@@pineapplepenumbra haha, no worries, I was short once too. In my 9th grade, I was shorter than my 4th grade cousin sister at 4 “8”. Then in the span of a year, I grew more than a foot and when I graduated high school, I was 6 feet which made me feel like a giant and I still haven’t adapted to this height yet. But yeah that saying sounds pretty accurate.
Correlation implies causation if that correlation is the result of a trial (experiment) in which the variables are controlled and experimental units are randomly assigned and independent. What is being described in the video is an observational study: 'look at world and record data' and yes narrowing down causal relationships in this case has to be done more carefully and never assumed.
What about unknown unknowns? Spuriousness isn't just about the island, it can pertain to anything (star-sign, solar activity, elections, stock market etcetc). How do we decide in Cats (C) and Height (H) that its Island (I) that is the third factor and not some other factor X? Or Y? Or Z?
Nightmare2077 the Cats and Heights are two characteristics to be measured and their correlation is checked. the unknown is brought in with the island, which represents the whole environment. it also can represent a chain of things/complex causations.
That's exactly my point - what is "the whole environment"? We don't know! And if we think we do know, there may be unknown unknowns: what if there's an undetectable deity on an an island that both causes vegetation and cats (if I think longer I'm sure I can come up with a better example).
Nightmare2077 agree, with deities/magic and multiple universes/Matrix/more dimensions we can never be sure to have a direct correlation. but we can just work in our reality and use our Imagination to go further. also, practically speaking, we can't stop drinking water because it might kill planets in other universes because of missing particles in a special spacetime. the butterfly-effect is powerful, but it's how it affects us that matters. the future is unkown.
Good point, but in order to truly demonstrate causality in the method described, we would need to account for all possible influencing factors in the causal map. The lack of our ability to take literally everything into account epistemologically limits our knowledge to "best guesses" about causation.
But in terms of research is does help with homing in to look for mechanical explanations. Also every part of our existence has been going on the best guesses we have. Gods existing still has a percentage to be true no matter how low it is.
While that's true, it can still help to massively restrict or rule out possible explanations. In a lot of cases people citing correlation =/= causation dismiss any argument as if that's enough.
I always heard the saying as "Correlation does not EQUAL Causation." correlation implying causation is possible, but there's no guarantee it's a definite relationship. Anyway, thank-you for the breakdown!
Yes he did. It's automatically ruled out when we explicitly state we're looking for a causal mechanism. We're trying to explain the correlation between H & C with some causal link. Therefore, we have to make the assumption first that H & C are somehow linked. Thus, we have ruled out the case where all three are independent. Additionally, this is also why we can rule out the other 16 options. Because we have no chance of explaining the correlation between H and C if only two of the three things are correlated and the third is independent.
@Jeremy Penn @minutephysics But in that case, our reasoning didn't prove anything! Well we proved that "if this correlation is due to a causal mechanism, af if we are sure to have listed all the possibilities, then it should be this precise mechanism" At no point have we proven that this causal mechanism was the answer! We decided to rule out spurious correlation. And if we assume that we've looked at it long enough, then we can consider said mechanism a good candidate to explain the correlation. But in no way is it a "proof". It's a deduction made on an assumption.
Where human decided he knows physics well enough to make theories about things under 0.00001% explored. Modern human theories about quantum mechanics are similar to the ones of cavemen about lightning.
it implies potential relationship, but that's already tainted data because of limitations placed upon the number of comparisons being made. unless comparisons are made across all potentials then meaningful results aren't resolved except against what's been compared. unless you compare all available potentials the outcomes are limited to what's being compared, and those are usually selected based on what is expected or typically not expected. there is inherent bias based on what researchers want to either prove or disprove compared against what is assumed to be useless or unrelated information. here's the fun part: researchers don't know what is more or less important to include unless it's tested, and they don't know to include it in the test unless it' done. it's all based on previous human understanding of whatever subject is being studied. which is pretty limiting.
It's funny that you came out with this video today. I actually had this thought, prior to watching this, where I was walking back to my car and noticed a spilled coffee cup next to the door of another car. It occurred to me that the possibilities exist where both of them have nothing to do with each other and were it was completely the their fault. I just think it's awesome how often this can be used in our daily lives!
problem is unknown causes. In the example, you assume that you know everything there is to know about the islands. In the real world, there is always some other unknown cause that also will correlate.
Known knowns: your actual data. Known unknowns: missing data, but you're aware that you don't have the information. Unknown unknowns: the bane of every scientist and statistician. These are factors that affect your conclusions and results, but you don't know how, by how much, or even what the factors are; you don't even realize that they are there, so you can't properly account for them.
if you say A implies B it means that if A is true B is necessarily true. if you find 1 counterexample it means A=>B is false so "doesnt imply", "doesnt necessarily imply" and "doesn't sufficiently imply" are all equivalent.
perfect timing for that sponsor... I was planning on finally learning and understanding maths once and for all... it's the language of the universe and yet so daunting to get behind.
Classical example is that people eat more ice cream on summer and people drown more often on summer but eating ice cream does not cause drowning nor drowning cause people to eat more ice cream.
Basically, a better way of saying it is that correlation does not ENSURE causation. If you use “imply” to mean “suggest that something might be true”, then yes, correlation can imply causation, and a correlation between two things can make it plausible that there is some causative relation between them, directly or with confounding factors. But it doesn’t ensure causation; you still need to look deeper to find how the causation works or if it even exists.
My big college statistics misconception: I took a statics (tension, torsion, compression) class because I read the title in the course catalogue too quickly. Turns out I liked the class better anyway, and it was more useful to my degree in physics.
As I've heard it, the saying is "Correlation does not prove causation", the important distinction being prove instead of imply. Which sort of nullifies the whole point you're trying to make, but I mean it's still a great point to show
From my experience it's only used when people are backed in a corner by research and are trying to disprove said research as much as possible. Rarely do i ever see someone outright claim that a correlation proves causation and the rebuttal being that phrase.
In logic, when it's said that "A implies B" it means that if A is true, then B is necessarily true. For example, the inverse square law of gravity implies that orbits are elliptical. If correlation did in fact imply causation, it would mean that if two things are correlated then there must be some causal relationship between them.
+Kaweta, you would be surprised... Indeed, I found this claim (that you can statistically show causality) in a few books written by statisticians and or mathematicians (relatively "famous" ones)... Epistemologically, however, I just do not see any way how statistics can show causation without information about the experimental design, i.e. 1.) cause preceeds effect, 2.) all alternative explanations can be ruled out or considered very unlikely/unplausible. But as I said, there are claims that certain *statistical* analysis-techniques can determine causation.
alex taws, I'd hazard a guess that the mathematicians and statisticians who made this claim were talking about some idealized model of causality that doesn't map onto the real world. I've never actually taken a statistics class, but I could imagine there being some way to demonstrate causality from correlation if infinite sample sizes are allowed.
1:17 given that each observation can be connected to another in one of three ways (no connection, x -> y, and x C is missing. On top of that, it seems like there are many possible relations not described in this network. Couldn't two observations cause eachother? Cats cause tallness AND tallness causes cats? How about positive feedback loops like cats causing more cats? What about negative relations like cats causing fewer cats or cats causing tallness but tallness inhibiting cats? If each observation can have a positive, negative, or neutral influence on each other observation including itself, that leads to 3^9 = 19,683 possible causal networks. I don't know an easy way to calculate how many of those would be consistent with a significant correlation.
I'm so glad there are so many comments that critique this video, how yes, if we assume we know every variable, then we can imply causation. However, since we're not omnipresent/omnipotent, it's not exactly realistic to the "real reality" to assume we know everything. It can be a practical and coincidental assumption that some variable did in fact cause something, but data doesn't ever really "imply" or in other words, "prove" that it must have caused it. That's not to say that we might not have ruled something out, but since we can't control the unknown, we cuds't possibly prove the cause either. Moreover, under the environment of our universe (or under the assumption for our universal laws), for an object/concept to cause something to another object/concept, it takes two or more to achieve. That being said, there can be many causes to one thing. I might have contributed to something depending how one person views it. Conversely, time I might've thought I caused it with my own free will but might not have caused in reality. That's to say, we are pretty limited in our knowledge of causation and in fact, determining causality might be subjective as well. I also get that many people suggests "practicality," but if we're talking about proofs that try to straighten out facts in black and white, it might fall flat when we test that "proof" in all situations. There is the statistical "law of large numbers" or however you call it. It's certainly useful for assumptions and practicality, so it's enough for an "implication" (in other words, "suggests" causation) under a confidence level or an assumption that suggests that a variable is independent from everything else (aka we assume no other variable causes something). This is probably why I'd say, unless we're somehow omnipresent/omnipotent, the only thing objective in this universe, is that it is objective under constraints/assumption. Statements can be objective if it literally adheres to it's definition. Under an agreement, we can only make objective statements under assumption of what we know or what we agree to limit the subject/conditions to. That being said, we may say something objective under our own scope/conditions, however, that statement might not bear weight over what really happens in our reality. Science/observations about the universe, are examples of what most of what I consider is subjective. Logic, is closest at heart to the objective, even if things seem improbable. For example, if I say that "anything is possible" mainly because there are infinite many unknowns, then there will be red flags going off in some people's heads because that doesn't sound right. "How can statements be in true and false at the same time?" Well they can, if the nature of the words used in that statement are ambiguous (similar to super positioning and thee logic that comes with it). The only way to get around that, is to strictly limit your definition and make it more specific, aka make the definition more known (just like determining a position from a nonzero velocity, the Heisenberg uncertainty principle is basically analogous to this). Besides, making a statement more objective is about making it more known and unambiguous to the point where it's basically the definition of another concept. I get that definitions can be "subjective," however, that doesn't relate to our concept of making an objective statement anyways, because things are objective only to it's observation. Moreover, we also have to unambiguous discern which of the two definition of "possible" are we using, that it is able to happen vs it might happen but we don't know. Like one thing to consider, if God can kill you and promise's that he'll never kill you (and we know he doesn't break promises), can we really say that it's "possible" for God to kill you? It's "possible" that he can kill you be cause he is capable of doing so, but it's also "impossible" because he made a promise to do so. Effectively it's impossible to happen, but it's possible because he's capable, which demonstrates two different meanings of "possibility" which gets straightened out as I break down into more specific components. So if we use the "capable" definition of "possible," then it would mean it is "possible that something is truly impossible" which is a contradiction in itself (which is related to Russell's paradox). And all that is possible because by our own definitions, we explicitly define the opposite of "possible" is "impossible." By the nature of that fact/logic, there's basically a set of known's in the universe that we can deduce more known statements from, in fact, an infinite many, and it's up to us to pick and choose to define. In the end, I just want to stress the importance of what unknown and known (and definitions) can bring, especially in quantum physics, statistics, philosophy, logic, math, science, etc... today. Under specific and constructive definitions, I can really say, there is objectivity at heart of pure logic. So if you're sad that not everything is constantly defined, straightforward, or answered, don't worry, we have foundation set up to know some universal truths under our concern and definitions. If you're sad that something you want "everything is possible" but find that an infinite many things are simply not by principle, that's ok, because most of the things that we are "certain that is impossible" are restrained to certain subjects and they must be worded so that their explicit definitions are direct opposites (so they will no matter what contradict each other making it impossible for both events to occur). So, we still have "endless possibilities" because of unknown/ambiguity, which is nearly just as good for skeptics and dreamers out there, just keep in mind, statistics is a strong form of evidence, not proof, so be mindful of what you make out of that.
Always a pleasure to find a useful video like this. Now whenever this argument comes up again (as it often does, particularly when working with inexperienced statisticians) I can simply send the other party here, instead of having to rehash this/similar explanations over and over again. Thanks 👍🏽
At 1:22: Notice that in 18/19 of the plausible models for C~H, C and H connect by following the arrow(s) in the stated directions. The only exception is the penultimate model (I -> C, I --> H). In epidemiology, this represents confounding: the correlation C~H is confounded by I.
The fact that the simplest possible 3-body relationship generates 20 causality hypotheses shows how difficult this is to apply in real life. The moment you throw in more variables, or substantial measurement errors, it becomes impractical to prove causation with pure logic. In real life human subjects research, there are a couple of ways to prove causation: You can do a randomized controlled trial, which is the only way to directly measure causation. In the cat-island example, you would have to run a 2x2 randomization grid of having human subjects spend their entire lives on Island A versus Island B, and force them to either own a cat or not own a cat. In this scenario, as with most epidemiological studies, it would be unethical and impossible to conduct a true randomized trial. The alternative (which is usually how epidemiology works) is to combine correlational observations with a rigorous theoretical model. In this case, the theoretical model would contain five hypotheses: 1) Island type determines food abundance 2) Food abundance affects human height 3) Food abundance affects cat abundance 4) Cat abundance affects cat ownership 5) Therefore, cat ownership and human height are correlated Each of these hypotheses would be supported by purely observational data (and common sense) as it would be unethical to obtain experimental data. With observational data and a logically sound theory you would have a good level of evidence ("level 2A") for your overall cat-height model. This may seem like a much weaker level of evidence than a logical or mathematical proof, and it is. But in medicine it's often the strongest level of evidence possible.
Of course it can imply it, the problem comes from the fact that many people use such data as if it does guaranteed when it doesn't. The only misconception I'm seeing here is your misconception of the use of that phrase, in other words, because when most of us use it, your suggestion at the end is what we mean.
Correlation can't imply causation. I know what you're getting at, that correlation usually alludes to some relationship between 2 events, but the whole idea of the statement is to carefully step back and analyze the relationship with careful reasoning, not to discard the idea of a relationship. Our brains are effective at parsing information and getting to a reasonable conclusion quickly, but sometimes the streamlined process in which we do this is to our detriment. You can go out of your way to make this happen simply by going to a magic show, but the mantra of "correlation doesn't imply causation" is simply a reminder to statisticians and leymen alike that sometimes there are chance circumstances that would deceive the brains natural train of thought.
Here's a short summary of this video: correlation CAN imply causality (if you use it correctly), correlation doesn't DIRECTLY imply causality, and quantum mechanics is weird,
Yes, thank you. So many people hear this phrase "correlation doesn't imply causation", and then just repeat it without fully understanding it. This is much welcomed.
1:24 actually there are 25. If C->I, C->H is seen as distinct from C->H, you should also account for the 3 others where there is no arrow between C and H, and no arrows out from I, as well as the two with no arrow between C and H and only one arrow from I. It's 25 because there are 3 options for each edge: A->B, A
Here's the issue: Inference of causality is not the same as proving a causality. The process of elimination of those different correlations merely narrows it down, but it doesn't "declare" a, "therefore, this must-have happen" in an objective way.
its important to note that statistics can tell you with certain if something has correlation, if that correlation is positive or negative ( if one variable is higher so is the other, or if one is higher other is smaller), and how strong the correlation is (if one variable goes up, how much will other one go up or down), that is the extent the statistic can tell you about correlation, now, how and why they are in correlation is dependent on more information and if it is all just and accident
1:36 The H->I link cannot be ruled out solely on the basis that people cannot move from one island to the next after they're born. One would assume that humans did not just spontaneously appear there one day. Their ancestors must have arrived there by boat at some point. Maybe something made the smaller colonists go to one island and the taller ones, to the other. Maybe that "something" is ethnic membership, for example. I think the overarching problem here is that you can't just have a variable (call it whatever you want) stand in for every other possible unknowns and then claim that you can measure it! What you CAN do is make sure you manipulate one of the variables at play. If you assign more cats to one of the islands and then check how the height of the inhabitants of each island changes as a result, you can make meaningful statement about the plausibility of C -> H or C not -> H. Similarly, you could manipulate the height of the inhabitants of the islands (with hormones or something) and then check if that changes the inhabitants' tendency to own cats. The existence of significant correlations is a prerequisite for finding causal links, but the nature of the experimental design is what truly enables one to say with any degree of certainty if those correlations point to causal links or something else. Purely observational designs will never be able to uncover causal links because of the "unknown unknowns" problem.
spurious correlation -It is effectively impossible to say that all variables/factors are known. The tall or short people could simply be a a different (sub) species thus their height would have nothing to do with food -which makes all your possible conclusions based on the islands and cats incorrect.
If this video is their best, then I will give their others a miss. This video is just plain wrong, and very obviously so. If the others are even worse, then they don't merit even a glance.
It is important to remind people that often is a correlation we just have to keep doing experimental research and observations to find out what the exact correlation is
In maths jargon, "implies" is a logical operator that means that if the first statement is true then the second statement must be true. "Does not imply" does not rule out the possibility that the second statement is true, only the claim that you can derive the second statement from the first. If you have correlation then you ight have causation, but you cannot assume that you do. In particular, it might be just chance, a possibility that you raised and then unobtrusively dropped from your final list of possibilities.
I think the spirit of the saying is the correlation does not NECESSARILY imply causation (unless you exclude all the other causal relationships) and that it doesn't CONFIRM causation (you have to exclude the possibility of a coincidence). We all know that statistics can lead us to reasonably guess that there could be a causal connection, though we still have to prove it.
Should't you have in your casual network a c--->h--->I--->c? I think this might be another posible outcome, which might imply that the system evolve in a complex manner.
When you say there is two choices remaining for causality, you forgot to mention the third one being “no relation between cat and height” as your explanation do not dismiss this scenario. Other then that, thank you for doing those educational video. It’s fantastic!
But that leaves 25 options, including H->I and C is independent, I->H and C is independent, C->I and H is independent, I->C and H is independent and (C and H)->I and they are independent from each other. These are the options that aren't in the video, but i don't now why they aren't.
There are a number that are already ruled out, like those with complete loops (A->B->C->A... etc, because of no time travel and relativity and such), or those that don't have any chance of explaining A~B, like just B->C or C->B or A->C
Recall that we're trying to explain the correlation H~C with some causal explanation. So we want some causal link between H and C. This rules out 6 cases: the 5 you mentioned plus the "all independent" scenario. So, since we must also remove the 2 loops, we have 3^3 - 6 - 2 = 19. Just what Henry said. :)
There isn't I->H and I->C at 1:29... I don't understand how the result is 19... What formula can I use to resolve this type of problem of possible relation between three variables... Can you explain?... I'm curious
There was a fairly recent paper where they managed to infer causality by assuming such causal networks and then looking at what kind of noise you'd expect under that: The independent variable isn't gonna have a special pattern, but since the dependent variable's noise will inevitably also depend on the independent variable's noise, you can model how that noise ought to look like and see if you get a good fit, effectively giving good evidence for your particular chosen causality. I wonder whether the following makes sense or is complete nonsense: What if we treat these causal nets like Feynman diagrams and try to infer their probability? If I understand them right, and I absolutely might not, you (or a computer) should be able to infer a distribution over causal relationships. Maybe even clues on hidden variables. Because if I saw that right, there are two cases you didn't consider here: - have a fourth source that causes all three of your variables - have variables in a feedback loop causing each other. Neither of those make a whole lot of sense here, but it's totally possible in general, right? So inferring a distribution over all possible causal networks (including ones with loops or additional hidden variables) weighted by their simplicity could tell us a lot, I think. I just have no idea how feasible that would be. (Oh I see some of that you covered in the supplementary video)
This video has proven (correlated to being?) genuinely useful so thank you! The thing about quantum mechanics. ;) I find it fascinating and of course a fundamental part of understanding the universe as well as advanced technologies, but for the majority of people trying to understand the problems around them it is mostly irrelevant, and is then co-opted by conspiracies to justify their own mystical BS.
An hypothetical causal relation can even be real despite correlations suggesting the opposite. Which is perhaps a kind of corollary to "correlation does not imply causation"; "lack of correlation doesn't rules out causation".
Thank you. I hate people who seem to take the correlation doesn't equal causation argument so far, that they seem to argue correlation disproves causation.
It's the plural that's important. a single correlation implies a connection, and it implies that further analysis is valuable. anticorrelations are also valuable.
Here's a related thought: _"People who consume fat reduced "light" products are statistically more overweight."_ Common assumption: _Low-fat products directly make people fatter._ But I think that fat people are more likely to try low-fat products in an attempt to lose weight.
Hi minutephysics! I am very interested in discussion on perpendicular magnetic fields! I've seen a few studies but it having a hard time visualizing. Just wanted to know if you had any input on this particular phenomenon.
right at the beginning when you use the word 'implies' it's not correct. 'Implies' just means suggests, it's not certain , but the common misconception you refer to is that correlation *_means_* causation. That is precisely the error that people fall into. You use it again at 0:40 . You say " _correlation doesn't imply causation. And it's true it doesn't_ " but that is not true. Correlation can, and often *does* imply causation, *that's* the problem. It 'suggests' causation but it is often wrong. That is why we say it doesn't *mean* causation, because other possible causes have not been ruled out. You have to get this right. One thing might _imply_ another i.e. suggest a causal relationship, but that doesn't mean there actually *is* one. That's the whole point, as you know So the phrase has to be 'correlation doesn't *_mean_* causation' ( though it may imply it).
How did you determine the number of causal relationships? There are clearly 27 (3^3) combinations. But for some reason you got rid of the 2 cyclic ones and 5 others with no causation between C and H. Are they not possible or just relevant? C->H H->I I->C CI CI H
Yeah, the 5 with no causation are summed up as "the correlation is just an accident" in the video. The two cyclic ones are rejected as being unphysical (i.e. how can C cause C?). Excellent question though!
I can't see any reason that C couldn't cause C. Positive feedback pops up in all kinds of real-world scenarios such as oscillating circuits, climate change and even animal populations.
+Jefferson Allan, for C to *cause* itself would be logically impossible (it puts you in an infinite regress: to cause C, C would have to exist. To exist, C would have to be caused by C. To exist C would be caused by C .....).
Just a note on brilliant for those interested: The lessons aren't anything special or something you cant get elsewhere for free, so don't pay for them. What's awesome about brilliant are the free community problems, which are great if you want to sharpen your math skills or just do some problems for fun (I have the app on my phone just for this purpose).
Maybe a better title would be the last line of the video? (The one that states correlation by itself can not imply causation, but with other information . . . ) But I do love this video.
I would go as far as to say that strong correlation does indeed imply causation. If the amount of data is huge, the probability of correlation is ramdom chance is basically zero. Now, there still are many, many pitfalls. Example: In the "C causes both A and B" C might be your lack of double blinding your tests, or some other part of your research methods that influences A and B.
Except you messed up the title, differently than the way it says in the video. "CorrelationS can imply causation" at 2:35 mysteriously becomes singular in the title. Allllmost as if it were "baiting" somebody into "clicking" it.
You have a different version of the saying than the way I learned it: "Correlation does not mean causation". It is how I reply to those that point to a correlation and say things like : "See, a causes b." without any other data.
So putting it in technical terms, what you're saying is that causation does imply correlation, which by contraposition suggests that things can not be causally related if they are not correlated. As such, lack of correlation in combination with Bayes' rule can be used to infer what the eventual causal relationship is. Does that make sense?
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I still prefer Randall Munroe's "Correlation doesn't imply causation, but it does wiggle its eyebrows suggestively while mouthing 'look over there' "
Never heard that one. You've just improved my life.
Awesome! Wait, do kids still say awesome?
Epic_Doughnut imagine if all midgets and regular height people were executed, leaving only y’all people
@@adarshsridhar6051 Reminds me of that song, "Short people got no reason to live...".
Btw, I'm short, so I'm not being a hater, here.
@@pineapplepenumbra haha, no worries, I was short once too. In my 9th grade, I was shorter than my 4th grade cousin sister at 4 “8”. Then in the span of a year, I grew more than a foot and when I graduated high school, I was 6 feet which made me feel like a giant and I still haven’t adapted to this height yet.
But yeah that saying sounds pretty accurate.
Minutephysics - because explaining everything with cats is an option.
well, explaining anything WITHOUT cats shouldn't be an option
Schrodinger's height is unknown still, perhaps he was both tall and short.
I’m good with that option
"except maybe not in Quantum Mechanics" is probably what the book on Quantum Mechanics should be called.
Hey, Vsauce, Michael here.
Except maybe not, in quantum mechanics.
Yes ⊙.☉
Except maybe not in quantum mechanics
"Correlation doesn't necessarily imply causation but it can if you analyse it with causal models, except maybe not in quantum mechanics?"
Catchy.
To remember it more easily, you can make it into an acronym: CDNICBICIYAIWCMEMNIQM.
Correlation implies causation if that correlation is the result of a trial (experiment) in which the variables are controlled and experimental units are randomly assigned and independent. What is being described in the video is an observational study: 'look at world and record data' and yes narrowing down causal relationships in this case has to be done more carefully and never assumed.
What about unknown unknowns? Spuriousness isn't just about the island, it can pertain to anything (star-sign, solar activity, elections, stock market etcetc). How do we decide in Cats (C) and Height (H) that its Island (I) that is the third factor and not some other factor X? Or Y? Or Z?
Nightmare2077 the Cats and Heights are two characteristics to be measured and their correlation is checked. the unknown is brought in with the island, which represents the whole environment. it also can represent a chain of things/complex causations.
That's exactly my point - what is "the whole environment"? We don't know! And if we think we do know, there may be unknown unknowns: what if there's an undetectable deity on an an island that both causes vegetation and cats (if I think longer I'm sure I can come up with a better example).
Nightmare2077 agree, with deities/magic and multiple universes/Matrix/more dimensions we can never be sure to have a direct correlation.
but we can just work in our reality and use our Imagination to go further. also, practically speaking, we can't stop drinking water because it might kill planets in other universes because of missing particles in a special spacetime. the butterfly-effect is powerful, but it's how it affects us that matters. the future is unkown.
I assume "the whole environment" is the entire island. Very basic ecological term, really.
noi000 welcome to the world of riddles and logic
Good point, but in order to truly demonstrate causality in the method described, we would need to account for all possible influencing factors in the causal map. The lack of our ability to take literally everything into account epistemologically limits our knowledge to "best guesses" about causation.
Absolutely
Perfect summary
But in terms of research is does help with homing in to look for mechanical explanations. Also every part of our existence has been going on the best guesses we have. Gods existing still has a percentage to be true no matter how low it is.
Daniel King Welcome to science but you'd be surprised what we've accomplished with our best guesses.
While that's true, it can still help to massively restrict or rule out possible explanations. In a lot of cases people citing correlation =/= causation dismiss any argument as if that's enough.
I always heard the saying as "Correlation does not EQUAL Causation." correlation implying causation is possible, but there's no guarantee it's a definite relationship.
Anyway, thank-you for the breakdown!
Wait - you didn't rule out the case of coincidence (the 20th variation)
See the footnote video!
I jumped the gun. Thanks!
Yes he did. It's automatically ruled out when we explicitly state we're looking for a causal mechanism. We're trying to explain the correlation between H & C with some causal link. Therefore, we have to make the assumption first that H & C are somehow linked. Thus, we have ruled out the case where all three are independent.
Additionally, this is also why we can rule out the other 16 options. Because we have no chance of explaining the correlation between H and C if only two of the three things are correlated and the third is independent.
Jeremy Penn he already admitted it lol
@Jeremy Penn
@minutephysics
But in that case, our reasoning didn't prove anything!
Well we proved that "if this correlation is due to a causal mechanism, af if we are sure to have listed all the possibilities, then it should be this precise mechanism"
At no point have we proven that this causal mechanism was the answer!
We decided to rule out spurious correlation. And if we assume that we've looked at it long enough, then we can consider said mechanism a good candidate to explain the correlation. But in no way is it a "proof".
It's a deduction made on an assumption.
Quantum mechanics:where the universe decided that laws are more like, suggestions
Or maybe it decided cause-and-effect can work backwards in time.
its like the pirate codex from Pirates of the Carribean
Where human decided he knows physics well enough to make theories about things under 0.00001% explored. Modern human theories about quantum mechanics are similar to the ones of cavemen about lightning.
They are more like guidelines.
Rules are more like guidelines really! Also rules are made to be broken.
"Correlation doesn't prove causation, but it's certainly a hint."
it implies potential relationship, but that's already tainted data because of limitations placed upon the number of comparisons being made. unless comparisons are made across all potentials then meaningful results aren't resolved except against what's been compared.
unless you compare all available potentials the outcomes are limited to what's being compared, and those are usually selected based on what is expected or typically not expected. there is inherent bias based on what researchers want to either prove or disprove compared against what is assumed to be useless or unrelated information.
here's the fun part: researchers don't know what is more or less important to include unless it's tested, and they don't know to include it in the test unless it' done.
it's all based on previous human understanding of whatever subject is being studied. which is pretty limiting.
"I know that sounds kinda nerdy" and that's supposed to be an issue? I mean, we're already here dude.
It's funny that you came out with this video today. I actually had this thought, prior to watching this, where I was walking back to my car and noticed a spilled coffee cup next to the door of another car. It occurred to me that the possibilities exist where both of them have nothing to do with each other and were it was completely the their fault. I just think it's awesome how often this can be used in our daily lives!
Yessssss🎉😂 good and bad…😊
problem is unknown causes. In the example, you assume that you know everything there is to know about the islands. In the real world, there is always some other unknown cause that also will correlate.
Known knowns: your actual data.
Known unknowns: missing data, but you're aware that you don't have the information.
Unknown unknowns: the bane of every scientist and statistician. These are factors that affect your conclusions and results, but you don't know how, by how much, or even what the factors are; you don't even realize that they are there, so you can't properly account for them.
@FIZIX the Fancader the data you forgot to account for even you it was written down already because you overslept
I think the short cut of "doesn't" is down to there being both a "doesn't necessarily" and "doesn't sufficiently" both being true.
if you say A implies B it means that if A is true B is necessarily true.
if you find 1 counterexample it means A=>B is false
so "doesnt imply", "doesnt necessarily imply" and "doesn't sufficiently imply" are all equivalent.
@@beep_doop yes, but the problem is how the information is processed for the average person
perfect timing for that sponsor... I was planning on finally learning and understanding maths once and for all... it's the language of the universe and yet so daunting to get behind.
Honestly, still one of the best videos on this channel, I find myself consistently coming back to this one.
Classical example is that people eat more ice cream on summer and people drown more often on summer but eating ice cream does not cause drowning nor drowning cause people to eat more ice cream.
Basically, a better way of saying it is that correlation does not ENSURE causation. If you use “imply” to mean “suggest that something might be true”, then yes, correlation can imply causation, and a correlation between two things can make it plausible that there is some causative relation between them, directly or with confounding factors. But it doesn’t ensure causation; you still need to look deeper to find how the causation works or if it even exists.
My big college statistics misconception: I took a statics (tension, torsion, compression) class because I read the title in the course catalogue too quickly. Turns out I liked the class better anyway, and it was more useful to my degree in physics.
As I've heard it, the saying is "Correlation does not prove causation", the important distinction being prove instead of imply. Which sort of nullifies the whole point you're trying to make, but I mean it's still a great point to show
From my experience it's only used when people are backed in a corner by research and are trying to disprove said research as much as possible.
Rarely do i ever see someone outright claim that a correlation proves causation and the rebuttal being that phrase.
In logic, when it's said that "A implies B" it means that if A is true, then B is necessarily true. For example, the inverse square law of gravity implies that orbits are elliptical. If correlation did in fact imply causation, it would mean that if two things are correlated then there must be some causal relationship between them.
+Kaweta, you would be surprised... Indeed, I found this claim (that you can statistically show causality) in a few books written by statisticians and or mathematicians (relatively "famous" ones)... Epistemologically, however, I just do not see any way how statistics can show causation without information about the experimental design, i.e. 1.) cause preceeds effect, 2.) all alternative explanations can be ruled out or considered very unlikely/unplausible. But as I said, there are claims that certain *statistical* analysis-techniques can determine causation.
alex taws, I'd hazard a guess that the mathematicians and statisticians who made this claim were talking about some idealized model of causality that doesn't map onto the real world. I've never actually taken a statistics class, but I could imagine there being some way to demonstrate causality from correlation if infinite sample sizes are allowed.
1:17 given that each observation can be connected to another in one of three ways (no connection, x -> y, and x C is missing.
On top of that, it seems like there are many possible relations not described in this network. Couldn't two observations cause eachother? Cats cause tallness AND tallness causes cats? How about positive feedback loops like cats causing more cats? What about negative relations like cats causing fewer cats or cats causing tallness but tallness inhibiting cats?
If each observation can have a positive, negative, or neutral influence on each other observation including itself, that leads to 3^9 = 19,683 possible causal networks. I don't know an easy way to calculate how many of those would be consistent with a significant correlation.
There are more than 20 variations, actually. 3^3=27. So, 7 are missing: (C->H->I->C), (C->I->H->C), (C H->I), (C I->H), (C->I H), (I->C H), (C->I
I think the more apt way of putting this is that correlation doesn't imply causation, but does help us determine possible causation.
I'm so glad there are so many comments that critique this video, how yes, if we assume we know every variable, then we can imply causation. However, since we're not omnipresent/omnipotent, it's not exactly realistic to the "real reality" to assume we know everything. It can be a practical and coincidental assumption that some variable did in fact cause something, but data doesn't ever really "imply" or in other words, "prove" that it must have caused it. That's not to say that we might not have ruled something out, but since we can't control the unknown, we cuds't possibly prove the cause either. Moreover, under the environment of our universe (or under the assumption for our universal laws), for an object/concept to cause something to another object/concept, it takes two or more to achieve. That being said, there can be many causes to one thing. I might have contributed to something depending how one person views it. Conversely, time I might've thought I caused it with my own free will but might not have caused in reality. That's to say, we are pretty limited in our knowledge of causation and in fact, determining causality might be subjective as well. I also get that many people suggests "practicality," but if we're talking about proofs that try to straighten out facts in black and white, it might fall flat when we test that "proof" in all situations. There is the statistical "law of large numbers" or however you call it. It's certainly useful for assumptions and practicality, so it's enough for an "implication" (in other words, "suggests" causation) under a confidence level or an assumption that suggests that a variable is independent from everything else (aka we assume no other variable causes something). This is probably why I'd say, unless we're somehow omnipresent/omnipotent, the only thing objective in this universe, is that it is objective under constraints/assumption. Statements can be objective if it literally adheres to it's definition. Under an agreement, we can only make objective statements under assumption of what we know or what we agree to limit the subject/conditions to. That being said, we may say something objective under our own scope/conditions, however, that statement might not bear weight over what really happens in our reality. Science/observations about the universe, are examples of what most of what I consider is subjective. Logic, is closest at heart to the objective, even if things seem improbable. For example, if I say that "anything is possible" mainly because there are infinite many unknowns, then there will be red flags going off in some people's heads because that doesn't sound right. "How can statements be in true and false at the same time?" Well they can, if the nature of the words used in that statement are ambiguous (similar to super positioning and thee logic that comes with it). The only way to get around that, is to strictly limit your definition and make it more specific, aka make the definition more known (just like determining a position from a nonzero velocity, the Heisenberg uncertainty principle is basically analogous to this). Besides, making a statement more objective is about making it more known and unambiguous to the point where it's basically the definition of another concept. I get that definitions can be "subjective," however, that doesn't relate to our concept of making an objective statement anyways, because things are objective only to it's observation. Moreover, we also have to unambiguous discern which of the two definition of "possible" are we using, that it is able to happen vs it might happen but we don't know. Like one thing to consider, if God can kill you and promise's that he'll never kill you (and we know he doesn't break promises), can we really say that it's "possible" for God to kill you? It's "possible" that he can kill you be cause he is capable of doing so, but it's also "impossible" because he made a promise to do so. Effectively it's impossible to happen, but it's possible because he's capable, which demonstrates two different meanings of "possibility" which gets straightened out as I break down into more specific components. So if we use the "capable" definition of "possible," then it would mean it is "possible that something is truly impossible" which is a contradiction in itself (which is related to Russell's paradox). And all that is possible because by our own definitions, we explicitly define the opposite of "possible" is "impossible." By the nature of that fact/logic, there's basically a set of known's in the universe that we can deduce more known statements from, in fact, an infinite many, and it's up to us to pick and choose to define. In the end, I just want to stress the importance of what unknown and known (and definitions) can bring, especially in quantum physics, statistics, philosophy, logic, math, science, etc... today. Under specific and constructive definitions, I can really say, there is objectivity at heart of pure logic. So if you're sad that not everything is constantly defined, straightforward, or answered, don't worry, we have foundation set up to know some universal truths under our concern and definitions. If you're sad that something you want "everything is possible" but find that an infinite many things are simply not by principle, that's ok, because most of the things that we are "certain that is impossible" are restrained to certain subjects and they must be worded so that their explicit definitions are direct opposites (so they will no matter what contradict each other making it impossible for both events to occur). So, we still have "endless possibilities" because of unknown/ambiguity, which is nearly just as good for skeptics and dreamers out there, just keep in mind, statistics is a strong form of evidence, not proof, so be mindful of what you make out of that.
Always a pleasure to find a useful video like this.
Now whenever this argument comes up again (as it often does, particularly when working with inexperienced statisticians) I can simply send the other party here, instead of having to rehash this/similar explanations over and over again.
Thanks 👍🏽
I like cats.
I love your videos.
Only one reply to your comment , what a shame
I like cats, too.
In fact, I'm suspicious of people who don't like them.
Henry this is one of your BEST videos !!!
"except maybe in quantum mechanics" should be an implied clause in every single rule.
At 1:22:
Notice that in 18/19 of the plausible models for C~H, C and H connect by following the arrow(s) in the stated directions. The only exception is the penultimate model (I -> C, I --> H). In epidemiology, this represents confounding: the correlation C~H is confounded by I.
The fact that the simplest possible 3-body relationship generates 20 causality hypotheses shows how difficult this is to apply in real life. The moment you throw in more variables, or substantial measurement errors, it becomes impractical to prove causation with pure logic.
In real life human subjects research, there are a couple of ways to prove causation:
You can do a randomized controlled trial, which is the only way to directly measure causation. In the cat-island example, you would have to run a 2x2 randomization grid of having human subjects spend their entire lives on Island A versus Island B, and force them to either own a cat or not own a cat. In this scenario, as with most epidemiological studies, it would be unethical and impossible to conduct a true randomized trial.
The alternative (which is usually how epidemiology works) is to combine correlational observations with a rigorous theoretical model. In this case, the theoretical model would contain five hypotheses:
1) Island type determines food abundance
2) Food abundance affects human height
3) Food abundance affects cat abundance
4) Cat abundance affects cat ownership
5) Therefore, cat ownership and human height are correlated
Each of these hypotheses would be supported by purely observational data (and common sense) as it would be unethical to obtain experimental data. With observational data and a logically sound theory you would have a good level of evidence ("level 2A") for your overall cat-height model.
This may seem like a much weaker level of evidence than a logical or mathematical proof, and it is. But in medicine it's often the strongest level of evidence possible.
Of course it can imply it, the problem comes from the fact that many people use such data as if it does guaranteed when it doesn't.
The only misconception I'm seeing here is your misconception of the use of that phrase, in other words, because when most of us use it, your suggestion at the end is what we mean.
Correlation can't imply causation. I know what you're getting at, that correlation usually alludes to some relationship between 2 events, but the whole idea of the statement is to carefully step back and analyze the relationship with careful reasoning, not to discard the idea of a relationship.
Our brains are effective at parsing information and getting to a reasonable conclusion quickly, but sometimes the streamlined process in which we do this is to our detriment. You can go out of your way to make this happen simply by going to a magic show, but the mantra of "correlation doesn't imply causation" is simply a reminder to statisticians and leymen alike that sometimes there are chance circumstances that would deceive the brains natural train of thought.
Here's a short summary of this video:
correlation CAN imply causality (if you use it correctly),
correlation doesn't DIRECTLY imply causality,
and quantum mechanics is weird,
Pretty sure "quantum mechanics is weird" sumarizes any word where those two words appear together.
"...except maybe not in quantum mechanics" might be the best description of quantum mechanics that I've ever heard.
Yes, thank you. So many people hear this phrase "correlation doesn't imply causation", and then just repeat it without fully understanding it. This is much welcomed.
1:24 actually there are 25. If C->I, C->H is seen as distinct from C->H, you should also account for the 3 others where there is no arrow between C and H, and no arrows out from I, as well as the two with no arrow between C and H and only one arrow from I.
It's 25 because there are 3 options for each edge: A->B, A
You finally uploaded the footnotes AFTER the video, thanks
Here's the issue: Inference of causality is not the same as proving a causality. The process of elimination of those different correlations merely narrows it down, but it doesn't "declare" a, "therefore, this must-have happen" in an objective way.
Well summarized.
Great job listing all the possible causation chains!
its important to note that statistics can tell you with certain if something has correlation, if that correlation is positive or negative ( if one variable is higher so is the other, or if one is higher other is smaller), and how strong the correlation is (if one variable goes up, how much will other one go up or down), that is the extent the statistic can tell you about correlation, now, how and why they are in correlation is dependent on more information and if it is all just and accident
Relevant sponsors??? This is better than ever!
That explanation is brilliant! 2:06 was pretty funny.
Thanks a lot and keep up the good work!
This is MinutePhysics. If I want to hear about statistics, I'd watch MinuteStatistics.
1:36 The H->I link cannot be ruled out solely on the basis that people cannot move from one island to the next after they're born. One would assume that humans did not just spontaneously appear there one day. Their ancestors must have arrived there by boat at some point. Maybe something made the smaller colonists go to one island and the taller ones, to the other. Maybe that "something" is ethnic membership, for example.
I think the overarching problem here is that you can't just have a variable (call it whatever you want) stand in for every other possible unknowns and then claim that you can measure it! What you CAN do is make sure you manipulate one of the variables at play. If you assign more cats to one of the islands and then check how the height of the inhabitants of each island changes as a result, you can make meaningful statement about the plausibility of C -> H or C not -> H. Similarly, you could manipulate the height of the inhabitants of the islands (with hormones or something) and then check if that changes the inhabitants' tendency to own cats. The existence of significant correlations is a prerequisite for finding causal links, but the nature of the experimental design is what truly enables one to say with any degree of certainty if those correlations point to causal links or something else. Purely observational designs will never be able to uncover causal links because of the "unknown unknowns" problem.
one of the best mindopening things i've ever seen
+MinutePhysics this is the essence of computational neural networks if not definition.
AsapSCIENCE AND minutephysics uploading on the same day at around the same time?? Day made.
Any island that has an abundance of cats is already a paradise.
So the crazy cat lady is your ideal partner?
spurious correlation -It is effectively impossible to say that all variables/factors are known.
The tall or short people could simply be a a different (sub) species thus their height would have nothing to do with food -which makes all your possible conclusions based on the islands and cats incorrect.
“except maybe not in quantum mechanics...?” Is a very accurate summary of modern developments in physics
In order to get the perfect causal model you need to assume that you know all the factors that might cause causation.
Best video so far. Pls more on that topic!
If this video is their best, then I will give their others a miss. This video is just plain wrong, and very obviously so. If the others are even worse, then they don't merit even a glance.
1:00 what do you mean 'one thing happened before the other' are these occurrences temporally separated? :3
It is important to remind people that often is a correlation we just have to keep doing experimental research and observations to find out what the exact correlation is
If not Henry
Then who else would do videos like this!!!
In maths jargon, "implies" is a logical operator that means that if the first statement is true then the second statement must be true. "Does not imply" does not rule out the possibility that the second statement is true, only the claim that you can derive the second statement from the first. If you have correlation then you ight have causation, but you cannot assume that you do. In particular, it might be just chance, a possibility that you raised and then unobtrusively dropped from your final list of possibilities.
I think the spirit of the saying is the correlation does not NECESSARILY imply causation (unless you exclude all the other causal relationships) and that it doesn't CONFIRM causation (you have to exclude the possibility of a coincidence). We all know that statistics can lead us to reasonably guess that there could be a causal connection, though we still have to prove it.
No matter what the game is, quantum mechanics seems to always refuse to play by the rules.
Should't you have in your casual network a c--->h--->I--->c? I think this might be another posible outcome, which might imply that the system evolve in a complex manner.
When you say there is two choices remaining for causality, you forgot to mention the third one being “no relation between cat and height” as your explanation do not dismiss this scenario.
Other then that, thank you for doing those educational video. It’s fantastic!
Wonderful! I've been looking for a resource to practice math with for some time now. Thanks
I am really hyped by the Quantum part
1:26. Shouldn't it be 27? Because 3^3 = 27.
Loops where everything causes everything else aren't allowed.
But that leaves 25 options, including H->I and C is independent, I->H and C is independent, C->I and H is independent, I->C and H is independent and (C and H)->I and they are independent from each other. These are the options that aren't in the video, but i don't now why they aren't.
There are a number that are already ruled out, like those with complete loops (A->B->C->A... etc, because of no time travel and relativity and such), or those that don't have any chance of explaining A~B, like just B->C or C->B or A->C
The first four aren't valid because then C and H wouldn't be correlated and it is said they are at 1:12
Recall that we're trying to explain the correlation H~C with some causal explanation. So we want some causal link between H and C. This rules out 6 cases: the 5 you mentioned plus the "all independent" scenario. So, since we must also remove the 2 loops, we have 3^3 - 6 - 2 = 19. Just what Henry said. :)
but how do you rule out the case where they are purely accidentally correlated (case 20)?
alright it's explained in the footnote video LOL
There isn't I->H and I->C at 1:29... I don't understand how the result is 19... What formula can I use to resolve this type of problem of possible relation between three variables... Can you explain?... I'm curious
1:17 that's super interesting! where can i learn more about it other than the references?
There was a fairly recent paper where they managed to infer causality by assuming such causal networks and then looking at what kind of noise you'd expect under that:
The independent variable isn't gonna have a special pattern, but since the dependent variable's noise will inevitably also depend on the independent variable's noise, you can model how that noise ought to look like and see if you get a good fit, effectively giving good evidence for your particular chosen causality.
I wonder whether the following makes sense or is complete nonsense:
What if we treat these causal nets like Feynman diagrams and try to infer their probability? If I understand them right, and I absolutely might not, you (or a computer) should be able to infer a distribution over causal relationships. Maybe even clues on hidden variables.
Because if I saw that right, there are two cases you didn't consider here:
- have a fourth source that causes all three of your variables
- have variables in a feedback loop causing each other.
Neither of those make a whole lot of sense here, but it's totally possible in general, right? So inferring a distribution over all possible causal networks (including ones with loops or additional hidden variables) weighted by their simplicity could tell us a lot, I think. I just have no idea how feasible that would be.
(Oh I see some of that you covered in the supplementary video)
Thank you for brilliant.org ! Best Ad ever :)
This video has proven (correlated to being?) genuinely useful so thank you! The thing about quantum mechanics. ;) I find it fascinating and of course a fundamental part of understanding the universe as well as advanced technologies, but for the majority of people trying to understand the problems around them it is mostly irrelevant, and is then co-opted by conspiracies to justify their own mystical BS.
An hypothetical causal relation can even be real despite correlations suggesting the opposite. Which is perhaps a kind of corollary to "correlation does not imply causation"; "lack of correlation doesn't rules out causation".
Thank you. I hate people who seem to take the correlation doesn't equal causation argument so far, that they seem to argue correlation disproves causation.
Cool this sounds like the intro to QM! Yay!
I usually feel like I know my subject (Physics), until I watch another video on this channel
It's the plural that's important. a single correlation implies a connection, and it implies that further analysis is valuable. anticorrelations are also valuable.
Here's a related thought:
_"People who consume fat reduced "light" products are statistically more overweight."_
Common assumption: _Low-fat products directly make people fatter._
But I think that fat people are more likely to try low-fat products in an attempt to lose weight.
I love her voice, it's the main reason I'm subscribed. Just deep enough to be husky, but high pitched enough to remain feminine.
yellowfolder he's a man. His name is Henry Reich.
Hi minutephysics! I am very interested in discussion on perpendicular magnetic fields! I've seen a few studies but it having a hard time visualizing. Just wanted to know if you had any input on this particular phenomenon.
This was an amazing video !
Thanks for your great videos! Very interesting!
This video somehow stood out form the rest i just lked it and understood it more than the rest
right at the beginning when you use the word 'implies' it's not correct. 'Implies' just means suggests, it's not certain , but the common misconception you refer to is that correlation *_means_* causation. That is precisely the error that people fall into.
You use it again at 0:40 . You say " _correlation doesn't imply causation. And it's true it doesn't_ " but that is not true. Correlation can, and often *does* imply causation, *that's* the problem. It 'suggests' causation but it is often wrong.
That is why we say it doesn't *mean* causation, because other possible causes have not been ruled out.
You have to get this right. One thing might _imply_ another i.e. suggest a causal relationship, but that doesn't mean there actually *is* one. That's the whole point, as you know
So the phrase has to be 'correlation doesn't *_mean_* causation' ( though it may imply it).
"Implies" has two different meanings. In this context it actually does mean "means"
Great stuff, thanks! Genuinely new for me, despite having several degrees...
How did you determine the number of causal relationships? There are clearly 27 (3^3) combinations. But for some reason you got rid of the 2 cyclic ones and 5 others with no causation between C and H. Are they not possible or just relevant?
C->H H->I I->C
CI
CI
H
They are not relevant because we're investigating the cause of the correlation between C and H.
Yeah, the 5 with no causation are summed up as "the correlation is just an accident" in the video. The two cyclic ones are rejected as being unphysical (i.e. how can C cause C?). Excellent question though!
I can't see any reason that C couldn't cause C. Positive feedback pops up in all kinds of real-world scenarios such as oscillating circuits, climate change and even animal populations.
+Jefferson Allan, for C to *cause* itself would be logically impossible (it puts you in an infinite regress: to cause C, C would have to exist. To exist, C would have to be caused by C. To exist C would be caused by C .....).
Doesnt it suffice that the cycle start at I? So then I can cause C, then C H, H I, and I again C, and so on?
Just a note on brilliant for those interested: The lessons aren't anything special or something you cant get elsewhere for free, so don't pay for them. What's awesome about brilliant are the free community problems, which are great if you want to sharpen your math skills or just do some problems for fun (I have the app on my phone just for this purpose).
Maybe a better title would be the last line of the video? (The one that states correlation by itself can not imply causation, but with other information . . . ) But I do love this video.
Wonderful video!
I would go as far as to say that strong correlation does indeed imply causation. If the amount of data is huge, the probability of correlation is ramdom chance is basically zero.
Now, there still are many, many pitfalls. Example: In the "C causes both A and B" C might be your lack of double blinding your tests, or some other part of your research methods that influences A and B.
"Except maybe not in Quantum Mechanics?" should be after every science video ever made on RUclips.
Except you messed up the title, differently than the way it says in the video. "CorrelationS can imply causation" at 2:35 mysteriously becomes singular in the title. Allllmost as if it were "baiting" somebody into "clicking" it.
Yes yes yes do more stats videos please!!!!! :D
Great video again, thank you
A to B , Then when do I get to C ?
EyeoftheYeti Thx bro, I like people like you --- This is the smart side of RUclips...
Error_D2C. Stay away from the other side
Nucularburrito2 lol
You have a different version of the saying than the way I learned it: "Correlation does not mean causation". It is how I reply to those that point to a correlation and say things like : "See, a causes b." without any other data.
"The abundance of cats turned it into a lush paradise" yes
So putting it in technical terms, what you're saying is that causation does imply correlation, which by contraposition suggests that things can not be causally related if they are not correlated. As such, lack of correlation in combination with Bayes' rule can be used to infer what the eventual causal relationship is. Does that make sense?
no
I think "A single correlation does not imply causation" would be more succinct.
Excellent video thank you
They need to teach this causal relationship stuff in first year statistics.