Are you REALLY sick? (false positives) - Numberphile
HTML-код
- Опубликовано: 5 сен 2024
- Bayes' Theorem applied to disease diagnosis. Featuring Lisa Goldberg from UC Berkeley Department of Statistics.
More links & stuff in full description below ↓↓↓
Extra footage: • Sickness and Stats (ex...
Monty Hall: bit.ly/MontyHal...
Support us on Patreon: / numberphile
NUMBERPHILE
Website: www.numberphile...
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberph...
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumb...
Videos by Brady Haran
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanb...
Sign up for (occasional) emails: eepurl.com/YdjL9
Numberphile T-Shirts: teespring.com/...
Other merchandise: store.dftba.co...
When my father built our house in the early 1990ies he went to a serial X-ray examination. Later he got a letter that said that he should visit the doctor, because they found some »abnormalities« on his heart.
To make things short: In the end it turned out that he forgot some screws in the left pocket of his shirt. :)
+Martin Steindl Wouldn't happen nowadays, except if you forget some screws in your underwear
+AldjinnTV dont they usually give u a huge lead sheet to hide your bits?
+Martin Steindl - Ironically, those were screws he was supposed to have fitted into one of his patients' artificial hips.
+Martin Steindl Lucky they didn't send him in for an MRI. :)
+Martin Steindl id be more worried about the houses missing screws than a patient able to to hospital (and alter receive results) who might "accidentally" somehow have screws around his heart. :D
)
u wut m8
thank you, you've saved my life
aquarium?
+x nick I actually see the right parenthesis. It's behind the computer.
+x nick thanks :D
I once tested positive to hepatitis-C when I gave blood. I looked up the accuracy of the screening test and, if I remember right, it was about 75% accurate. I figured (incorrectly) that I had a 75% chance of having the disease. If I had thought of Bayes rule, I would've realized that, since people who have no symptoms or risk factors have a tiny chance of having hep-C, I had a very tiny chance of being sick.
Luckily, my doctor knew this and told me to not worry. He said that he would test me again, but even that wasn't necessary. Of course, I wasn't sick.
Bottom line: this video might save some people a lot of heartache. Thanks.
+David Messer
great story! I wish some of the other commenters had read it.
in slightly more disturbing news, apparently there was a study on doctors where they were asked about the chance that a patient with a positive on a routine breast cancer screening actually had the disease if : a very large percentage said 80%
T.T
ThoperSought cool stuff man, thanks for sharing!
Fiddling Beelzebot
I'm glad it was helpful
I had a false positive because I have an auto immune illness.
Happened to em this year! They immediately send my blood to another institution for more detailed test which was negative, so they told me not to worry (but to take precautions) as it was probably false positive but I had to wait half a year for another test so they could be sure I am safe to donate blood again.
"Sorry, you aren't sick"
+KpilotRCHelis I'm sorry you are healthy.
+Fundemort Grey Prime Defender of Truth and Justice Brutal.
There's an important variable neglected here. A test is usually performed on a patient who is SUSPECTED to be ill, which makes the occurence of tests subjects being ill higher than the average population. Depressing, I know! :P
+Frogasmol sometimes, but not always - some screening is done quite randomly... check the extra footage, BTW, I did ask about this.
Numberphile I suppose I'm biaised just for being Canadian. Prevention gets tossed aside quickly when hospitals are government-funded... Wow I'm a real bummer today.
I will check the extra footage, though, and I'm not surprised you though about it. Keep up the great work!
+Frogasmol This. The reasoning only applies when entire populations are screened.
Vegard Lobben Yeah, I don't retract from the statement that reality is always crappier than you account for it. xD
Gerarda Cronin Well put. I was being more pessimistic than mathematically accurate, eh.
If only we could determine what the false positive and false negative rate was for the tests we're making right now.
I dig your representation of the testing computer.
Statistics and probability should be taught more in schools. I love knowing algebra, trig, differentiation, integration, complex numbers, higher-dimensional geomertry etc., but I hardly ever need to use them for anything. Probability is vital to all our lives.
You know people pray to RNGesus everyday right?
+TheCordlessOne not just algebra - probability theory is heavily reliant on our understanding of integration too! Really probability calculations are a special case of measure theory. Lots of very pure areas of maths turn out to be vital to the way we see probability.
+Phil Hibbs Well, here in Serbia if you are in middle school there's 25% chances you will class statistics in 4th year of middle school.
Is that 25% in the 4th year the peak of a normal distribution? What's the standard deviation?
Phil Hibbs What do you mean by deviation? It's rather simple, 25% of people in high school go to math gimnasium (math, natural sciences) and in 4th year during mathematical classes you have around 4 months of statistics. Of course, don't hold me on 25%, it's more like 25%-ish. It's not some national statistics, just my life experience.
2:32 "Well, I should call the undertaker" That escalated quickly!
It might have been interesting to explain that false positive and false negative are in some sense complementary: you have to accept a great number of false positive in order to NOT miss a true positive. That is the case in many life-threatening situation: "Better be safe than sorry". This leads nevertheless to unappropriate decisions if you only have a small positive sample.
This accounts for all of those stories I hear where someone was diagnosed with cancer, prayed about it, went back to the doctor and the cancer was gone. It's a mathematical miracle!
Brady,
I feel like the animations in Numberphile are getting extraneous. In this video alone we were shown an animation of a patient being tested several times, something I feel is easy to understand without an example. I'd also prefer to see the equations as they were written on the brown paper rather than animated. Animations can be really helpful, but I think they're currently being overused and are gilding the lily.
I love your channels though, and thank you for putting so much effort into them.
+Cailean Douglas cheers for your feedback. Animations are not always lily gilding. Sometimes they are covering things that were wrong, incomplete or were not filmed. Or were just filmed poorly (by me). Or they cover unsightly edits and cuts.
Or sometimes they are just gilding the lily. :)
Is gilding the lily a uk thing because I don't believe I've come across the phrase before.
+Vincent Marroquin nah, I'd say it's a little more universal than that, but it could be that I'm familiar with it from writers I didn't realize where british
+Numberphile To add to the constructive feedback, I noticed, especially lately, that you have a tendency to over expose the shot. This is a shame since it can be easily prevented. It really makes a huge difference in quality!
+Vincent Marroquin It's used occasionally in the US. From Shakespeare "...to paint the lily gold..." i.e. Nothing is added; it's already great.
ugh,,, one of the most convoluted explanations of Bayes theorem i've ever heard.
+Bill McCollam I felt the same way. I've read articles that explained it a lot better and more concisely.
+NoriMori Yes - but on the whole, I love NumberPhile (lol - just having a cranky day yesterday).
More on Bayes and Bayesian statistics, please. You are so good at clarifying difficult concepts, I would love to see it.
I'm surprised you made it through that whole explanation without using the terms "sensitivity" and "selectivity" as those are the terms used when evaluating medical tests.
+Animuldok Sensitivity, specificity, predictive value of a positive test, and predictive value of a negative test.
JL Software why do you think I need to be told definitions of words that I use on a daily basis?
Animuldok
1) I didn't tell you any definitions.
2) In fact, it would be great if you'd post the formulae for PPV and NPV, so people could calculate them for the case that was presented in the video.
3) You didn't say anything about using anything on a daily basis.
Is selectivity different from specificity?
I have a highly sensitive test for all conditions , literally . For a given condition -- I point at the patient and say 'you test positive' . I never miss a case . Great , in fact , to be specific , it's brilliant .
If you get a letter with positive test results for a bad disease, then you should go to another doctor.
Not necessarily, because the result may be a fals positive, but because your current doctor has no bedside manners whatsoever.
Seriously.
+akakalliba Agreed. I am a physician and I ALWAYS called my patients personally with results like this. Even at night if they had said they wanted to know as soon as possible. Sending a letter with a "positive" result can result in people aborting a fetus, or even killing themselves. All for the saving of a few pennies by the office manager.
4:52 i thought i sent an email by accident
The animations are good and all, but I quite miss the actual writing on paper moments
The cutoff point for what counts as a positive test has to be balanced with regards to both sensitivity and specificity. In an ideal world, you'd have an extremely sensitive test that was also extremely specific. In reality, however, more sensitive tests have to be less specific, and vice versa. A hyper-sensitive test like in the example tends to get a lot of false positives.
The video explained sensibility, usually the first tests are more sensible than specific, wich means it gives you little false negatives, and then you comfirm the diagnosis with other tests more specific, that gives you less false positives
No lady, you shouldn't call the Undertaker.
You should call...
JOHN CEEENAAAAAA!!!
TANANANAAA
+Vlad KSP JOHN CENA!!!!
+Vlad KSP 🎺 🎺 🎺 🎺
+Vlad KSP I thought you were gonna say "GHOSTBUSTERS!!!"
Just before 3:53 I was thinking : "that reminds me SpamBayes, the best python antispam filter based on Bayes theorem" and boom, here we go !
This is just about my Homework!! exactly the same example (not the same numbers) with a rare disease. Aaand i did it right!!
Thx :)
So, this is a mathematical proof justifying denialism?
+Brandon Fesser
What does that even mean?
+randomjunkohyeah1 "In the psychology of human behavior, denialism is a person's choice to deny reality, as a way to avoid a psychologically uncomfortable truth." -- Wikipedia
+Brandon Fesser That's not what the video says at all though. It's not saying 'you're ill but you shouldn't think so', it's saying 'you're probably not ill if they've only done one test'. Any other implications are down to the viewer.
+Adrian Mungroo
Because people's "feels" get in the way.
+Ewelyn Vince
What you're talking about is very nicely encapsulated by the phrase "a little knowledge is a dangerous thing".
Funnily enough, I'm only here this early because I'm at home, sick.
+rareroe305 I called in sick today - told my boss I was having vision problems, and just couldn't see going in to work.
+neonjoe529 Me too
Oh no. A video on Bayes' theorem. You know what that means - hordes of commenters claiming that it's wrong because they think they know better even though they evidently don't know anything about conditional probability...
+Hwd405 Probably.
+HistoricaHungarica ...was that a probability joke?
Hwd405
Chances are... it was. :)
HistoricaHungarica that joke took me a while to _process_ ;)
***** sounds very interesting! I'll have to give it a read!
2:35 - Of course you should call The Undertaker. A Tombstone Piledriver and you'll be fine :D
This is why confirmatory tests, physical exam, history taking, and the entire body of knowledge at a healthcare providers disposal are used in diagnosing patients. No doctor worth their salt places all of their basis for diagnosis and treatment on one lab test.
And yet, it happens all the time with urinary tract infection, albeit in the other direction: negative culture → “the patient doesn’t have an infection” → “must be psychosomatic”.
See “Confronting the urinalysis tyrant” in BJGP Life.
Another good use of Bayes' Theorem is with the roadside breathalyzers that police use to test for drunk driving. If you do the math, it doesn't actually catch drunk people, but rather let's non-drunk people go. That's why you're given a 2nd more accurate test at the police station.
So the moral of the story is... get a second test.
FullTimeSlacker
_"Or calibrate the machine with a known sick person and a known healthy person."_
that's really, just _really_ not how this works.
first of all, it's simply not possible. in the case of routine mammograms, a radiologist is interpreting the data from a scan. this is necessarily subject to error, since there's an interpretation. in the case of blood tests, there's generally some marker which has been shown statistically to correlate with a disease condition. sometimes the best correlation that's possible isn't really clear.
second, the tests _Are_ calibrated to known sick people, and-as far as possible, which is generally not very far-to known healthy people. but correlations are correlations, and the prevalence of most diseases is low enough to make confirmatory tests necessary.
AIDS tests are among the best medical tests available, meaning that it's relatively easy to test for various markers of the disease, and that the tests are _highly_ developed. recently, there was an announcement (I don't recall, but maybe by the WHO?) that a negative on an AIDS test was strong enough to count as a confirmed negative. I don't recall if this was for a specific test, group of tests, or type of test, but for whichever it was, it's a very strong result.
but, there's still a tiny, tiny possibility of a false negative, and you still need a confirmatory test for a positive.
the moral of _this_ story is... medicine doesn't work the way you think it does, and neither does statistics.
Hi Willythecomposer! :D
+JoesephGaming #FreetheCorn
Fester Blats
_"No matter how many tests you get, you will never be 100% sure."_
I kinda feel like we weren't even watching the same video, if you can say something like this.
It's all about the clinical signs that go with the test.
Very good to touch upon this subject and upon Bayes theorem!
However I think it would be good to mention the term sensitivity and specificity.
Also, just use a + and a - to make the animation (and a S for sick and NS for not sick), the signs used make the formula in the animation VERY difficult to follow (i think) for someone that is new to this theorem. You should have paid much more attention to making it come across as a very logical relation (which it is).
This year I have been for half a year false positive, the doctors strongly suspected it from the beginning, but it was rather annoying as I had to inform my other doctors and could not donate blood. Even though I was pretty sure I am false positive, it was a long wait for the next test.
This is exactly why breast cancer screening guidelines have been (controversially) revised. Still, I'd much rather suffer a false positive then undergo further screening to rule out illness, than to have the illness and never know it.
I think part of the reason this video may seem "wrong" to people is that the example she is using is actually pretty ridiculous. The test gives a false positive 10% of the time, even though it only affects 0.1% of people. If 1000 people are tested, 100 people get a positive, but only 1 is sick. So it makes sense that someone with a positive result only has a 1% chance of being sick - the test is terribly inaccurate and would probably not be used by a doctor. It's still interesting to think about.
This is actually a great test because if the test gives a negative result, then you're 100% sure to be healthy.
Tests are usually either made to rule in a disease or to rule it out.
A ~10% positive rate in healthy people is the performance of breast cancer screening (except it doesn’t catch all cases either, unlike the example in the video).
A 1 in 1000 disease is a pretty common disease...
+Esa Ahmad Yeah, like catching a cough or a cold, basically
Thank you so much brady for editing this video in time because I have a test about this tomorrow and I did not get it before. I am so in luck that you posted this just in time. :)))))
Here is a flower emoji to do something in return 🌹 😉
Hopefully someone explains this to patients that are getting tests with high rates of false positives. I know if I was getting tested for something bad, and the results came back positive, it would be a pretty bad time indeed, especially if I didn't understand the test could say I was positive when I wasn't.
Great video! Very interesting and easy for us simple folk to understand :)
bayes theorem is so hard to digest, thanks for such a well produced explanation, you rock brady!
glad to see this here, im studying this at my faculty :D
I'm going to agree that this video (and others of yours?) seem quiet relative to most other things I watch on youtube.
Neat video as usual.
Anyone clicked on and watching this video during covid19 pandemic?
Well done. That's a difficult situation, well explained.
Why is the test 99% accurate at measuring whether you're ill or not but only 90% accurate at measuring whether you're healthy?
Excellent video, very intuitive :D
Isn't there a much easier way of looking at this? You are either 1 in 10 false positives or 1 in 1000 true positives. The probability of former is 0.1 and the probability of the latter is 0.001. One is 100 times more likely than the other, so the probability of being a true positive is 1 in 101, which is basically 0.01. Much easier calculations that way
Sure, lets ignore the reliabilty of the tests. Next time I'll be worried if I have a disease I'll just roll some dice
It wasn't intuitive to me why the frequency in the general population
mattered until I thought of it this way. If you gather 1000 people, one
of them is likely to have this rare disease. If you run the test on
all of them, around 100 will test positive but only 1 is actually sick
+thaneross Aha! Very smart!
Please make a video on Tachyons or the speed of gravity which is recently discovered to be 3.003•10^8
Great video! Counter intuitive concept explained so eloquently!
I remember when I first learned about Bayesian statistics in a computer science course (it's used all the time in software; almost all modern spam filters depend on it!), and we were given a similar example. Because apparently, medical tests are just the standard explanation for this. And I was dumbfounded by how an extremely accurate test could give so many false positives just because the disease is rare. Sometimes, maths are counter-intuitive. Just another reason why we need to stop trusting our guts and take the time to analyze everything! :)
The key to remember is that perfect tests are basically impossible. Given that, we have two options: Do we want a test that is more likely to give a false positive, or a test that is more likely to give a false negative?
In medicine, we deliberately design tests to have a high false-positive rate in order to make sure that as few people as possible will test negative if they really have the disease. Being told you have cancer when you don't is really bad, but being told you're healthy when you really do have cancer is even worse.
A false positive leads to more tests to reveal the real truth, whereas a false negative leaves the patient completely on their own with a serious illness and no medical help.
Thanks for making this video, after 8 misdiagnoses it's hard to stay positive. I've had both false positives and false negatives, though only the false positives count as misdiagnoses. I think, I don't know anymore what does or does not count. I've been labeled as mentally deficient at birth and treated all my life based on that.
ADHD, bipolar disorder, borderline, schitzotypical and paranoid personality disorder are some of the misdiagnoses I've been given. If I actually had all those disorders I'm lucky to be alive...
Three minutes into the video and I can't watch any further, still, thanks for making it. This is important information.
+Sebastiaan van der Heide
I know people who have ADHD, borderline personality disorder, and dissociative identity disorder.
None of them are incapable of living ordinary lives, advancing in their careers, etc.
In fact, people who aren't close friends and family don't even know about those conditions.
I'm not sure why you think you'd be "lucky to be alive" if you had those disorders.
neonjoe529 My point was that having a disorder of any kind makes things harder, having multiple at the same time increases the difficulty further. Having over half a dozen disorders of which a few can be seriously debilitating makes things even harder.
With all those things stacked against you it's easy to lose will and commit suicide. Which happens all the time sadly. Just look at the correlation of mental disorder and suicide.
- msrc.fsu.edu/system/files/Harris%20et%20al%201997%20Suicide%20as%20an%20outcome%20for%20mental%20disorders-%20a%20meta-analysis.pdf
Sebastiaan van der Heide
Since I know the people I previously mentioned very well, I disagree that those conditions are 'seriously debilitating'.
Do they have challenges that others without those conditions don't have to deal with? Yes.
But.... "seriously debilitating"?
No.
I'm still unsure why you think you'd be "lucky to be alive" if you had these disorders. Do you already have suicidal thoughts or something?
neonjoe529 Yes I have, for close to two decades by now. Not that that matters in this discussion though, have you read the study I linked?
Because while it might be that those in your direct surroundings aren't experiencing the worst symptoms, that does not mean they can't be seriously debilitating.
People are ending their lives because of those disorders, I call that debilitating.
Sebastiaan van der Heide I read the summary - and wasn't surprised by it.
My argument is that calling these conditions "debilitating", or saying you'd be "lucky to be alive" is over-stating the impact that these conditions have on people's lives.
Now - if you already have issues with being suicidal, then *that* is the issue you're facing. You'd only by "lucky to be alive" if you also had one of these conditions because you're *already suicidal*.
This result may seem weird, but it's actually the best way to diagnose rare diseases. Erring on the side of false positives usually means you can trust negative results. If you get a positive, you can take a repeat test - if you get a negative, you are guaranteed negative, and if you get another positive you can be quite sure you really are positive. The HIV blood test is very similar to the test described in the video, and doctors use this procedure to accurately diagnose it.
+Vanderlism Actually they use a followup lab test which is much more expensive and elaborate, to confirm initial positives. The followup test has much more specificity (ability to identify negatives).
the illustrations seemed somewhat... tactless here. I don't know maybe that's just me.
Is it just me or is this video really quiet?
+Ryan N it is
+Ryan N its just you
Yeah I had to turn the volume up really high. Need to make sure I turn it down before I click on another video
No you are going deaf!
+Blindboard100 It's a 0.01% accurate test for deafness.
Lisa is a great teacher!
how do people and doctors know how accurate a test is for a sickness if they haven't tested it on a whole bunch of people, especially for rare diseases, since there are not a lot of people to test.
+Hollus Elsfik
Those probabilities are derived in clinical trials, where they actively search and enroll people that are known to have the disease
There is a difference between possibilities and outcomes. ofc you can get false positives BUT in (analytical) testing most of these occasions are removed due to testing muliple times and limiting the possibilies for false outcomes.
It should be standard practice for test results to include this information
If you really want to do this properly, you need to know the risk / reward of each situation.
What is the cost of taking care of the disease vs. the cost of being sick.
Holy cow. I got a 50 min ad :o
I don't know if it helps, but I'm leaving it on the entire time in the background for that sweet sweet ad $$$$
Just diagnosed with hep c. Cancelling appointment with under taker.
How is the base rate (1 in a thousand people get this disease) determined? You can't go by this test, because that will give you a wrong answer. So how is it done?
Timothy Jamison i think you can find it in reverse if you know the chances of the machine not working, and the chances someone is 'tested' positive.
This video felt so wrong. It made me so very uncomfortable to hear all that from a trusted channel. You could've picked any other analogy without going over "this letter" again and again and again...
This is fascinating, it took me a few minutes to wrap my head around it.
I do have to say, though, this seems it would be accurate for a disease that is tested for in a routine test. That way the sample is pretty representative of the overall population which is where data like the probability that you're sick/healthy comes from.
I believe this might be less applicable for tests where you're tested based on suspicion, since the pools from which data is pulled wouldn't be the same. Either: A) The proportions of sick and healthy people should be based on the people that take the test. If the test is ordered due to suspicion, this would skew any sick to healthy or healthy ratios that could be found on the formula; or B) the false positives and true positives proportions should be based on the overall population, which would skew any false to true positives ratios and vice-versa.
ThoperSought you're right, not less applicable, just that the data has to fit the test
+Numberphile, maybe you should have explained the difference between a screening and a diagnostic test. A screening test is done either to the general population or to a sub-population that is at risk of the disease, and that is the test you are talking about here. A diagnostic test instead is more invasive and it is done after a positive screening test, also being much more precise. Love your videos :)
Not nearly as simple as that.
Be that as it may, if I get a letter in the mail telling me I have cancer, I will assume I have cancer.
I think this is really important information! So for once Numberphile is being more than merely recreational. A lot more, I'd say!
I also think this is fantastic information that the general public should at least be aware of so that we can start to have a better sense of how much investigation needs to be done to be sure of something. It makes the point of how valuable properly implemented extra information is.
I don't like that she uses the word "accurate" to describe these tests... "Accuracy and precision" are different from "Sensitivity and specificity"... I work in a hospital lab, and the system for the types of tests that she's talking about (i.e. an HIV test) uses "sensitivity and specificity". We use statistics A TON in the lab, and the S&S of a test is a very reliable indicator for getting the correct diagnosis.
Statistics sound boring as fuck, but when you get into it it's very interesting!
+Matthew Smith the same can be said about women when you are a 12 years old
should be noted that is only given the test telling 1 in 10 people who are healthy that they are actually sick, im pretty sure most tests which are actually used commonly have better rates than that and therefore it wouldnt be 1 in 100, so most tests being positive should give you more reason to worry than a 1/100 would.
Hey Brady!!
The video is a few hours old so you might not see this. Just some constructive criticism.
The video up until the 3:30 mark or thereabouts could have been edited down a bit. A lot of stuff was repeated over and over. Isn't there some law? about the first 3 tenths of a video being irrelevant?
A lot of "but the question is" just waiting for an answer any time now.
+Zachary Taylor I felt exactly the same way!
Great video! Is anyone else distracted by the need to clean that laptop screen?
Especially interesting video for me after three doctors diagnosed me with lyme disease, but the blood test says otherwise (which is said to be relatively unreliable)
Why don't doctors include the probability in the letter? It seems like that would help keep people rational.
Wow, that's incredible, 1 in a 100!
I have a rare disease. My eyes were killed by the over exposure in this video.
So do the test results letters state what the probability of being sick is given a positive test?
4:33 Bayesic statistic course?
If 1 out of 10 tests are false and you've recieved a letter then it's 9 in 10 that you're sick isn't it?
the sadistic part of this is that i am currently sick
I hate the way she did the conditional probability. Easier just to make it P(told you are sick given you not actually sick)= (A*B)/B where B is equal to the probability of the given event and A is the probability you are told you are sick.
how does one know how accurate a test is without testing a whole bunch of people? especially if its a rare disease?
WHAT'S THE PROBABILITY THAT TODAY I LEARNED THIS EXACT PROBLEM IN MATH CLASS ?!?!!
4:55 Shouldnt a lower probability of the test catching a disease if you actually have it increase your chances of having it when you're tested positive? In the formula its the other way round. You should think that if the test does not always catch the desease (higher chance of false negative) that you'd be more likely to have it no matter what the test result.
"I should call the undertaker. I should let my relatives know."
hahaha
Are medical statistics made public so we can actually put this to use?? Also if you were to find that the chances of a false positive were high, surely doctors would be aware of this and test twice?
This is so cool, and really useful
I can follow the calculations, but I have no idea where the equation came from or where the items in the equation came from. So I'd be scared getting the letter.
I've heard the same problem but with drug tests at the workplace. If 1 in 100 people are using heroine and the test is 98% accure at not giving false positives that means every person you fire for using drugs is twice as likely to be innocent than guilty. For every 100 people you test it will likely flag the drug user and 2 random innocents in this example.
I think this is why a lot of places will retest before giving you the axe as well.
I remember looking at this problem in my stats class
The audio on this video is rather low.
Try increasing it.
+TrueFireAnt I noticed that, too!
If the test is that inaccurate then how certain can you be that the disease affects only 1 in 1000 people if that test is the only way to determine if anyone has it?
Assuming that the disease always has SOME eventually unmistakable result such as lesions, tumors, or death, that's where the "actual" statistics come from. For example, how can you distinguish Alzheimer's disease from other causes of dementia or apparent dementia? Some doctors say (or once said) the only sure diagnosis is the autopsy. If a disease has been known long enough, there is at least that statistic.
I think Bayes' theorem is much easier to memorize in the form P(A|B)*P(B) = P(B|A)*P(A)
I kind of like it in odds form:
O(H|D) = O(H) × P(D|H) / P(D|¬H)
(posterior odds = prior odds × likelihood ratio)
(for very small probabilities, odds ≈ probability; and symmetrically, for very high probabilities, 1/odds ≈ 1−probability)
depending on how you claim accuracy wouldn't 1 false positive in 10 healthy people make it closers to 90%accurate? or are we only counting accuracy to catch ALL positives (no false negatives) or should we calculate an accuracy for both contingencies seperately?
Not saying it's not the more important part. This question was answered moments after I hit play again though
Suppose the test say I'm sick. Should I call the Undertaker or John Cena?
I tested for THC I take ibuprofen Aleve and Advil I'm always needing Advil for sleep and ibuprofen for pain after working out.
Completely unrelated, but what are those 2 sticks on Numberphile's desk/chest?
this video was a waste of time, im sorry.. like it's irrelevant unless you are really interested in probability of being sick... Hope the next one is better