8 ms·

If correlation doesn’t imply causation, then what does? (2012)

173 points by Rickasaurus 13y ago

gazd 13y ago
Isolated correlation?!
da-bacon 13y ago
Also see the follow up with responses from Judea Pearl: http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-correlation-causation-and-the-psychology-of-simpsons-paradox/ http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-...
- kenjackson 13y ago
  Thanks. This is a treat to see this article. I've long wanted to read Pearl's book on this topic, but haven't had the chance to carve out the time. I'm going to dive into this article now.
memla 13y ago
No amount of correlation seems to imply causation. Suppose there is some event X that always causes two other events, Y and Z. Let's also say that Y and Z are exclusively caused by X. Then Y has a 100% perfect correlation with Z, but ex hypothesi it is not caused by it.
kevinalexbrown 13y ago
Good reading in addition to Pearl himself is via Cosma Shalizi. Ref list: http://vserver1.cscs.lsa.umich.edu/~crshalizi/notebooks/causality.html http://vserver1.cscs.lsa.umich.edu/~crshalizi/notebooks/caus... Chapters: http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch22.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch22.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch23.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch23.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch24.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch24.pdf Incidentally, Shalizi is a great source for going back to the basics. His course at CMU "Advanced Data Analysis from an Elementary Point of View" has course notes and exercises available gratis: http://www.stat.cmu.edu/~cshalizi/uADA/13/ http://www.stat.cmu.edu/~cshalizi/uADA/13/. And any time I need to get a reading list, the best place to start is usually his 'notebooks' page.
- saint-loup 13y ago
  I concur. His notebook is a wonder of great resources on many (many many) subjects, with often interesting comments. http://vserver1.cscs.lsa.umich.edu/~crshalizi/notabene/ http://vserver1.cscs.lsa.umich.edu/~crshalizi/notabene/
- Rickasaurus 13y ago
  Also, if you're interested in doing this computationally, you should check out Probabilistic Graphical Models. There's a great Coursera course.
logical42 13y ago
Correlation does imply causation. It just doesn't necessarily establish it as a fact.
- JoshTriplett 13y ago
  Correlation correlates with causation, but "correlation correlates with causation" doesn't imply "correlation implies causation".
  - logical42 13y ago
    Depends what you mean by 'imply'.
    - foobarbazqux 13y ago
      http://dictionary.reference.com/browse/imply http://dictionary.reference.com/browse/imply The third meaning is the one that "correlation does not imply causation" refers to. There is no other meaning for that word in that context.
      - mortehu 13y ago
        As described in the article, "correlation does not imply causation" would hold true even if you take "imply" to mean "is weak evidence for". This is due to Simpson's paradox[1], which says that correlation can be inverted when you take into account an additional distinguishing factor in your data. A specific example. Look at [2] and take the "y" axis to be "cigarettes per day" and the "x" axis to be "life expectancy in years". The overall trend is that more cigarettes leads to a shorter life. However, if we find that the blue group are people who do not inhale, and the red group are people who do inhale, the correlation is reversed for all smokers -- smoking more leads to a longer life. 1. https://en.wikipedia.org/wiki/Simpson's_paradox https://en.wikipedia.org/wiki/Simpson's_paradox 2. https://en.wikipedia.org/wiki/File:Simpson%27s_paradox_continuous.svg https://en.wikipedia.org/wiki/File:Simpson%27s_paradox_conti...
nsxwolf 13y ago
This is seriously in need of a tl;dr
- jrn 13y ago
  I've read the book, a scattered 2 times and couldn't give you a tl;dr.
  - physicslover 13y ago
    I read chapters of it a few years back, too, but forgotten the details. All in all, I was pretty convinced of the soundness of the approach at the time. My recollection is that this framework of causal inference allows one to ask questions about a probabilistic model that one can then try and measure to test causality. These questions are interventions or assertions (the do operators) that something happened. So one would start out with a Graphical Model like in the smoking example which defines a probability model, and then make do assertions on the model for various candidate causes and see what that would imply about the change in probabilities and then design an experiment to measure them and confirm them.
    - jrn 13y ago
      I thought it was a good approach as well, but I have a hard time fitting it into the math I know. I've been learning category theory so I may take another stab at placing it. But this all takes time. And the book's layout is fairly disjointed. I may just begin experimenting with the theory, rather than placing it, my life is short.
- cheald 13y ago
  Words, words, words. A lot of words.
nbouscal 13y ago
Relevant XKCD: http://xkcd.com/552/ http://xkcd.com/552/
- surement 13y ago
  Thanks! That's a great one.
nhebb 13y ago
> North: Democrat (145/154, 94 percent), Republican (138/162, 85 percent) > South: Democrat (7/94, 7 percent), Republican (0/10, 0 percent) > Overall: Democrat (152/248, 61 percent), Republican (138/172, 80 percent) This example is often cited for Simpson's Paradox, but because the South headcount for Republicans (10) and Democrats (94) had such a wide disparity and the Republican headcount was so low, it always seemed more like twisting the data to fit a political narrative than to make a statistical argument. Like other statistical methods, there should be a minimum population size for the paradox to be meaningful.
- haldujai 13y ago
  http://www.bmj.com/content/309/6967/1480.full http://www.bmj.com/content/309/6967/1480.full https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone_treatment https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone... Has larger sample sizes, all would be valid for statistical analysis. Although this paradox isn't really dependent on a sample size, it is not so much a statistical test. It's a trend that can be observed when looking at sub groups compared to overall averages. In the above example open surgery was better for both small and large kidney stones and is a prime example of Simpson's paradox. However, one should note that Simpson's paradox can also be subject to further confounding variables. Perhaps patients that were suitable for open surgery were in better medical condition and therefore the open surgery sample was non-random and caused the higher success rate. The presence of Simpson's paradox, similar to correlation, also does not imply causation.
- jtc331 13y ago
  And contrary to the OP, these results don't demonstrate a reversal of the predictors (i.e., that actually being a Democrat predicts voting for the Civil Rights Act and vice versa), but rather than we're possibly using the wrong predictors. That is, rather than demonstrating that there is a different correlation between party and vote, it demonstrates that there is a (stronger) correlation between geography and vote.
skatenerd 13y ago
https://en.wikipedia.org/wiki/David_Hume https://en.wikipedia.org/wiki/David_Hume
dschiptsov 13y ago
multiple causation.))
javert 13y ago
> We can’t have X causing Y causing Z causing X! At least, not without a time machine. You should be able to have cyclic graphs, though. W could cause X which causes Y which causes Z which causes more X.
- bigfudge 13y ago
  Perhaps you just need to include time. Does X_1 causing Y causing Z causing Z_2 solve your problem without requiring cyclic graphs?
  - javert 13y ago
    Yes, but then the nodes in the graph become even more disconnected from the concretes in reality that they are supposed to represent. I am actually highly skeptical of the entire notion of the article, but I haven't had time to finish the article yet. My skepticism comes from the fact that causal relationships can be explained by identifying and understanding the causal factors at play and drawing relevant conclusions. For example, smoking causes lung cancer because exposure to toxic chemicals causes genetic mutations. Existing mathematics (such as basic statistics, including correlation) can be used as additional empirical evidence to support such an explanation.
maaku 13y ago
A predictive model and Bayes theorem.
snowwrestler 13y ago
This article is largely focused on epidemiological studies. These are a very well-known type of scientific investigation, particularly among the tech crowd--because it is tech-intensive to manage and analyze large volumes of data. But, epidemiology is not all of science, it's just one way to do science. So this statement is wrong, or, at least, not complete: > The standard scientific answer to this question is that (with some caveats) we can infer causality from a well designed randomized controlled experiment. The more general scientific answer is that we need an hypothesis that can be tested and disproven by observation. Such observations can come from a randomized controlled trial, but a surprising amount of important scientific observations do not. For example, a major confirming test of relativity was to measure the apparent displacement of stars due to gravitational lensing during an eclipse. Obviously there is no way to create a random double blind study of this. (Unless one were to stare too long without eye protection! [rimshot]) But wait, I could hypothesize that saying "blutarski" when flipping a coin will make it land heads up, and if I only do the observation once, my stupid hypothesis might get confirmed. Right? In this case, yes, a lengthy trial would help provide much better observations. But the more general answer is that a reasonable hypothesis must propose a physical system that could plausibly cause the predicted result. There is no known physical system that connects "blutarski" with coins, or Facebook traffic with Greek bonds. But there is a plausible physical mechanism by which smoke inhalation could lead to lung cancer. This is what scientists are talking about when they say things like "there's more to science than curve-fitting." But most people do not understand the difference, and that's why we see things like global climate circulation models get mixed up with historical climate reconstruction, or paleontology get mixed up with evolutionary biology.
- Goladus 13y ago
  This is an excellent explanation. I'm not sure what you mean by paleontology being mixed up with evolutionary biology, though.
  - snowwrestler 13y ago
    A lot of critics of evolutionary theory believe that the fossil record is the most important piece of supporting evidence--hence the focus on "missing links" between species. The scientific reality is that Darwin formulated his theory by looking at living species, and the modern study of evolutionary processes does too--primarily viruses, bacteria, and insects, because their lifespans are so short.
joe_the_user 13y ago
Correlation + plausible based on your knowledge of the world implies causation (obviously to the appropriate degree). It's the flip-side of extraordinary claims require extraordinary evidence. Facebook driving Greek debt is implausible and two vaguely shaped curves aren't enough. A formula that predicts to many decimal places over a fair period, prospectively, would be really weird but hard to ignore. Spanish debt, gold prices or something related on the other hand, would require proportionately less evidence for causation. This disturbs people because it implies you can get stuck in a pathological view of the world and statistics and evidence won't get you out. Sorry about that. Edit: And this is pretty the Bayesian Approach. It's just that Bayesian Statistics and Pearl arguments, are themselves just models of the world. You can have others but, even more, you need more of an arguments than "stuff that seems implausible needs more evidence" and all of the more elaborate stuff is going to be specific to a given situation and thus might be applicable to a different one.
- raverbashing 13y ago
  "Facebook driving Greek debt is implausible" Yes, but in reality you don't know that Plausibility is a subjective measure, and while I would say that, yes, it can be a hint, you cannot disregard something merely because it's implausible
  - Robin_Message 13y ago
    > a hint, you cannot disregard something merely because it's implausible Coming back to Bayesian statistics, the word for this is prior, and its not that you disregard evidence, its that you can quantify both your existing beliefs about reality and the change in your beliefs according to the evidence you see. Firstly, our hint: we have a prior assumption of the probability that the popularity of Facebook is driving up Greek debt (call it P(Fg)). Then, we observe a correlation between these two things. For the sake of argument, I'm going to make this 0.001 (I'd probably estimate less). Now, once we see this correlation, we now need to calculate two things: 1. The probability of observing that correlation (call that P(C)). Note that the more extraordinary the correlation, the less probable it is, and the smaller this term would be. In this case, the graph matches vaguely, I'm going to give it a probability of 0.1. 2. Given a world where there is a causation, what is the probability we'd see this correlation (Q: I'm not 100% on this part). Now, Greek debt could plausibly be driven by other things, which would mask the Facebook effect, so there's no guarantee there would be a correlation. This term is called P(C | Fg), and I have no idea what value to give it. Let's try 0.5. What we want to know is: P(Fg | C), that is, the probability of a connection given we have observed a correlation. Boom! P(Fg | C) = P(C | Fg) x P(Fg) / P(C) So our posterior probability (after observing this correlation) changes from 0.001 to 0.001 x 0.5 / 0.1 = 0.005
im3w1l 13y ago
>Obviously, it’d make no sense to have loops in the graph: I stopped reading here. Not saying models without loops cannot be useful though.
- davorak 13y ago
  Here is my understanding from a non-expert. The obviousness is suposed to come from if `a` causes `b`, `b` can not have caused `a` because that would need some form of time travel. `b` could cause `a2` though which is very similar to `a` but is separated in time from `a`.
  - im3w1l 13y ago
    Yeah that makes sense. But then he uses the model wrongly, since he puts "hidden factor" "smoking" "lung cancer" in the vertices, and not "hidden factor (t=0)", "smoking(t=1)" and "lung cancer(t=2)". Further if used like that, then a possible hidden factor could actually be "lung cancer(t=0)", since it could (conceivably) cause both "smoking(t=1)" and "lung cancer(t=2)".
    - davorak 13y ago
      > But then he uses the model wrongly, since he puts "hidden factor" "smoking" "lung cancer" in the vertices, and not "hidden factor (t=0)", "smoking(t=1)" and "lung cancer(t=2)". The direction of the arrows shows causation with also implies time has passed though the amount of time is not specified in the model he is using, though it could be added. He has a section latter in the article about why he left it absent earlier and covers how it could be included. > Further if used like that, then a possible hidden factor could actually be "lung cancer(t=0)", since it could (conceivably) cause both "smoking(t=1)" and "lung cancer(t=2)". If lung cancer actually caused smoking then yes that would a simple solution. If that was the answer though the very next question would be what caused "lung cancer(t=0)". Which "smoking(t=-1)" if existed would be suspect, and another "hidden factor"(s) of course as well.
  - deleted 13y ago
    [deleted]
zalmkleurig 13y ago
http://en.m.wikipedia.org/wiki/Granger_causality http://en.m.wikipedia.org/wiki/Granger_causality
SagelyGuru 13y ago
It is dangerous to assume causality from any data alone. (Data and statistics are over-rated nowadays). You need to do the harder work of discovering the proper mathematical model (equation) relating explicitly the dependent (caused) variables to the independent (causing) variables. In the absence of such a verified and proven model, you just can not take a shortcut of pulling causality out of statistics, like a rabbit out of a hat. Incidentally, the "Simpson's paradox" to which so much attention is given here, is a trivial illustration of the fact that you can not meaningfully add percentages from differing amounts. Something every school kid ought to learn.
- tedsanders 13y ago
  Can you expand on this idea? To me it seems fine to draw causal inferences from data alone.
  - klipt 13y ago
    It depends where the data comes from. The gold standard in science is a controlled, randomized experiment - but obviously that standard is not always attainable.
  - gngeal 13y ago
    I think it helps a lot if you have a plausible explanation for the chain of causes. For example, the correlation of dead people in houses with shitty stoves and furnaces in those houses is interesting, but once you discover that said stoves and furnaces leak carbon monoxide, AND that carbon monoxide binds to hemoglobin with much greater affinity than oxygen, AND that the affected people don't receive any specific warning symptoms when that happens, you suddenly have a reason to stop wondering whether or not they were committing suicide at a heightened rate because of poverty-related depression.
- AlexFinks 13y ago
  But why is it dangerous, on balance, to make assumptions of causality from data and statistics alone? Animals, such as rats and ravens, face this problem all the time, and yet they can meaningfully effect the world in such manner that would imply causal understanding, and a sensitivity towards the difference between mere correlation or a correlation with causal potential. Humans do the same as well, naive people who have never learned about experimental design, or have never learned the concept of correlation, also make useful judgments on the causal model behind ordinary problems and events. How did these machines make actionable judgments on causality with nothing more than noisy inputs to their sensory systems? Through what technique did they discern the difference between mere correlation, and a correlation with exploitable causality?
tlarkworthy 13y ago
This is the fundamental reason why general AI might not be possible on a computer without a body. To infer causality, you must form a hypothesis then design an experiment to confirm/deny it. Passively observing the world can't disambiguate between complex correlations or causality (even with a fancy calculus). You need action to learn the intricacies of the world. Think how the discovery of electricity led to electronics. There is nothing like electronics in the natural world, the only route to electronics is via an iteratively refined causal model of the universe.
- gwern 13y ago
  > This is the fundamental reason why general AI might not be possible on a computer without a body. 'Body' is a rather misleading term to use for what a general AI might need. And I say 'might' because part of the motivation for the Pearlean program is for discovering under what data and conditions one can infer causality without randomized interventions.
cousin_it 13y ago
Sometime ago I tried to come up with the simplest possible explanation for Simpson's paradox. This was the result: 1) Imagine that most women with a certain disease survive, while most men die. 2) Imagine that most women with the disease take a certain medicine, while most men don't. 3) Imagine that the medicine has absolutely no effect. Women just happen to have better innate resistance to the disease, and also just happen to buy the medicine more because it's marketed to women. Now if you do a statistical analysis without counting men and women separately, you will conclude that the medicine is very correlated with survival! Note that there's no way to know in advance that you should slice the population along such-and-such variables, which can be a lot more subtle than just gender. Also note that the example works even if the medicine has a slight negative effect, i.e. you can reverse the direction of correlations by choosing to slice or not to slice. I think such results make it clear that you can't easily trust conclusions from statistics. One minute you're thinking that cholesterol causes heart disease, and the next minute you're asking yourself, what if cholesterol is part of the body's response to heart disease? That's why we need randomized controlled studies, and theories of causality.
- TillE 13y ago
  > most women with the disease take a certain medicine, while most men don't Unless "most" = nearly all, this kind of situation is not difficult to untangle if you have sufficient and appropriate data.
  - raverbashing 13y ago
    Still, numbers are important. What's most? 50.1%? 70%? 99.9999%?
  - ChikkaChiChi 13y ago
    The point is well made. Any sort of deviation from control that exhibits a pattern will directly influence the outcome of your results.
- saalweachter 13y ago
  Also note that slicing the data too many ways is also dangerous. Every time you slice the data a different way, you increase the chances that you will find a spurious correlation. It is very easy for a naive researcher to fail to adjust their p-values and mistake the spurious correlation for a real one. It is also very easy for a biased researcher to cherry-pick the correlations which match their expectations.
deleted 13y ago
[deleted]
graycat 13y ago
> what does? (1) A clear mechanism. Data. My car won't run. Cause. The universal joint at the differential for the rear wheels failed leaving the rear end of the drive shaft on the ground. (2) A solid scientific theory. Data. I let go of the 2 x 4, and it hit my foot and hurt. Cause. Newton's law of gravity. (3) Other. Data. There is a correlation between smoking and lung cancer. Cause. Guess that there are some chemicals in cigarette smoke that cause lung cancer. Without actually finding the chemicals, basically test the heck out of the connection, i.e., look for and reject (statistically as in an hypothesis test) other candidate causes, see if cigarette smoke does cause mutations (causing mutations are easier to test for than causing cancer, and nearly every chemical that causes cancer also causes mutations; so, if a chemical doesn't cause mutations, then it likely doesn't cause cancer; if the chemicals in cigarette smoke do cause mutations, then can't reject that they cause cancer and have to keep entertaining that the chemicals might cause cancer and have to keep testing), reject spurious correlations, do some more tests that might reject causality and observe that they do not reject, look for other causes, work hard, get tired, give up, and finally conclude that have done enough work and time to stop smoking.
- new_test 13y ago
  Doesn't sound like you understand what the discussion is about.
  - graycat 13y ago
    I responded directly to the question in the title of the post here at HN: > If correlation doesn’t imply causation, then what does? not directly to the article or the discussion here on HN. I don't think that the article makes much sense. I gave a very simple answer, (1) and (2). For (3), that's a mess and closer to the discussion. My view is that for causality, what I gave with (1) and (2), simple, childishly simple, dirt simple, is, unfortunately, in reality, about all there is to the poor, struggling subject. Put more respectfully, beyond my simplistic (1) and (2), working with causality is super difficult and quite unpromising as in mostly just f'get about it. For my (3) it boils down to ways to reject causality and then we accept causality once we get so tired trying to reject it we just give up and accept it. Why? Because without something detailed and mechanical, say, from chemistry, biochemistry, and the forbiddingly complicated, detailed biochemistry of cells, we are missing anything very solid to call causal. E.g., in my (1), with the universal joint that failed, we have a simple explanation that makes a solid cause; getting something so simple and solid for a cause of cancer from smoking will be super difficult. Don't worry, I don't smoke, but neither do I claim really to know a cause of cancer. Causality is a great, intuitive idea for humans and animals, but looked at in detail it's tough to establish in all but some narrow situations. For causal networks, path analysis, Markov random fields, directed acyclic graphs, lots of diagrams with circles and arrows, f'get about it. For getting causality out of data analysis, mostly just a fool's errand -- f'get about it. There is a significant reason I concentrated on (1) something mechanical and (2) something from classic physics -- those two darned near cover what can be done with causality. For the biological sciences -- causality is really important but really tough. For the social sciences, they try and try, and my wife did in her Ph.D. in essentially mathematical sociology and my brother did in his Ph.D. in political science, but, net, watching my wife and brother struggle with trying to make causality work in social science, where it's so easy to make it with (1) and (2), I just said f'get about it. You can entertain my views and my first very short post as a contribution to the discussion based on a lot of background and a claim that more is a fool's errand or just chalk it up to my ignorance. One more point: I didn't even mention correlation. Why? Because correlation is so far from causality that it's hardly worth even mentioning.
wissler 13y ago
David Hume said it first: http://en.wikipedia.org/wiki/Constant_conjunction http://en.wikipedia.org/wiki/Constant_conjunction

173 points by Rickasaurus 13y ago

gazd 13y ago

Isolated correlation?!

Also see the follow up with responses from Judea Pearl: http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-correlation-causation-and-the-psychology-of-simpsons-paradox/ http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-...

kenjackson 13y ago
Thanks. This is a treat to see this article. I've long wanted to read Pearl's book on this topic, but haven't had the chance to carve out the time. I'm going to dive into this article now.

memla 13y ago

No amount of correlation seems to imply causation. Suppose there is some event X that always causes two other events, Y and Z. Let's also say that Y and Z are exclusively caused by X. Then Y has a 100% perfect correlation with Z, but ex hypothesi it is not caused by it.

kevinalexbrown 13y ago

Good reading in addition to Pearl himself is via Cosma Shalizi. Ref list: http://vserver1.cscs.lsa.umich.edu/~crshalizi/notebooks/causality.html http://vserver1.cscs.lsa.umich.edu/~crshalizi/notebooks/caus... Chapters: http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch22.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch22.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch23.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch23.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch24.pdf http://www.stat.cmu.edu/~cshalizi/uADA/13/lectures/ch24.pdf Incidentally, Shalizi is a great source for going back to the basics. His course at CMU "Advanced Data Analysis from an Elementary Point of View" has course notes and exercises available gratis: http://www.stat.cmu.edu/~cshalizi/uADA/13/ http://www.stat.cmu.edu/~cshalizi/uADA/13/. And any time I need to get a reading list, the best place to start is usually his 'notebooks' page.

saint-loup 13y ago
I concur. His notebook is a wonder of great resources on many (many many) subjects, with often interesting comments. http://vserver1.cscs.lsa.umich.edu/~crshalizi/notabene/ http://vserver1.cscs.lsa.umich.edu/~crshalizi/notabene/
Rickasaurus 13y ago
Also, if you're interested in doing this computationally, you should check out Probabilistic Graphical Models. There's a great Coursera course.

logical42 13y ago

Correlation does imply causation. It just doesn't necessarily establish it as a fact.

JoshTriplett 13y ago
Correlation correlates with causation, but "correlation correlates with causation" doesn't imply "correlation implies causation".
- logical42 13y ago
  Depends what you mean by 'imply'.
  - foobarbazqux 13y ago
    http://dictionary.reference.com/browse/imply http://dictionary.reference.com/browse/imply The third meaning is the one that "correlation does not imply causation" refers to. There is no other meaning for that word in that context.
    - mortehu 13y ago
      As described in the article, "correlation does not imply causation" would hold true even if you take "imply" to mean "is weak evidence for". This is due to Simpson's paradox[1], which says that correlation can be inverted when you take into account an additional distinguishing factor in your data. A specific example. Look at [2] and take the "y" axis to be "cigarettes per day" and the "x" axis to be "life expectancy in years". The overall trend is that more cigarettes leads to a shorter life. However, if we find that the blue group are people who do not inhale, and the red group are people who do inhale, the correlation is reversed for all smokers -- smoking more leads to a longer life. 1. https://en.wikipedia.org/wiki/Simpson's_paradox https://en.wikipedia.org/wiki/Simpson's_paradox 2. https://en.wikipedia.org/wiki/File:Simpson%27s_paradox_continuous.svg https://en.wikipedia.org/wiki/File:Simpson%27s_paradox_conti...

nsxwolf 13y ago

This is seriously in need of a tl;dr

jrn 13y ago
I've read the book, a scattered 2 times and couldn't give you a tl;dr.
- physicslover 13y ago
  I read chapters of it a few years back, too, but forgotten the details. All in all, I was pretty convinced of the soundness of the approach at the time. My recollection is that this framework of causal inference allows one to ask questions about a probabilistic model that one can then try and measure to test causality. These questions are interventions or assertions (the do operators) that something happened. So one would start out with a Graphical Model like in the smoking example which defines a probability model, and then make do assertions on the model for various candidate causes and see what that would imply about the change in probabilities and then design an experiment to measure them and confirm them.
  - jrn 13y ago
    I thought it was a good approach as well, but I have a hard time fitting it into the math I know. I've been learning category theory so I may take another stab at placing it. But this all takes time. And the book's layout is fairly disjointed. I may just begin experimenting with the theory, rather than placing it, my life is short.
cheald 13y ago
Words, words, words. A lot of words.

nbouscal 13y ago

Relevant XKCD: http://xkcd.com/552/ http://xkcd.com/552/

surement 13y ago
Thanks! That's a great one.

nhebb 13y ago

> North: Democrat (145/154, 94 percent), Republican (138/162, 85 percent) > South: Democrat (7/94, 7 percent), Republican (0/10, 0 percent) > Overall: Democrat (152/248, 61 percent), Republican (138/172, 80 percent) This example is often cited for Simpson's Paradox, but because the South headcount for Republicans (10) and Democrats (94) had such a wide disparity and the Republican headcount was so low, it always seemed more like twisting the data to fit a political narrative than to make a statistical argument. Like other statistical methods, there should be a minimum population size for the paradox to be meaningful.

haldujai 13y ago
http://www.bmj.com/content/309/6967/1480.full http://www.bmj.com/content/309/6967/1480.full https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone_treatment https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone... Has larger sample sizes, all would be valid for statistical analysis. Although this paradox isn't really dependent on a sample size, it is not so much a statistical test. It's a trend that can be observed when looking at sub groups compared to overall averages. In the above example open surgery was better for both small and large kidney stones and is a prime example of Simpson's paradox. However, one should note that Simpson's paradox can also be subject to further confounding variables. Perhaps patients that were suitable for open surgery were in better medical condition and therefore the open surgery sample was non-random and caused the higher success rate. The presence of Simpson's paradox, similar to correlation, also does not imply causation.
jtc331 13y ago
And contrary to the OP, these results don't demonstrate a reversal of the predictors (i.e., that actually being a Democrat predicts voting for the Civil Rights Act and vice versa), but rather than we're possibly using the wrong predictors. That is, rather than demonstrating that there is a different correlation between party and vote, it demonstrates that there is a (stronger) correlation between geography and vote.

skatenerd 13y ago

https://en.wikipedia.org/wiki/David_Hume https://en.wikipedia.org/wiki/David_Hume

dschiptsov 13y ago

multiple causation.))

javert 13y ago

> We can’t have X causing Y causing Z causing X! At least, not without a time machine. You should be able to have cyclic graphs, though. W could cause X which causes Y which causes Z which causes more X.

bigfudge 13y ago
Perhaps you just need to include time. Does X_1 causing Y causing Z causing Z_2 solve your problem without requiring cyclic graphs?
- javert 13y ago
  Yes, but then the nodes in the graph become even more disconnected from the concretes in reality that they are supposed to represent. I am actually highly skeptical of the entire notion of the article, but I haven't had time to finish the article yet. My skepticism comes from the fact that causal relationships can be explained by identifying and understanding the causal factors at play and drawing relevant conclusions. For example, smoking causes lung cancer because exposure to toxic chemicals causes genetic mutations. Existing mathematics (such as basic statistics, including correlation) can be used as additional empirical evidence to support such an explanation.

maaku 13y ago

A predictive model and Bayes theorem.

snowwrestler 13y ago

This article is largely focused on epidemiological studies. These are a very well-known type of scientific investigation, particularly among the tech crowd--because it is tech-intensive to manage and analyze large volumes of data. But, epidemiology is not all of science, it's just one way to do science. So this statement is wrong, or, at least, not complete: > The standard scientific answer to this question is that (with some caveats) we can infer causality from a well designed randomized controlled experiment. The more general scientific answer is that we need an hypothesis that can be tested and disproven by observation. Such observations can come from a randomized controlled trial, but a surprising amount of important scientific observations do not. For example, a major confirming test of relativity was to measure the apparent displacement of stars due to gravitational lensing during an eclipse. Obviously there is no way to create a random double blind study of this. (Unless one were to stare too long without eye protection! [rimshot]) But wait, I could hypothesize that saying "blutarski" when flipping a coin will make it land heads up, and if I only do the observation once, my stupid hypothesis might get confirmed. Right? In this case, yes, a lengthy trial would help provide much better observations. But the more general answer is that a reasonable hypothesis must propose a physical system that could plausibly cause the predicted result. There is no known physical system that connects "blutarski" with coins, or Facebook traffic with Greek bonds. But there is a plausible physical mechanism by which smoke inhalation could lead to lung cancer. This is what scientists are talking about when they say things like "there's more to science than curve-fitting." But most people do not understand the difference, and that's why we see things like global climate circulation models get mixed up with historical climate reconstruction, or paleontology get mixed up with evolutionary biology.

Goladus 13y ago
This is an excellent explanation. I'm not sure what you mean by paleontology being mixed up with evolutionary biology, though.
- snowwrestler 13y ago
  A lot of critics of evolutionary theory believe that the fossil record is the most important piece of supporting evidence--hence the focus on "missing links" between species. The scientific reality is that Darwin formulated his theory by looking at living species, and the modern study of evolutionary processes does too--primarily viruses, bacteria, and insects, because their lifespans are so short.

joe_the_user 13y ago

Correlation + plausible based on your knowledge of the world implies causation (obviously to the appropriate degree). It's the flip-side of extraordinary claims require extraordinary evidence. Facebook driving Greek debt is implausible and two vaguely shaped curves aren't enough. A formula that predicts to many decimal places over a fair period, prospectively, would be really weird but hard to ignore. Spanish debt, gold prices or something related on the other hand, would require proportionately less evidence for causation. This disturbs people because it implies you can get stuck in a pathological view of the world and statistics and evidence won't get you out. Sorry about that. Edit: And this is pretty the Bayesian Approach. It's just that Bayesian Statistics and Pearl arguments, are themselves just models of the world. You can have others but, even more, you need more of an arguments than "stuff that seems implausible needs more evidence" and all of the more elaborate stuff is going to be specific to a given situation and thus might be applicable to a different one.

raverbashing 13y ago
"Facebook driving Greek debt is implausible" Yes, but in reality you don't know that Plausibility is a subjective measure, and while I would say that, yes, it can be a hint, you cannot disregard something merely because it's implausible
- Robin_Message 13y ago
  > a hint, you cannot disregard something merely because it's implausible Coming back to Bayesian statistics, the word for this is prior, and its not that you disregard evidence, its that you can quantify both your existing beliefs about reality and the change in your beliefs according to the evidence you see. Firstly, our hint: we have a prior assumption of the probability that the popularity of Facebook is driving up Greek debt (call it P(Fg)). Then, we observe a correlation between these two things. For the sake of argument, I'm going to make this 0.001 (I'd probably estimate less). Now, once we see this correlation, we now need to calculate two things: 1. The probability of observing that correlation (call that P(C)). Note that the more extraordinary the correlation, the less probable it is, and the smaller this term would be. In this case, the graph matches vaguely, I'm going to give it a probability of 0.1. 2. Given a world where there is a causation, what is the probability we'd see this correlation (Q: I'm not 100% on this part). Now, Greek debt could plausibly be driven by other things, which would mask the Facebook effect, so there's no guarantee there would be a correlation. This term is called P(C | Fg), and I have no idea what value to give it. Let's try 0.5. What we want to know is: P(Fg | C), that is, the probability of a connection given we have observed a correlation. Boom! P(Fg | C) = P(C | Fg) x P(Fg) / P(C) So our posterior probability (after observing this correlation) changes from 0.001 to 0.001 x 0.5 / 0.1 = 0.005

im3w1l 13y ago

>Obviously, it’d make no sense to have loops in the graph: I stopped reading here. Not saying models without loops cannot be useful though.

davorak 13y ago
Here is my understanding from a non-expert. The obviousness is suposed to come from if `a` causes `b`, `b` can not have caused `a` because that would need some form of time travel. `b` could cause `a2` though which is very similar to `a` but is separated in time from `a`.
- im3w1l 13y ago
  Yeah that makes sense. But then he uses the model wrongly, since he puts "hidden factor" "smoking" "lung cancer" in the vertices, and not "hidden factor (t=0)", "smoking(t=1)" and "lung cancer(t=2)". Further if used like that, then a possible hidden factor could actually be "lung cancer(t=0)", since it could (conceivably) cause both "smoking(t=1)" and "lung cancer(t=2)".
  - davorak 13y ago
    > But then he uses the model wrongly, since he puts "hidden factor" "smoking" "lung cancer" in the vertices, and not "hidden factor (t=0)", "smoking(t=1)" and "lung cancer(t=2)". The direction of the arrows shows causation with also implies time has passed though the amount of time is not specified in the model he is using, though it could be added. He has a section latter in the article about why he left it absent earlier and covers how it could be included. > Further if used like that, then a possible hidden factor could actually be "lung cancer(t=0)", since it could (conceivably) cause both "smoking(t=1)" and "lung cancer(t=2)". If lung cancer actually caused smoking then yes that would a simple solution. If that was the answer though the very next question would be what caused "lung cancer(t=0)". Which "smoking(t=-1)" if existed would be suspect, and another "hidden factor"(s) of course as well.
- deleted 13y ago
  [deleted]

zalmkleurig 13y ago

http://en.m.wikipedia.org/wiki/Granger_causality http://en.m.wikipedia.org/wiki/Granger_causality

SagelyGuru 13y ago

It is dangerous to assume causality from any data alone. (Data and statistics are over-rated nowadays). You need to do the harder work of discovering the proper mathematical model (equation) relating explicitly the dependent (caused) variables to the independent (causing) variables. In the absence of such a verified and proven model, you just can not take a shortcut of pulling causality out of statistics, like a rabbit out of a hat. Incidentally, the "Simpson's paradox" to which so much attention is given here, is a trivial illustration of the fact that you can not meaningfully add percentages from differing amounts. Something every school kid ought to learn.

tedsanders 13y ago
Can you expand on this idea? To me it seems fine to draw causal inferences from data alone.
- klipt 13y ago
  It depends where the data comes from. The gold standard in science is a controlled, randomized experiment - but obviously that standard is not always attainable.
- gngeal 13y ago
  I think it helps a lot if you have a plausible explanation for the chain of causes. For example, the correlation of dead people in houses with shitty stoves and furnaces in those houses is interesting, but once you discover that said stoves and furnaces leak carbon monoxide, AND that carbon monoxide binds to hemoglobin with much greater affinity than oxygen, AND that the affected people don't receive any specific warning symptoms when that happens, you suddenly have a reason to stop wondering whether or not they were committing suicide at a heightened rate because of poverty-related depression.
AlexFinks 13y ago
But why is it dangerous, on balance, to make assumptions of causality from data and statistics alone? Animals, such as rats and ravens, face this problem all the time, and yet they can meaningfully effect the world in such manner that would imply causal understanding, and a sensitivity towards the difference between mere correlation or a correlation with causal potential. Humans do the same as well, naive people who have never learned about experimental design, or have never learned the concept of correlation, also make useful judgments on the causal model behind ordinary problems and events. How did these machines make actionable judgments on causality with nothing more than noisy inputs to their sensory systems? Through what technique did they discern the difference between mere correlation, and a correlation with exploitable causality?

tlarkworthy 13y ago

This is the fundamental reason why general AI might not be possible on a computer without a body. To infer causality, you must form a hypothesis then design an experiment to confirm/deny it. Passively observing the world can't disambiguate between complex correlations or causality (even with a fancy calculus). You need action to learn the intricacies of the world. Think how the discovery of electricity led to electronics. There is nothing like electronics in the natural world, the only route to electronics is via an iteratively refined causal model of the universe.

gwern 13y ago
> This is the fundamental reason why general AI might not be possible on a computer without a body. 'Body' is a rather misleading term to use for what a general AI might need. And I say 'might' because part of the motivation for the Pearlean program is for discovering under what data and conditions one can infer causality without randomized interventions.

cousin_it 13y ago

Sometime ago I tried to come up with the simplest possible explanation for Simpson's paradox. This was the result: 1) Imagine that most women with a certain disease survive, while most men die. 2) Imagine that most women with the disease take a certain medicine, while most men don't. 3) Imagine that the medicine has absolutely no effect. Women just happen to have better innate resistance to the disease, and also just happen to buy the medicine more because it's marketed to women. Now if you do a statistical analysis without counting men and women separately, you will conclude that the medicine is very correlated with survival! Note that there's no way to know in advance that you should slice the population along such-and-such variables, which can be a lot more subtle than just gender. Also note that the example works even if the medicine has a slight negative effect, i.e. you can reverse the direction of correlations by choosing to slice or not to slice. I think such results make it clear that you can't easily trust conclusions from statistics. One minute you're thinking that cholesterol causes heart disease, and the next minute you're asking yourself, what if cholesterol is part of the body's response to heart disease? That's why we need randomized controlled studies, and theories of causality.

TillE 13y ago
> most women with the disease take a certain medicine, while most men don't Unless "most" = nearly all, this kind of situation is not difficult to untangle if you have sufficient and appropriate data.
- raverbashing 13y ago
  Still, numbers are important. What's most? 50.1%? 70%? 99.9999%?
- ChikkaChiChi 13y ago
  The point is well made. Any sort of deviation from control that exhibits a pattern will directly influence the outcome of your results.
saalweachter 13y ago
Also note that slicing the data too many ways is also dangerous. Every time you slice the data a different way, you increase the chances that you will find a spurious correlation. It is very easy for a naive researcher to fail to adjust their p-values and mistake the spurious correlation for a real one. It is also very easy for a biased researcher to cherry-pick the correlations which match their expectations.

deleted 13y ago

[deleted]

graycat 13y ago

> what does? (1) A clear mechanism. Data. My car won't run. Cause. The universal joint at the differential for the rear wheels failed leaving the rear end of the drive shaft on the ground. (2) A solid scientific theory. Data. I let go of the 2 x 4, and it hit my foot and hurt. Cause. Newton's law of gravity. (3) Other. Data. There is a correlation between smoking and lung cancer. Cause. Guess that there are some chemicals in cigarette smoke that cause lung cancer. Without actually finding the chemicals, basically test the heck out of the connection, i.e., look for and reject (statistically as in an hypothesis test) other candidate causes, see if cigarette smoke does cause mutations (causing mutations are easier to test for than causing cancer, and nearly every chemical that causes cancer also causes mutations; so, if a chemical doesn't cause mutations, then it likely doesn't cause cancer; if the chemicals in cigarette smoke do cause mutations, then can't reject that they cause cancer and have to keep entertaining that the chemicals might cause cancer and have to keep testing), reject spurious correlations, do some more tests that might reject causality and observe that they do not reject, look for other causes, work hard, get tired, give up, and finally conclude that have done enough work and time to stop smoking.

new_test 13y ago
Doesn't sound like you understand what the discussion is about.
- graycat 13y ago
  I responded directly to the question in the title of the post here at HN: > If correlation doesn’t imply causation, then what does? not directly to the article or the discussion here on HN. I don't think that the article makes much sense. I gave a very simple answer, (1) and (2). For (3), that's a mess and closer to the discussion. My view is that for causality, what I gave with (1) and (2), simple, childishly simple, dirt simple, is, unfortunately, in reality, about all there is to the poor, struggling subject. Put more respectfully, beyond my simplistic (1) and (2), working with causality is super difficult and quite unpromising as in mostly just f'get about it. For my (3) it boils down to ways to reject causality and then we accept causality once we get so tired trying to reject it we just give up and accept it. Why? Because without something detailed and mechanical, say, from chemistry, biochemistry, and the forbiddingly complicated, detailed biochemistry of cells, we are missing anything very solid to call causal. E.g., in my (1), with the universal joint that failed, we have a simple explanation that makes a solid cause; getting something so simple and solid for a cause of cancer from smoking will be super difficult. Don't worry, I don't smoke, but neither do I claim really to know a cause of cancer. Causality is a great, intuitive idea for humans and animals, but looked at in detail it's tough to establish in all but some narrow situations. For causal networks, path analysis, Markov random fields, directed acyclic graphs, lots of diagrams with circles and arrows, f'get about it. For getting causality out of data analysis, mostly just a fool's errand -- f'get about it. There is a significant reason I concentrated on (1) something mechanical and (2) something from classic physics -- those two darned near cover what can be done with causality. For the biological sciences -- causality is really important but really tough. For the social sciences, they try and try, and my wife did in her Ph.D. in essentially mathematical sociology and my brother did in his Ph.D. in political science, but, net, watching my wife and brother struggle with trying to make causality work in social science, where it's so easy to make it with (1) and (2), I just said f'get about it. You can entertain my views and my first very short post as a contribution to the discussion based on a lot of background and a claim that more is a fool's errand or just chalk it up to my ignorance. One more point: I didn't even mention correlation. Why? Because correlation is so far from causality that it's hardly worth even mentioning.

wissler 13y ago

David Hume said it first: http://en.wikipedia.org/wiki/Constant_conjunction http://en.wikipedia.org/wiki/Constant_conjunction