The Bayes Theorem: What Are the Odds?

This is probably the most important account on youtube. Please don't stop making videos.

[@healthcaretriage]

We don't plan to stop!

[@bitterjack]

I like this video better than your other videos because you are helping people learn how to think as opposed to what to think. while i understand that helping people learn how to think may have been the intent of your other videos, I think people are just taking your word for it and thus perpetuate the cycle of just people thinking whatever is told to them last. Keep it up.

[@JanCRefsgaard]

I agree... Are you correct or has the cycle simply been perpetuated ;)

[@bitterjack]

Jan Christian Refsgaard I trust that as someone who is trying to help people understand critical thinking that you can answer that question yourself. though i would be careful about stressing the importance of negative studies without proper context in your future videos

[@kennedyryder5359]

He could talk about anything and make it interesting.

[@healthcaretriage]

Thanks!

[@nicholasparliament4648]

As a medical student, this video has been the absolute best teacher of this topic. We spent a four hour class discussing these topics, but this captured it so much better and made it so concrete.

[@kujmous]

KZbin is nice in that I can watch this at my own pace. Excellent work.

[@kathrayres]

This, in tandem with the last video, was really eye-opening. Never thought about tests this way!

[@WarrenGarabrandt]

I found this video to be a very straightforward tutorial to an otherwise complex concept. Disclosure: I have a strong math background, and already knew about Bayes Theorem, but it had been a long time since I've reviewed it. Thanks for the great video!

[@TheNerdReport]

"Is Marijuana Harmful?" is the subject of next week's video. I feel a fire-storm brewing!

[@elliottmcollins]

Karaukorghh And lo, it is cool.

[@Stygianstevedore]

I know this probably isn't your most popular video, given its mathematical and abstract subject matter, but I really appreciate this one. I really enjoy the thought experiment comparing the women with different pre-test risks, and just the general analysis of the statistics in the video

[@kendrabeewings]

As someone who has studied lots of probability, I approve. I turned out not wanting to be an actuary after all, but studying for the first actuarial exam left me looking at probabilities and statistics in a whole new way. Also, looking forward to the marijuana episode. I'm very interested to see what you have to say about it.

[@evilcam]

We come for Healthcare real talk, and stay for the excellent use and explanation of Bayesian Analysis. HCT is doing it right.

[@4epblogadmin]

healthcare triage does a 1hour lecture in 8minutes. love this so much

[@saizai]

Suggestion: cover re-testing, where the pre-2nd-test-odds = post-1st-test-odds, but you have to consider how well the test is retest-independent, and you can get more post-multitest certainty.

[@healthcaretriage]

I've thought about it. I have a beef to pick with the culture that often follows rapid strep tests...

[@saizai]

Healthcare Triage I think it's an important question. If you have a positive (or negative-but-high-risk) test, but your post-test odds are ~10-90% (i.e. not very certain), what are you supposed to do to get a *definitive* yes/no diagnosis? (E.g. you'd want to have post-all-tests confidence on the order of 99%, especially for things where the treatment if true-positive is very burdensome) Natural topic combinations would be with e.g. whole-body scans (which I bet I can guess your position on…) and how to derive the original pre-test probability estimate (where does one come up with e.g. "30%"? how do you know that the population stats are reliable in the first place, given that _those_ are composed of aggregating a whole bunch of potentially not-definitive results?). PS In case you use this, a video of mine that's relevant: Which are deadlier: sharks or horses? (availability heuristic)

[@icanrememberthis]

6:51 took you this long to make sense, worth the wait, great video. You really should have started with the mammogram example.

[@caseybv74]

icanrememberthis Pay attention and do your homework when you take stats and you can enjoy the whole video. Also this formula pretty much disproves lie detector tests.

[@Borian]

thanks for doing the math ! I recently used Bayes in a different context(machine learning), so it was not difficult to understand. yay, Math !

[@Ziraya0]

You guys should remake this episode, the production quality and presenting skill has increased by leagues, and it'd provide the chance to correct the errors; I think this topic is worth the consideration

[@adambt]

Thank you for bringing the logic and the math. Really enjoying your videos

[@ericwright7643]

I know this was awesome and explained very well but, I'm going to re-watch tomorrow morning after a cup of coffee just to make sure.

[@KeepMeChilled]

a little difficult to follow through if you're new to this, i had to write out the formulas to fully comprehend this video.

[@Kram1032]

Xin Xiong eh, there is value in trying to understand the formulas. And really, those formulas aren't even hard. Understanding them once makes it easier to remember how to use them when googling them later down the line.

[@elliottmcollins]

Much respect that you bothered to work it out.

[@geniusmp2001]

Based on my background evidence on this topic, I predicted on the last video that there was a good probability that this video would be about Bayes' Theorem. Turns out I was right. Clearly, the theorem works. :-)

[@IDecisive]

Help please. I don't get what's going on with the Fagan's Nonogram. In the example given, the pre-test probability is .5%, the likelihood ratio is 8.9, and the post-test probability is about 4%, correct? So why does the black line that is drawn make it seem that the numbers labeled "Pre-test probability" and "Likelihood Ratio" should be switched in order for the graph to be correct? The black line makes it seem that the pre-test probability is about 7.5%-8.9% and the likelihood ratio is .5.

[@NthPortal]

I appreciate that you pointed out this important bit of statistics (it's important for people to understand), but you explained it in a thoroughly unintuitive fashion. You basically gave an equation which does magic to get you to the right answer. I would recommend an explanation (such as this one: yudkowsky.net/rational/bayes ) which explains, intuitively, how and why probability works like this, and teaches you to think about probability in a Bayesian fashion, rather than having to apply a magical formula.

[@zelda12346]

LOL. My comment on the last video was summed up as: "I really wish he had snuck in some conditional probability so he could just shock people with how much conditional probabilities mess with our minds." >This video. >My reaction: =O It's like you read my mind! (or I just guessed a very likely part II and was right, DON'T RUIN MY AMAZEMENT MOMENT) For future videos: there are studies that support/negate certain correlations and/or causations of diseases with interesting problems. Critics of these studies cite "clusters" which do indeed occur at random instead of saying the studies are valid. Since some of these diseases are deadly or potentially dangerous, could you do a video of a collection of these studies as follow up to those studies since some of those have the medical community baffled and/or divided?

[@XiaosChannel]

Welcome to Healthcare Triage where we talk about math and probability! should be the opening line of this episode.

[@Overonator]

Bayes theorem can be applied to all beliefs to determine the likelihood of a belief being true and provides a rational way of updating one's beliefs given new evidence.

[@NthPortal]

Thank you so much for saying that.

[@SSGranor]

Only as long as one had a rational way of assigning prior probabilities in the first place.

[@NthPortal]

Parlyne How does one go about doing that, by the way?

[@SSGranor]

NthPortal It depends on the context. In some cases (such as the one discussed in the video), priors can come from population statistics. In other cases, the priors you use have already been updated using the results of previous tests of some sort. For some applications, priors can even be predicted on totally theoretical grounds. But, sometimes there's really no existing information to go on; and, in such cases, priors come down to a quantification of your own biases (which can be a bit of a problem, really).

[@NthPortal]

Parlyne The best I've heard for getting accurate base-level priors is that good priors might be evolutionarily selected for (in that intelligences with poor priors will tend to be less successful at passing them on), but...it's certainly not clear.

[@vanmaren962]

I'm liking this channel a lot more!

[@cloudluminate]

you are the best!!!!!!!!!! thank you for taking time and making this valuable video!!!!

[@CygnusExOne]

I read in a book by R. Dawkins (IIRC) where he mentioned a 'rule of thumb' for writing popular science literature which said that 'for every equation included in the book you halve your readership'. Do you think this applies similarly to KZbin videos as well?

[@healthcaretriage]

Yeah, well we hold the viewers of HCT in high regard. We think you want to see the math sometimes. At least I do. :)

[@CygnusExOne]

I 120% agree.

[@googolplexbyte]

Healthcare Triage The question is sexist but fuck it. Do equations lower the number of female viewers?

[@CottonDrifting]

googolplexbyte I doubt he knows, youtube stats probably aren't that helpful in that regard, but I think asking questions like that probably adds to women preconceiving of maths as something not for them.

[@laurenlobue]

@@googolplexbyte A very important question! That is, important if one needs to decide whether or not to assign you any credibility or respect. Your question helped me a lot with that. Thanks!

[@dapamico1]

A little confusing at first, but helpful. I struggle, however, with how to apply this knowledge. If I get a positive test for cancer, do the math, and find that I have a 10% chance of having cancer, do I just shrug my shoulders and forget about it? Is there no way to know for sure if you have a disease until symptoms make it obvious? If so, I thought the wisdom was treatment is more effective with early detection. On an objective level, I get what you're saying, but I'm not sure what that means when it's my positive test I'm looking at. Thanks for the great videos, I'm really appreciating them!

[@MeisterHaar]

well the most important thing is to not freak out. you do the math and then research talk to your doc about treatments. if there is a secure treatment you could probably take it but with a 10% chace of having cancer you would probably not do a chemotherapy. its more likely you will have a different test or get checked more often.

[@DanThePropMan]

With most diseases, and especially cancer, there are multiple tests doctors can do. So you don't have to go off just one test - in all likelihood they would send you for two or three or more different ones as soon as possible, so the doctors (and you) can compare the results.

[@RyanGatts]

I love this channel. Thank you so much

[@Implicacean]

Someone design a poster explaining this stuff and send it to ALL the doctors. Doctors love posters.

[@girlgoplayer]

+ I would by that!

[@tkdyo]

probability was the one area in college that was really hard for me. I can do complex circuit analysis, diff eq, and statistics with fly colors, but my probability class destroyed me. Thanks for explaining why I should concentrate on improving in this area more. For some reason just cant wrap my mind around why some of these equations are true.

[@eva01iastate]

I learn a lot from this show love it.

[@Manodragon]

at 2:25 in the top left corner i think you should have written Negative Likelihood

[@AliceNLi]

That was beautiful. Thank you!

[@TheHumanFlag]

@aaroncaroll does this hold true for examinations like CT scans and MRIs?

[@DVSPress]

Shane Killian did a great video on this awhile back that's worth watching. He uses mammography results as an example. Really puts tests results for things like this in perspective.

[@artillerysmith1]

Thanks for thos video. People are getting way too caught up in medical test results.

[@romantheflash]

This was very interesting, and yeah very important information. We sometimes put too much trust in tests, just because we believe there is an authority behind them. However don't many of these tests come with an instruction manuel on how to interpret the test? Or is that just for psychological tests, I don't know

[@TheLukeskywalker2]

To be more accurate, this weird jump between likeliness of the test result giving a false positive and an actual false positive only occurs when the condition is rare. If they are testing for something like the cold, this does not apply. (I am currently studying this in my math class.)

[@AlexRMcColl]

Reminded me of why I'm proud to be a McMaster graduate.

[@kibromfesseha9960]

Are there other tests for breast cancer than mammograms? How do those work out in regard to the sensitivity/specificity spectrum and LRs in comparison?

[@CDGM94]

Can you do more videos on relevant math in the medical field thanks.

[@reenadurai]

how do we know the sensitivity and specificity of the diagnostic instruments that we are using to calculate the likelihood ratio?

[@edoist16]

Healthcare Triage You rock! This came in so handy for a test result today! It allowed to make a much better choice! Why is this not required education in secondary schools health class?

[@j.hanlan4102]

I'm used to be great at math, but I'm out of practice, so while I understood the general idea of this video (medical tests aren't definitive the way we think they are), the formulas turned into number soup in my head.

[@mathnerd97]

What happens if you try testing twice? Does the pre-test ratio of the second test equal the post-test ratio of the first?

[@davidpeterson9930]

Where do these statistics come into play with the doctor's diagnosis? If the percentage is high enough will they call for another test, or are the numbers just for reassuring the patient?

[@Haefaciel]

I think a video explaining HIPAA and it's importance would be helpful.

[@omarkbrown]

This would have been a nice opportunity to talk about p-values as well.

[@cellogirl0096]

This is awesome - thanks!

[@sammartinez8091]

What is one key implication of Bayes’ theorem for screening for disease? Would it be the formula? Meaning that the probability of having fakitis given a pos. test result is =to having a positive test result if having fakitis x probability of having fakitis/ probability of having a positive test result.?

[@moonlitfractal]

Can we show this to the doctors who implied that my illness was all in my head or that I was complaining to get attention when I got negative test results, even though I was clearly displaying symptoms? How about the fact that several chronic diseases sometimes just never test positive?

[@barrettfb]

I love your videos, but man, this one, and last week's were so calculations/data driven that, although I watched the whole videos, I was lost or bored most of the time. Looking forward to more videos. What happened to the French Healthcare video promised?

[@WeAreGRID]

Yes youre right, a positive test result doesnt mean you have the disease, it only means the non specific test said you most likely had it. a SPECIFIC test such as literally "is there too much iron in your blood" is 100% accurate though because it is a test of the cause, not a test of the effect of a disease.

[@rparl]

I took a class which included nomography when I was in college. First time I've seen it in the real (non-academic) world.

[@muppetmastera]

I would love a discussion about STI's :)

[@YoungTheFish]

Wow, what happened to your microphone? It sounds different.

[@Wokanshutaiduo13]

Can you do the Australian Health Care System?

[@itisdevonly]

Good video!

[@sion8]

Also couldn't we create much more definitive test instead of likely-hoods? Or would that require invasiveness in order to be sure, because it seems that in order to be sure the patient's condition (or lack thereof) has to progress so that the physician "sees" in more detail.

[@saikoujikan]

That depends on what the physician is looking for. If they don't know what they are looking for, then where exactly can you start but with the general tests?

[@geniusmp2001]

Yes, a more sensitive test changes the equation. But that's what the last video was about; making the test more sensitive often has tradeoffs in terms of specificity.

[@healthcaretriage]

Matthew Prorok Exactly.

[@sion8]

Ok, so apparently "Sensitivity" can also be called "true positive rate" and "Specificity" can also be called "true negative rate". I still feel there must be a way to be sure with the understanding that everyone is different.

[@absojake]

Bayes statistics is really taking over all of science. However, I am also easily confused by the meaning of the formulas, despite being so mathematically simple. I am not sure if it is due to being exposed to frequentist statistics for so long, or something deeper.

[@_SaadJamil]

How is pretest odds calculated? Based on History and Physical Examination?

[@AllisonMarlyn]

I hate math, but this was really quite interesting and it actually made sense.

[@MidwestMedic]

My head hurts, but this sort of applied math is stuff that more people need to understand. Not to jump on the "there's an app for that" why don't people, including doctors get this math spit out automatically for them when they receive the test results? The sentence of "hey, your prescreening exam said you had a x% chance of having fakeitis, now with this test result you are at x% chance." ...... My thoughts

[@JanCRefsgaard]

because priors are hard to estimate, they depend on age, ethnicity and prior beliefs ect., I do agree that an app where a doctor types in the tests odds and his prior estimate would be helpful!

[@geniusmp2001]

Jan Christian Refsgaard There's at the very least a web page for that. www.richardcarrier.info/bayescalculator.html

[@MidwestMedic]

Yeah, I agree the pretest % would likely need to be manually entered by the physician. But, that should just reinforce the importance of the actual examination and history taking. Look at the big picture, not just one test.

[@MaximumNewbage]

Useful information. But I'm also thinking that the vast majority of people who don't work with numbers frequently will have a hard time following the information in this video. You probably should have mentioned the shortcut up front. Or at least mention that you'll be giving a shortcut at the end. Seems unlikely that most people who are unable to follow the math would stick around until the end of the video otherwise.

[@ljmastertroll]

Is all this going to be on the test?

[@HaranYakir]

You didn't explain the logic behind the formula. Why is that equation correct? Why should it be used?

[@elliottmcollins]

Derivations are pretty widely available if you google the theorem; it's actually pretty intuitive if you think about the first three lines here: mathworld.wolfram.com/BayesTheorem.html It gets used *everywhere*. It's how mathematicians and scientists describe the way we learn about the world given new data.

[@starbuckwhy]

HOW DO YOU FIND OUT YOUR PRE TEST LIKELIHOOD OF HAVING A DISEASE?

[@lugosky02]

Healthcare Triage two things: 1. What happened to the healthcare system of france? 2. You're wrong. I got a Positive test for handsome and it was 100% true. P.S.: This brings me memories from my probability class. god I hate probability!

[@DanThePropMan]

What did your handsome test entail? I'm worried mine wasn't very reliable.

[@lugosky02]

DanThePropMan Well I basically stood in front of the mirror looking at my sexy beastliness. So, according to Bayes theorem we have: P(I'm a utterly handsome given that I say so) = [P(I say I'm handsome given that I am utterly handsome) * P(I am utterly handsome)] / P(I say I'm handsome) where: P (X) - probability of X. Now P(I say I'm handsome given that I am utterly handsome) = 1 P(I am utterly handsome) = 1 P(I say I'm handsome) = 1 P = [1 * 1]/1 = 1 --> 100%

[@markthomasnoonan]

I'm a big fan of using this method to deal with uncertainty but it always seems weak in that initial decision of how likely you think something is. I've never really gotten my head around that. I can see that you might think somebody could have cancer based on various things, but how you get to a 30% figure or whatever.. I guess the formula accounts for some fuzziness at that end which makes it okay.

[@NthPortal]

Yes, the question of how you get priors in an interesting one.

[@JanCRefsgaard]

If the doctor is off by a factor of 3: - same math with a prior probability of 90% and 10% - you would get 99% and 50% I am sure a doctor would order further testing no matter whether he thinks there is a 50%, 79% or 99% chance of cancer. If the doctor is off by a factor of 10: - prior 3% => 22% posterior probability So this is only a problem in the event where the doctor gets the prior very very wrong AND the test is wrong

[@markthomasnoonan]

Thanks. So pretty much, if anything makes a person seem like they have above the baseline chances for an illness and you get a positive result, you take it more seriously than if a person seems fine but has a positive result. Actually, that makes sense. And, as you've shown, you probably know when you make your first assessment that it's not too precise and can accommodate ranges and still get useful information.

[@JanCRefsgaard]

Mark Noonan exactly!, Your intuition is 100% correct, bays theorem is in essence a mathematical formulation of human intuition. In real world scenarios it only a problem to 'guess a prior' if you have little data, imagine that you did 100 (independent) test and 90% of them were positive, then it doesn't matter much whether you belied that the prior probability was 0.000001% or 50%, because after 100 updates you will be way over 99.99% The way you do this is by using test 1 as prior for test 2 and test 2 as prior for test 3 ect...

[@healthcaretriage]

That's the hard part of being a doctor...

[@waikikiman007]

As you point out the normal rule is the higher the Sensitivity the lower the Specificity Can you explain then why Rapid HIV Test Kits can claim 99.6 % Sensitivity and a 99.7 Specificity (Ora Quick Advance - CDC) Do you think this to be unusual ?

[@dangquangtinh]

+Peter Bourne nope, it depends on the nature of your disease, and the marker you've chosen to measure, any comorbid conditions that can cause false pos or neg,.... you have to understand the concept of 'cut-point' to see this through. take this simplified example, your test measure the amount of HIV antibodies, and if it exceeds concentration X, it will be marked positive, otherwise it will be negative. the normal population has a range of HIV antibodies from 0 to Y , and the HIV-affected population has a range from Z to V like this: 0--------------Z----X-----Y-----------------V So there is always a range (from Z to Y) that your concentration of HIV Ab can not tell you if this person is HIV positive or not, thus we come up with a cut-point. If you choose your cut-point (X) at Y, your Specificity will be 100%, but your Sensitivity will be lower. If you choose your X at Z, your Sn will be 100% and your Sp will be lower, So usually, we will take a cut-point somewhere between Z and Y, so that your Sn and Sp will be better overall. This explains why the higher your Sn, the lower your Sp and vice versa. In reality, like your rapid HIV test kits, Sn and Sp are also affected by lots of other co-morbid conditions, bad sampling at wrong moments, HIV Ab are not produced yet,.....

[@dangquangtinh]

+Dang Quang Tinh and also, some tests like HIV Ab is so specific and sensitive, because normal the population will never ever have any kind of HIV Ab concentration, thus your point Y above will mostly be near zero, so in most situation when HIV Ab is found, it's very likely to be a true positive, hence the Specificity of 99,7%

[@waikikiman007]

+Dang Quang Tinh "because normal the population will never ever have any kind of HIV Ab concentration," What is the basis or evidence for this statement?

[@waikikiman007]

+Dang Quang Tinh Thank you for this very clear explanation

[@ahmedsheikh100]

Hi, love your channel. very informative. Could you please discuss the adverse short term effect of cannabis and its long term complications? Is cannabis a "gateway" drug (i.e is their research to suggest that use of cannabis will lead to individual using more additive drugs like crack or herion) ? . Also could you discuss cannabis from a public safety and policy point of view?, Thanks.

[@healthcaretriage]

Ask, and ye shall receive...

[@ahmedsheikh100]

Healthcare Triage :D

[@LZKS]

Wow. Great information. I knew that mammograms were not accurate, but after applying the Bayes' Theorem, the resulting true accuracy is alarming to say the least. We really need to get going on this research of making better tests instead of wasting time on thousands of absolutely useless research (you could do an episode on this).

[@healthcaretriage]

They're not bad. Lots of tests have similar characteristics. We just need to use them appropriately.

[@pantsrevolutions]

I get that this makes some sort of sense, but then how do you find out if you have cancer or not? What's the point of even testing to find out if there is no way? I have relatives with cancer, how did someone find out they had cancer if these tests or so inconclusive?

[@ChocolateTeapot93]

So how do they know if you actually have cancer or not? Why don't the automatically move on to the "how you actually know they have cancer" test for people who are at high risk and skip the mammogram entirely. And are smear tests the same? Are they just not worth having too?

[@chengyanboon]

Dr Carroll explained that the tests become much more relevant when your pre-test odds go up. Some ways to narrow the possibilities: family history of the disease, lifestyle (like smoking for lung cancer), demographics, other tests and symptoms.

[@minwang52]

If there is evidence suggesting that you have a higher chance of having cancer already - say a family history of cancer or a lump in your body, for example, then a positive/negative test result would be a much. much better indicator of whether you have it or not.

[@NthPortal]

Because the more precise and accurate tests are only more so because they gather more data, and they consequently tend to be far more expensive. And there's no point in paying for tons of really expensive tests for things you don't really think you have.

[@saikoujikan]

There is no all encompassing "how do you know you have cancer" test as cancer is an umbrella term covering a whole range of very different diseases. Which cells are cancerous, what defects make them cancerous, and where the cancer is, and if it moves are all factors which will affect how any given test reads. Some tests are general tests, like counting white blood cells, in that thy will tell you things about the body which may change due to illness, they don't tell you what has changed these things, just that these things have changed. Other tests are much more specific , like tests for genetic defects, and will look only for the thing you are looking for. General tests taken individually are useless, a high white cell count could mean leukaemia, but could also mean common infection like a cold. Specific genetic tests are not useful early on as you new to know what it is you are looking for in order to find it, and it tells you nothing of whether or not there is something else happening that you aren't looking for. In theory it might be possible I just run every single test to know everything, but the sheer number of variables to consider makes this impractical and unnecessary, and is very costly and time consuming. Also consider that you are not the only one being tested for, and that the more people that are tested, the longer the wait for your results.

[@healthcaretriage]

They often find out later. That's the problem.

[@megmotherwort]

How are laypeople supposed to find the sensitivity, specificity, odds ratios, etc for the tests a healthcare provider is running on us?

[@michealakinsey7270]

My brain hurts, but this is still important so... *Like.

[@Krystalcove]

Are those statistics for breast cancer and mammograms accurate?

[@Jigkuro]

yes

[@MathAndComputers]

He mentioned in the previous video that the numbers in the table are from a real study on the effectiveness of mammograms.

[@MidwestMedic]

I just thought of this series of videos as a sideways way to talk about the mammograms debate. The math is just complicated enough that it took two videos. But still the same style as always. Instead of "let's talk about the studies" it was "just look at the math".

[@saumitrachakravarty]

2:26 Wrong header at top left. It should read *Negative* .

[@hussainali1990]

Bleugh, it's like studying for step 1 again.

[@JustinAlexanderBell]

Healthcare Triage Can you please do an episode on ASMR?

[@jaywelborn]

Where is the France Healthcare Video?

[@FrancoisBothaZA]

I've studied statistics and I'm comfortable with Bayesian probabilities, but I still struggled to follow the train of thought in this video.

[@ablestmage]

Requires a belief in odds, though..

[@chewyshoey]

What?

[@davidkimlive]

Don't worry! Bayesian analysis will inevitably trend towards the true outcome with repeated test and circumstances. The 'error' can be neglected!

[@Animalcrossing35]

Aren't odds the probability of something being true over something being false and true combined?

[@healthcaretriage]

I don't think so...

[@geniusmp2001]

I think you're thinking of the extended form of Bayes' Theorem. In this simplified formulation, we're looking at P(B) as though that's fixed, because for our purposes, it is. However, we sometimes have to calculate P(B), which we do with this: P(B|A)*P(A) + P(B|~A)*P(~A) . You'll notice that the first part of that is the same thing we had in the numerator; the probability of getting evidence B if A is true times the probability that A is true. The second part is the probability that you'll get evidence B if A is false times the probability that A is false. Those two added together make the total probability of getting evidence B. Total probability isn't really connected with odds, at least not in any direct way.

[@sage5296]

Um 8:00 doesn’t quite look like 0.5% and 8.9 lmao

[@knucklecorn]

Very elucidating.

[@mysteepulcine2510]

Do mammograms cause cancer if done too often?

[@TheWizardofLimes]

Pfft, a positive always means a somethings bad and negative means good, god I thought this guy was a doctor. I mean, I was just tested last week, the test showed a negative for any blood in my body, this obviously means Im fine, right?

[@CottonDrifting]

You didn't understand, trying watching again and thinking about it more :) All he saying is that your family history or symptoms can be more informative than tests alone.

[@TheWizardofLimes]

I was joking haha, I don't think anyones been tested for 'having blood'

[@AlJahhaaf]

Awesome.

[@HannibalPoptart]

Cool thing is, if you understand this, you can probably ace a statistics course!

[@DavidCaugheyJr]

Found this video a little inaccessible to the lay viewer... a combination of it being really math-centered and on drier topic material. What happened to the healthcare of france video?

[@Lovemaxman1234]

Haven't I seen this from xkcd?

[@tomasfernandez9045]

I consider myself a fast lerner, but this episode was a bit overwhelming :s

[@qwaqwa1960]

Toronto: Natives pronounce it Turonno :-)) Nice vid - thx!

[@themanwiththeplan1401]

the hard part is finding the pre-test probabillity lol.

[@Aimez-da-Llama]

Wow. Mind=blown

[@anonharingenamn]

This is waaay too complicated for my brain at 6:56AM.

[@healthcaretriage]

Watch it later!