May 3 14:31:26 2020 No.11633030 File: 461 KB, 917x681, 1542956225200.jpg [View same] [iqdb] [saucenao] [google] >this thread Conditional probability threads are really the GOAT shitposts you can make on /sci/. Not even .999... threads can hold a candle to them.

Anonymous Sun May 3 14:33:24 2020 No.11633040

>>11633009
>You take a test, it confirms you as postive. This is untrue 5% of the time.
Thats if you take 5% to be the false positive rate. Remember that false negatives also exist. If instead you take 95% it to mean the proportion of true positives and true negatives out of the total (which makes more sense), you get 1/51 (assuming 0 false negatives)

>>	Anonymous Sun May 3 14:35:44 2020 No.11633048 >>11633040 I worded this in a way that sounds a bit contradictory >Remember that false negatives also exist would be better as >Remember that true and false negatives also exist

>>	Anonymous Sun May 3 14:36:54 2020 No.11633052 >>11631436 its wrong though.

>>	Anonymous Sun May 3 14:39:57 2020 No.11633061 >>11632722 "has an accuracy of 95%" IS defined, "is 95% accurate" is not.

Anonymous Sun May 3 15:00:53 2020 No.11633126

>>11633040

Wow you really don't understand how percentages work. If 95% of positives are true positives and 95% of negatives are true negatives, then the total proportion of true positives and negatives is *still* 95%. You don't add the true positives and negatives together to work out the overall proportion.

>>	Anonymous Sun May 3 15:05:47 2020 No.11633145 >>11632813 >Wrong, it means 95% of the times it is true. Yes, you realize the test can be true without giving a positive result, right?

>>	Anonymous Sun May 3 15:09:41 2020 No.11633156 >>11632848 >The OP messed up his calculations Just like you did. The answer is indeterminate, get over it.

>>	Anonymous Sun May 3 15:11:41 2020 No.11633162 >>11633009 >You take a test, it confirms you as postive. This is untrue 5% of the time. Incorrect. You're confusing accuracy with sensitivity.

Anonymous Sun May 3 15:23:12 2020 No.11633212

>>11633126
>Wow you really don't understand how percentages work. If 95% of positives are true positives and 95% of negatives are true negatives,
you're an idiot. thats not what 95% accuracy means and no where did I add together any percentages. I added together counts. "true positives" is a count, not a percentage.

>>	Anonymous Sun May 3 15:28:04 2020 No.11633228 it babbies argue about most basic high school bayesian problem

>>	Anonymous Sun May 3 15:29:06 2020 No.11633232 This question is the utlimate bait question. Even better than conditional probability ones, because it baits fags who passed high school statistics into misapplying conditional probability.

Anonymous Sun May 3 15:29:20 2020 No.11633234

>>11633126
>If 95% of positives are true positives and 95% of negatives are true negatives, then the total proportion of true positives and negatives is *still* 95%.
That's still wrong. It's impossible for 95% of positives to be true because there have to be a lot more false positives than true positives for the test accuracy to be 95%.

TP = x =< 0.001
TN = 0.95-x
FN = 0.001-x
FP = 0.05-(0.001+x)

TP/(TP+FP) = x/(0.049+2x) =< 0.001/(0.049+0.002) = 1/51

>>	Anonymous Sun May 3 15:30:19 2020 No.11633239 >>11629594 based and redpilled

>>	Anonymous Sun May 3 15:30:48 2020 No.11633244 >>11633156 your father is indeterminate, get over it

Anonymous Sun May 3 15:30:54 2020 No.11633245

>>11632145
The problem with your reasoning is that you cannot have a test with a constant "accuracy" as you are describing. You're essentially taking for granted a constant accuracy and working backwards to solve for sensitivity and find the proportion from there but it isn't possible for a test like this to have a dynamic sensitivity and constant accuracy in the way you are describing. Accuracy for a test will always be a function of the input sample sizes and thus will be dynamic, where as sensitivity deals with the physical properties of the test and will be determined by factors dealing with the test methodology, not something which can be dependent on the sample size as your reasoning implies. Maybe in an abstract mathematical sense there could be a dynamic sensitivity test, but a test with dynamic sensitivity in practice would produce something with very little utility because you would have no way of determining the accuracy afterwards as a function of sensitivity/sample size. Accuracy of a test is not something which can be knowable and fixed independent of the properties of the sample space in the way sensitivity is.

Basically you're doing the problem backwards and then saying everyone is wrong. While everyone else (including myself) used the "95% accurate" statement to imply 95% sensitivity because a static accuracy and dynamic sensitivity doesn't make sense, you basically just took the poor wording as license to solve a completely incoherent problem.

Anonymous Sun May 3 15:50:42 2020 No.11633306

>>11633245
>The problem with your reasoning is that you cannot have a test with a constant "accuracy" as you are describing.
Accuracy in general just describes the proportion of true test results among all evaluated cases. What sample size is it dependent on?

>it isn't possible for a test like this to have a dynamic sensitivity
I didn't say it has dynamic sensitivity, I said the sensitivity is unknown.

Your entire post is pretty silly since accuracy can be calculated from specificity, sensitivity, and prevalence. So if you claim that specificity and sensitivity are constants based on physical properties of the test, then accuracy must be as well.

>>	Anonymous Sun May 3 15:53:06 2020 No.11633312 >>11629594 Christ I hope you are never given any responsibility for anything, moron.

>>	Anonymous Sun May 3 15:55:32 2020 No.11633320 >>11631225 Schizo detected

>>	Anonymous Sun May 3 15:56:42 2020 No.11633324 >>11633320 Impressive, did you think of that response all by yourself?

Anonymous Sun May 3 16:29:05 2020 No.11633431

>>11633306
The proportion of true test results evaluated among all cases is inherently dependent on the proportions of the true/false positives which are dependent on your sample space. You can't have a fixed accuracy test because one test cannot produce a situation where eg. a 99% sensitivity when applied to one group of samples and a 90% sensitivity when applied to a different group. That would essentially provide you an uninformational test because it relies on knowledge of the number of "true positives" without having a reference to the proportion of positives among your test population (eg what sensitivity would tell you) prior to running the test in your sample set.

Think of it this way. If you had a test with a fixed accuracy, it would require the testing methodology (which determines the sensitivity/specificity) to change depending on the sample proportions. That doesn't make sense for an actual test because changing the testing methodology to fit a fixed accuracy rate presupposes "true positive" population information that you can't have prior to running the test.

>>	Anonymous Sun May 3 16:29:45 2020 No.11633433 >>11633145 >you realize the test can be true without giving a positive result, right? Is what >>11632565 said you pathetic autist, imagine trying to correct people but being unable to read

Anonymous Sun May 3 16:36:08 2020 No.11633445

>>11633306
>Accuracy in general just describes the proportion of true test results among all evaluated cases.
exactly. out of all tests, whether the test came back positive or negative, 95% of them were correct. The test can be true even if the result is negative.

Theres actually a wikipedia page for this exact problem, and below I will basically be rewording the examples they give on the wikipedia page
https://en.wikipedia.org/wiki/False_positive_paradox

Assume there are no false negatives, which we have to do because one "accuracy" figure is not enough to completely describe the problem, and in general, in the real world, tests for diseases aim for 0 false negatives. Then suppose that the infection rate is 80%. In a population of 100 people, we would expect 80 true positives, 15 true negatives, and 5 false positives. 80 + 15 true tests / 100 gives us the 95% accuracy figure. Then, 80 / 85 = 94% is the probability that you are infected if you test positive.

Now assume the infection rate is 2%. That means that out of 100 people with a 95% accurate test, 2 is a true positive, 93 are true negatives, and the last 5 are false positives. Now the probability that you are infected if you test positive is a mere 2/6 = 33%

If we assume false negatives is nonzero, then the chance that you are infected if you test positive goes down. E.g. in the second case, if we make 1 true positive into a false negative, that means that now we have 1 false negative, 1 true positive, 94 true negatives and 4 false positives. Now the chance that you are infected if you test positive is 1/4 = 25%.

>>	Anonymous Sun May 3 16:38:53 2020 No.11633450 File: 32 KB, 1298x539, Untitled.png [View same] [iqdb] [saucenao] [google] >>11629529 I'm 18 and was withdrawing from caffeine at the time of doing this, what's my IQ

>>	Anonymous Sun May 3 16:41:06 2020 No.11633460 >>11633450 Oops it should be 10/509.5, around same answer though, ~2%

Anonymous Sun May 3 16:42:37 2020 No.11633466

>>11633431
>The proportion of true test results evaluated among all cases is inherently dependent on the proportions of the true/false positives which are dependent on your sample space.
It's dependent on prevalence in the population, which is constant.

>You can't have a fixed accuracy test because one test cannot produce a situation where eg. a 99% sensitivity when applied to one group of samples and a 90% sensitivity when applied to a different group.
Again, where did I say the sensitivity changes?

>Think of it this way. If you had a test with a fixed accuracy, it would require the testing methodology (which determines the sensitivity/specificity) to change depending on the sample proportions.
No it wouldn't. Accuracy is determined by sensitivity, specificity, and prevalence. If none of these change, accuracy doesn't change.

Nothing you've said responds to anything I said. Read my post again.

Anonymous Sun May 3 16:46:33 2020 No.11633478

>>11631225
>>11633234
This is so wrong, please go to high school and take basic probability.
>TP = x =< 0.001
Wrong, TP = 0.95 from the problem.
>TN = 0.95-x
TN = 0.95 from the problem
And FN = FP = 0.05 from the problem.
All you have to do is to apply Baye's theorem.
P(corona|positive) = TP * P(corona) / P(Positive)
And P(Positive) = TP*0.001+0.999*FN
Just like the only correct answer that is ~1.87%: >>11629594

>>	Anonymous Sun May 3 16:48:39 2020 No.11633485 >>11633450 >>11633460 nvm it should be 9.5/509.5, it was definitely rounded up in the question because that's like 0.186

Anonymous Sun May 3 16:49:24 2020 No.11633487

>>11633433
LOL, the irony of saying I'm unable to read without being able to read my post correctly. >>11632565 conflated the chance of a positive testing positive (sensitivity) with the chance of a test being true (accuracy). So he in effect ignored that negative tests can be true by saying accuracy = sensitivity.

>>	Anonymous Sun May 3 16:49:32 2020 No.11633488 >>11633312 already do - in no small part because I passed intro stats for my B.S.

Anonymous Sun May 3 16:50:58 2020 No.11633491
File: 14 KB, 368x64, Screen Shot 2020-05-03 at 1.49.28 PM.png [View same] [iqdb] [saucenao] [google]

>>11633478
>Wrong, TP = 0.95 from the problem.
wrong, accuracy is not equal to the proprotion of true positives out of the total tests, and you're blantantly a retard if you think accuracy automatically means 95% of all people tested have corona virus and will test postive.

See:
https://en.wikipedia.org/wiki/Sensitivity_and_specificity

pic related. accuracy is well defined and you chose perhaps the most retarded way to interpret it.

>>	Anonymous Sun May 3 16:51:15 2020 No.11633492 >>11632148 it's literally given in the problem statement. any other interpretation of the word 'accuracy' renders the problem unsolvable - and "not possible to solve" isn't one of the multiple choice answers

Anonymous Sun May 3 16:54:12 2020 No.11633495

>>11633445
>Assume there are no false negatives, which we have to do because one "accuracy" figure is not enough to completely describe the problem
Then the problem is under-determined. We don't have to assume anything the problem doesn't give us.

Nothing you said responds to anything I said. I already explained how to do the problem by splitting the population into TP, TN, FP, and FN very early in the thread. You are essentially agreeing with me that the vast majority of posts in this thread are wrong.

Anonymous Sun May 3 16:55:26 2020 No.11633499
File: 13 KB, 296x170, school_of_hard_skulls.jpg [View same] [iqdb] [saucenao] [google]

this thread is the strongest evidence that the vast majority of /sci/ has never progressed past high school education

OP's problem is a template used in every single statistics class to explain why Bayes' Theorem is important for understanding counter-intuitive conditional probabilities. Anyone who successfully made it through their first two years of college would have seen this problem before and would understand exactly why the answer is 1.866%

pic related: every /sci/tard's education on Facebook

>>	Anonymous Sun May 3 16:56:32 2020 No.11633502 >>11633478 >Wrong, TP = 0.95 from the problem. LOL, how the fuck can true positives be 95% when positives are only 0.1%??? In order to get a TP, you have to actually be positive. Get the fuck out of here, Dunnin Kruger retard.

>>	Anonymous Sun May 3 16:57:37 2020 No.11633503 >>11633488 So did you forget what accuracy means or did you just never learn it?

Anonymous Sun May 3 16:57:51 2020 No.11633506

>>11633502
>Get the fuck out of here, Dunnin Kruger retard.

How did you solve this question template when you took your college statistics course?

If you're gonna condescend people for not actually having educational qualifications, I really wanna know how you convinced your prof to accept a bullshit answer.

Anonymous Sun May 3 16:58:43 2020 No.11633509

>>11633492
>it's literally given in the problem statement.
It's literally not. Accuracy is not sensitivity.

>any other interpretation of the word 'accuracy'
There is only one interpretation of the word accuracy in the context of statistics and diagnostic tests.

>renders the problem unsolvable - and "not possible to solve" isn't one of the multiple choice answers
So what?

Anonymous Sun May 3 16:59:05 2020 No.11633512

>>11633245
Yeah, accuracy In epidemiology is calculated like this (TP+TN)/(TP+TN+FP+FN).
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4614595/
You don’t have enough information to calculate the positive predictive value in this case. You need to know other data (like sensitivity and specificity) to calculate PPV for the given prevalence or you need to calculate the PPV by PPV = TP/(TP+FP).

Anonymous Sun May 3 17:00:24 2020 No.11633517

>>11633503
The problem is unsolvable unless you assume [math]P(B|A) = 0.95[/math] and [math]P(B|\neg A) = 0.05[/math].

The technical definition for accuracy is that a probability that a test returns the correct outcome for a case. If a truly-sick person gets tested, a 95% accurate test has a 95% probability of saying 'POSITIVE'. If a truly-healthy person gets tested, a 95% accurate test has a 95% probability of saying 'NEGATIVE' - and there a 5% probability of saying 'POSITIVE'.

If you have a different theory for how this works, tell me what you would substitute for these two probabilities and show your work.

Anonymous Sun May 3 17:01:06 2020 No.11633523

>>11633487
>>11633502
>>11633491
>>11633509
>>11633503
Schizo poster detected.
This >>11632565 is 100% true. And you literally can't refute it.
The probability is 1.866%, you have not used Baye's theorem because you are a high school dropout. You can't just sum and rest perentages.
>>11633499
Based, high school dropout schizo seething

>>	Anonymous Sun May 3 17:01:42 2020 No.11633525 >>11633517 I shouldn't listen to music with lyrics while posting because this is riddled with writing mistakes. But you can gather what I'm trying to say here.

Anonymous Sun May 3 17:01:56 2020 No.11633526

>>11633499
This post is a great example of the Dunning-Kruger effect at work. Since you never learned what basic statistical terms mean, you think every problem that looks like conditional probability must be interpreted to be solved by Bayes' Theorem. Accuracy = P(true test|test) =/= P(positive test|positive). Get it through your thick skull.

>>	Anonymous Sun May 3 17:03:04 2020 No.11633530 >>11633523 >Based, high school dropout schizo seething I wrote this post though >>11629594 why are you throwing stones at me? my mockery is directed at everyone else who's trying to wordfuck the definition of accuracy to get a nonsensical answer

>>	Anonymous Sun May 3 17:04:15 2020 No.11633532 I interpret accuracy to mean positive detection vs failing detection, rather than false-positive detection.

Anonymous Sun May 3 17:04:16 2020 No.11633533

>>11633526
>Since you never learned what basic statistical terms mean, you think every problem that looks like conditional probability must be interpreted to be solved by Bayes' Theorem. Accuracy = P(true test|test) =/= P(positive test|positive). Get it through your thick skull.

Alright, so what are the values of these probabilities? Show me how you arrived at your answer.

[math]P(B|A) = ?[/math]

[math][P(B|\neg A) = ?[/math]

Anonymous Sun May 3 17:04:44 2020 No.11633534
File: 11 KB, 574x144, Confusion Matrix.png [View same] [iqdb] [saucenao] [google]

>>11633506
>How did you solve this question template when you took your college statistics course?
By learning what accuracy means: https://en.wikipedia.org/wiki/Confusion_matrix

Anonymous Sun May 3 17:06:59 2020 No.11633538

>>11633534
>By learning what accuracy means: https://en.wikipedia.org/wiki/Confusion_matrix

Cool. so what did you get for:
[math]P(B|A) = ?[/math]
[math]P(B|\neg A) = ?[/math]

I see a lot of seething about how people think this isn't just a Bayes Rule problem but also a complete reluctance to actually write out the individual probabilities they're using to solve this.

>>	Anonymous Sun May 3 17:07:07 2020 No.11633539 >>11633530 But I'm not throwing stones at you. I called you based (Upvote), newfriend. The other one is the high school faggot.

>>	Anonymous Sun May 3 17:08:17 2020 No.11633545 >>11633539 oh that wasn't clear - but cheers regardless

Anonymous Sun May 3 17:10:04 2020 No.11633551

This is one of those fallacies of linearity, isn't it?

I learned this was a Bayesian problem, but Bayes doesn't make monotonic relationships.

I quick rule of thumb I learned was if the false positives - the 5% in this case - is greater than the percentage of people in the population that have it - .1%, then there will be more false positives than positives, but if for example the same false positives were applied to a population where 80% got it, then you could expect that 95% to be pretty close.

This works the same with false negatives and when they are different.

If you do a Venn diagram this is very visually obvious.

Anonymous Sun May 3 17:10:11 2020 No.11633552

>>11633517
>>11633517
>The problem is unsolvable unless you assume
Wrong, there are many different assumptions you can make to make the problem solvable. Doesn't change the fact that the problem is indeterminate. We can however restrict the answer to between 0 and 1/51.

>The technical definition for accuracy is that a probability that a test returns the correct outcome for a case. If a truly-sick person gets tested, a 95% accurate test has a 95% probability of saying 'POSITIVE'.
WRONG, as I've already explained. The probability of a sick person testing positive is sensitivity, not accuracy. Sensitivity does not have to be and is often not equal to accuracy.

>If you have a different theory for how this works, tell me what you would substitute for these two probabilities and show your work.
I already have, read the thread, or just look at the definition of test accuracy. I'm tired of repeating myself.

Anonymous Sun May 3 17:11:56 2020 No.11633559

>>11633523
>This >>11632565 is 100% true. And you literally can't refute it.
I already did, read the reply.

>The probability is 1.866%, you have not used Baye's theorem because you are a high school dropout.
Bayes Theorem is useless here since we don't know P(positive test|positive).

>You can't just sum and rest perentages.
There are plenty of cases when you can.

You have no argument so your post is pretty pointless.

>>	Anonymous Sun May 3 17:14:30 2020 No.11633563 >>11633552 In other words, the answer is indeterminate if you ignore the intended setup of the problem. Very useful.

Anonymous Sun May 3 17:19:27 2020 No.11633573

>>11633533
>>11633538
>Alright, so what are the values of these probabilities? Show me how you arrived at your answer.
See the image in >>11633534. Are you really not capable of reading it? It already answers you questions.

>P(B|A)=?
That's just TP/(TP+FN) = x/0.001

>P(B|¬A)=?
That's just FP/(FP+TN) = (0.049+x)/0.999

>I see a lot of seething about how people think this isn't just a Bayes Rule problem but also a complete reluctance to actually write out the individual probabilities they're using to solve this.
Why would someone who thinks Bayes Rule is unnecessary to solve the problem solve for probabilities that are only relevant to Bayes Rule?

Anonymous Sun May 3 17:22:07 2020 No.11633579

>>11633563
The intended setup of the problem is for the answer to be 2%. So does that mean we should make some arbitrary assumption such that the answer is 2%? I don't see how the intended setup is relevant when the person who made it is evidently retarded.

>>	Anonymous Sun May 3 17:22:22 2020 No.11633580 >>11633450 I solved it using numbers, can anyone tell me if my working is correct?

Anonymous Sun May 3 17:26:01 2020 No.11633591

>>11633573
So you're doubling down with this being an unsolvable problem based on a narrow interpretation of 'accuracy'?

In the real world, nobody pays you a salary to bend the premise of a question such that there's no answer anymore. Sometimes the answer really is indeterminate, but it's pretty obvious how this problem statement is meant to be interpreted if you understand what it's supposed to teach a student. Nobody is hired to obfuscate things into uselessness.

Maybe the question could have been more explicit about the test's accuracy. Something like: "the sensitivity and specificity of the test is 95%"

Anonymous Sun May 3 17:31:31 2020 No.11633604

>>11633591
>So you're doubling down with this being an unsolvable problem based on a narrow interpretation of 'accuracy'?
Not a "narrow" interpretation, the correct interpretation of accuracy in the context of diagnostic tests and statistics in general.

>In the real world, nobody pays you a salary to bend the premise of a question such that there's no answer anymore.
I'm not bending the premise, you are in order to get to a preconceived result based on the naive intution that this MUST be a Bayes Theorem problem because it seounds like one. Not every problem has an exact answer, deal with it.

>it's pretty obvious how this problem statement is meant to be interpreted if you understand what it's supposed to teach a student.
It's pretty obvious the person who made the problem is retarded and should not be teaching anyone anything. But you did learn what accuracy means today so you're right that a student learned something.

>>	Anonymous Sun May 3 17:34:28 2020 No.11633611 >>11633580 You're on the right track and did better than most in this thread, but you assumed there are no false negatives when that info is not given in the problem.

Anonymous Sun May 3 17:34:30 2020 No.11633612

>>11633591
its sad that even after you realize you are in fact wrong and a retard who has no idea what they are talking about, you are still trying to cope and justify your answer by changing what the problem means. you keep falling back to "hurr durr its a test question therefore it must have one right answer and whoever wrote it is infalliable" when I am almost 100% certain that this is not a test question or anything of the sort written for students. Its something slapped together real quick in a small effort to teach people about testing.

Anonymous Sun May 3 17:38:45 2020 No.11633617

>>11633612
>I am almost 100% certain that this is not a test question or anything of the sort written for students. Its something slapped together real quick in a small effort to teach people about testing.

It's word-for-word exactly the same as the Bayes Theorem problems I had to solve as a sophomore undergraduate. It's a test-bank problem meant to teach people one specific thing about how probability works.

I'll give you this: if you pedantically obsess over what 'accuracy' is supposed to mean in this context, it is possible to change the problem so that there is no answer. Again, very useful insight.

Anonymous Sun May 3 17:43:38 2020 No.11633624

>>11633617
When I took stats, we did not solve these problems by making out accuracy to mean whatever we wanted and misapplying bayes theorem. "I took a college course" is not an argument. you were already proven wrong numerous times and are still trying to cope by using logical fallacies. you clearly don't remember your course right.

>>	Anonymous Sun May 3 17:43:47 2020 No.11633625 >>11633617 >It's word-for-word exactly the same as the Bayes Theorem problems I had to solve as a sophomore undergraduate. Then your teacher was utter shit and so are you for thinking this is an acceptable excuse for misinterpreting a problem.

>>	Anonymous Sun May 3 17:46:40 2020 No.11633629 >>11633538 >hurr durr I don't see any numbers see >>11633234 you illiterate retard

Anonymous Sun May 3 17:47:29 2020 No.11633633

>>11633624
>>11633625

So do you folks actually have an answer, or are you sticking with this being an elaborate test for your ability to make a problem unsolvable and indeterminate?

I wish that when I was taking stats, willfully misinterpreting the question and writing 'NO ANSWER' could win me full points. That would have made things way easier.

>>	Anonymous Sun May 3 17:49:01 2020 No.11633635 >>11633629 >see >>11633234 you illiterate retard I'm not autistic enough to keep track of every anon's post chain from their writing style. Link back to your original work or stfu

>>	Anonymous Sun May 3 17:50:18 2020 No.11633640 >>11633633 Maybe if you read the thread instead of whining about how shitty your education was you would have found the answer posted already.

>>	Anonymous Sun May 3 17:51:37 2020 No.11633644 >>11633635 It's not even that far into the thread >>11631225

>>	Anonymous Sun May 3 17:52:39 2020 No.11633645 >>11633640 The answer is 1.866%. If anons want to listen to your retards, they can deal with the consequences when they fail classes and have their publications rejected. No more well-written, LaTeX typeset explanations for you kiddos - I'm out.

Anonymous Sun May 3 17:53:51 2020 No.11633648

>>11633635
??? link to what? the work is right there. you said you haven't seen anyone use actual numbers and concrete probabilities to solve it without bayes but clearly it has been done. here it is again earlier in the thread >>11631225

My original work? If you want me to solve it again, here you go, this time as a function of false negatives instead of true positives:
TP+FN=0.001
TP+TN=0.95
FP = 0.05 - FN

TP/(TP+FP)= (0.001 - FN) / ((0.001 - FN) + (0.05 - FN))
TP/(TP+FP)= (0.001 - FN) / (0.051 - 2FN)

>>	Anonymous Sun May 3 17:59:23 2020 No.11633664 >>11633645 >The answer is 1.866% F- time to go back to stats class.

>>	Anonymous Sun May 3 17:59:41 2020 No.11633667 probability theory is complete nonsense, prove me wrong.

>>	Anonymous Sun May 3 18:19:00 2020 No.11633726 >>11633648 >>11631225 >TP/(TP+FP)= (0.001 - FN) / (0.051 - 2FN) >P(A\|B) = TP/(TP+FP) Not science or math.

>>	Anonymous Sun May 3 18:26:55 2020 No.11633753 >>11633726 Not an argument, you lose.

>>	Anonymous Sun May 3 18:34:07 2020 No.11633772 >>11629529 95%

>>	Anonymous Sun May 3 20:16:33 2020 No.11634198 File: 34 KB, 732x772, 1527678986486.png [View same] [iqdb] [saucenao] [google] >>11633726 >statistics isn't math but bayes theorem is?

>>	Anonymous Sun May 3 23:06:50 2020 No.11634779 >>11631251 >Ex bush official is a fucking liberal >Ex bush official is compares whiny maga-tard crybabies to actual American heroes, finds Trumpers wanting FTFY You don't have to be a liberal to realize the protesters are self-important immature fools.

>>	Anonymous Mon May 4 01:01:11 2020 No.11635077 >>11634779 https://youtu.be/E6lxKOfn8_E

>>	Anonymous Mon May 4 01:53:54 2020 No.11635174 >>11632165 Its completely dishonest to average something with such pronounced spatial variation over the whole country. Do the exercise in the OP with 0.04% for the global population and pretend that answer means anything I fucking dare you.

>>	Anonymous Mon May 4 08:50:24 2020 No.11635841 File: 221 KB, 285x450, flag.png [View same] [iqdb] [saucenao] [google] >>11634779

>>	Anonymous Mon May 4 09:03:22 2020 No.11635864 >>11629690 Correct

>>	Anonymous Mon May 4 09:24:52 2020 No.11635925 >>11635864 retard

Anonymous Mon May 4 09:33:35 2020 No.11635945
File: 108 KB, 676x485, 395565F7-4AD2-41DF-8743-51D16E8D3939.jpg [View same] [iqdb] [saucenao] [google]

>>11633551
The op left out the part “you are randomly tested”. Or more often on tests “you randomly test someone, what is....”
But yes.
Look at it the easy way.
You test 1000 people, (.1 is 1/1000)
You expect one person to have the coof
Out of the remaining 999 people, about 50 will be Id’d as having the coof (5%)
The correct answer is the probability of being afflicted with the disease over number of true and false positives; 1 in 51 or 1.96% which is rounded up on tests due to convention.
Btw according to taleb less than 1 in 5 doctors got this right when asked. Which means you are likely to be given meds for shit you don’t have.
(Assuming no false negatives)

Anonymous Mon May 4 09:52:39 2020 No.11635973
File: 202 KB, 620x420, 19FF2769-138A-467F-A2BD-9167A0306015.jpg [View same] [iqdb] [saucenao] [google]

>>11629699
The answer to your query lies in the fact half a person can’t have it, something something discrete like.
In basic classes they just have you round up. In advanced classes they use a weird complex formula to determine where to go.

>>	Anonymous Mon May 4 10:08:06 2020 No.11636005 >>11629581 Fucking hell you're dumb.

>>	Anonymous Mon May 4 12:04:55 2020 No.11636375 >>11635925 stupid cunt

>>	Anonymous Mon May 4 12:07:02 2020 No.11636383 >>11633648 Schizo

>>	Anonymous Mon May 4 12:10:04 2020 No.11636391 >>11629529 Answer is B, 95%. Now we move onto problems more difficult than 6th grade.

Anonymous Mon May 4 12:10:42 2020 No.11636393

>>11629529
C is the correct answer. The probability of having Corona and a positive test is 0.1% * 95% == 9.5%.

Basically Corona is a fraudulent virus created to destroy the American economy. So, whether you have the virus or not is conditional on having a positive test.

>>	Anonymous Mon May 4 12:13:40 2020 No.11636402 >>11636375 >projecting

>>	Anonymous Mon May 4 12:33:58 2020 No.11636457 The answer is B and everyone who disagrees is retarded

Anonymous Mon May 4 12:40:24 2020 No.11636480

>>11630060
After reading it immediately, this was my thought. Well, it may very well still be, but I believe the question is just worded poorly like all dumb stupid macro image problems and there are multiple interpretations as already stated in the thread.

Anonymous Mon May 4 12:44:31 2020 No.11636491

>Buses leave every 15 minutes, the last bus left 10 minutes ago, when will the next one come?
>normal person
in 5 minutes
>sci
let's evaluate the chances of the bus not coming on a normal curve and then calculate the odds the next one will come at the scheduled time, then factor in different time zones and adjust for manual timing. Everything has to be more complicated because I have no life and overcomplicating things makes me look smart

>>	Anonymous Mon May 4 12:56:42 2020 No.11636523 >>11636480 >question is just worded poorly every retards cope, errytime

>>	Anonymous Mon May 4 12:57:46 2020 No.11636527 >>11636480 >question is just worded poorly every retard's cope, errytime

>>	Anonymous Mon May 4 13:01:33 2020 No.11636540 >>11636527 Just like the retarded images with ambiguous notations that can be correct either way, but are not equally correct

Anonymous Mon May 4 13:12:16 2020 No.11636576

.1% of people have disease.
A test for the disease is 95% accurate, meaning that 95% of positive results represent an actual case of disease.
You test positive.
There is a 95% chance you have the disease.
Can anyone explain to me without braindead cracker memes why this is wrong?

Anonymous Mon May 4 13:12:22 2020 No.11636577

>>11636527
technically its worded correctly, it just is incomplete (like many other image macro problems are) so anyone who took a stats course and isn't a retard should immediately see this problem and think "thats unsolvable". You need two figures to completely describe a test like this. With just one figure, the best you can do is give a range of values, like >>11631225

Anonymous Mon May 4 13:23:40 2020 No.11636602

>>11636576
>There is a 95% chance you have the disease.
IF you have the disease, the test will be accurate with 95% percentage. You might as well be fine, and tested positive.
However, being sick in the first place changes this probability.
Being sick AND tested positive (the chance we want to calculate): probability of having corona (0.1%) * (95%)
Possible outcomes being tested positive: sick & positive, not sick & positive (99.9%).
Overall, even with the classical definition (intuitively) we divide the probability of being positively sick with the probability of (positively not sick + positively sick)
and the correct answer is >>11629594

>>	Anonymous Mon May 4 13:26:21 2020 No.11636611 >>11635864 Probably the worst answer in this thread. The first interpretation describes precision and the second describes sensitivity, neither of which are the same as accuracy. If 95% is the sensitivity then the answer is indeed 1.87%.

>>	Anonymous Mon May 4 13:26:52 2020 No.11636613 >>11636576 Don't listen to this fool. He doesn't understand what hes talking about. 95% accuracy has a well defined meaning but he uses the wrong meaning >>11636602 Come see the light: >>11631225

Anonymous Mon May 4 13:28:48 2020 No.11636618

P(positive) = 0.001
P(negative) = 0.999
This is debatable depending how you interpret the first statement

P(test positive | positive) = 0.95
P(test positive | negative) = 0.05
Again i pulled the definition of accuracy out of my ass but it works i guess

Sum both cases to get
P(test positive) = P(test positive | positive) P(positive) + P(test positive | negative) P(negative)
= 0.95 * 0.001 + 0.05 * 0.999

Apply bayes rule
P(positive | test positive) = P(test positive | positive) P(positive) / P(test positive) = 0.95 * 0.001 / (0.95 * 0.001 + 0.05 * 0.999) = 1.87%

>>	Anonymous Mon May 4 13:30:09 2020 No.11636621 File: 69 KB, 640x640, f9lk4ew4d7e31.png [View same] [iqdb] [saucenao] [google] >>11636618 >P(test positive \| positive) = 0.95

Anonymous Mon May 4 13:35:37 2020 No.11636628

>>11635945
>Out of the remaining 999 people, about 50 will be Id’d as having the coof (5%)
Well that's not a very good way of staying because the person with the cool could either get a true positive or a false negative. So either 49 or 50 people will get a false positive. Either 0/50 or 1/51 people who got positive tests will have the coof.

See >>11633534

>>	Anonymous Mon May 4 13:38:37 2020 No.11636633 >>11636602 >>11636613 I'm still not quite understanding, it seems to me that the only relevant variables are how accurate the test are and whether or not 'you've' tested positive. Since you have, the only thing to consider is how accurate is the test.

Anonymous Mon May 4 13:40:37 2020 No.11636637

>>11636393
>The probability of having Corona and a positive test is 0.1% * 95% == 9.5%.
Totally wrong and has nothing to do with the question. The question doesn't ask for the probability of having coronavirus and getting a positive test, it's asking for the probability of having coronavirus given you have a positive test. And 95% is not that probability.

>>	Anonymous Mon May 4 13:41:59 2020 No.11636640 >>11636540 There's nothing ambiguous in the question if you know basic statistics.

>>	Anonymous Mon May 4 13:43:07 2020 No.11636643 >>11636576 >A test for the disease is 95% accurate, meaning that 95% of positive results represent an actual case of disease. No, accuracy is the probability that a positive or negative result is true, not just positive results.

>>	Anonymous Mon May 4 13:44:31 2020 No.11636646 >>11636643 But I've tested positive, so only the probability of a positive result is relevant to the question of whether I have it or not.

Anonymous Mon May 4 13:46:25 2020 No.11636652

>>11636602
>IF you have the disease, the test will be accurate with 95% percentage.
Nothing in the problem tells you that.

>Being sick AND tested positive (the chance we want to calculate):
That's not what the problem is asking. We already know we tested positive.

>>	Anonymous Mon May 4 13:48:23 2020 No.11636659 >>11636652 >being tested positive is the same as being sick ok

>>	Anonymous Mon May 4 14:00:06 2020 No.11636687 >>11636618 >Again i pulled the definition of accuracy out of my ass but it works i guess You could just look up the definition of test accuracy.

>>	Anonymous Mon May 4 14:01:08 2020 No.11636691 >>11636633 Look up what accuracy means.

>>	Anonymous Mon May 4 14:02:34 2020 No.11636697 >>11636646 Yes, that's called the precision of the test and that isn't given. Only the accuracy is given.

>>	Anonymous Mon May 4 14:03:35 2020 No.11636698 >>11636659 >>being tested positive is the same as being sick Who are you quoting?

>>	Anonymous Mon May 4 14:03:37 2020 No.11636699 File: 108 KB, 1302x349, Screenshot_20200504-140226_Adblock Browser.jpg [View same] [iqdb] [saucenao] [google] >>11636691 My confusion continues as before.

>>	Anonymous Mon May 4 14:04:27 2020 No.11636701 >>11636698 you

>>	Anonymous Mon May 4 14:06:43 2020 No.11636712 >>11636701 I never said that. Are you lying or illiterate?

>>	Anonymous Mon May 4 14:08:50 2020 No.11636721 >>11636712 quit trying to be smart

Anonymous Mon May 4 14:09:24 2020 No.11636722

>>11636699
You should be able to figure it out from that third definition. Accuracy of a test is the probability a positive or negative result is true. In other words, the proportion of true positives and true negatives among all test results. But what you need to know to answer the question is the proportion of true positives among positive results.

>>	Anonymous Mon May 4 14:09:26 2020 No.11636723 >>11636699 see >>11633491

>>	Anonymous Mon May 4 14:10:27 2020 No.11636732 >>11636721 Sure, as soon as you quit being stupid.

>>	Anonymous Mon May 4 14:18:08 2020 No.11636752 >>11636722 I just assumed that a 95% accuracy meant that 95% of positive results are true positives and 95% of negative results are true negatives.

>>	Anonymous Mon May 4 14:22:06 2020 No.11636765 >>11636752 Those are called positive predictive value and negative predictive value, not accuracy.

Anonymous Mon May 4 14:22:57 2020 No.11636767

>>11636633
the test gives a correct diagnosis 95% of the time. If the population is 50% infected, that means that 50% of the population will test true positive, 45% will test true negative, and the last 5% will get false negatives. The chance that you are infected if you got a positive diagnosis is then 50/(50+5)=91%.

If you decrease the infection rate from 50%, then you will get less true positives and more true negatives, while the number of false positives will remain constant (if it didn't then accuracy would change from 95%). If the infection rate is 1%, then 1% will test true positive, 94% will test true negative, and 5% will test false positive. The chance you are infected if you test positive is now 1/(1+5)=16.7%

this is assuming no false negatives. if you allow false negatives, the percentages just go down even further, since an increase in false negatives requries decreasing both true positives and false positives ( 2/(2+4) > 1/(1+3) )

>>	Anonymous Mon May 4 14:24:27 2020 No.11636773 >>11636767 *false negatives -> false positives in the first paragraph

>>	Anonymous Mon May 4 14:36:03 2020 No.11636814 >>11636765 >>11636767 Okay, I get it now, thank you very much.

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