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Correlation is usually not causation. But why not?

gwern.net

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Re: Correlation is usually not causation. But why not?

#31

Post by aaron695 »

ghshephard wrote: post #25

The article is a little dense for me, and presumes knowledge about Probabilistic Graphical Models (PGMs) and directed acyclic graphs / causal Bayesian networks (DAGs) without introducing the background knowledge - so, I expect my reading of it missed a lot of the details. But the one thing I came out wondering, is if you do a proper randomized double-blinded study with a large population sample, say, taking 1000 peop…

Well it's fair to say that experiment shows causation but no I don't think you can say the correlation shows it works. I think it goes against the definition of the word.....

I found the article too dense to get as well, but I do think 'perhaps' we could use correlation more to assume causation. I think we are too cautious and certainly the haters always bring in correlation to stop science articles they think don't follow their beliefs. Not sure if that's compatible with the OP or not, it hurt my head.

Re: Correlation is usually not causation. But why not?

#32

Post by dj-wonk »

jerf wrote: post #13
dj-wonk wrote: post #9

This article starts off with a common mistake. It is ok to create the 3 categories: > If I suspect that A→B, and I collect data and establish beyond doubt that A&B correlates r=0.7, how much evidence do I have that A→B? > you can divvy up the possibilities as: 1. A causes B 2. B causes A 3. both A and B are caused by a C So far so good, but here is the problem: > Even if we were guessing at random, you’d expect us to…

First, keep reading. Second, when gwern says "you'd expect 33%", he [1] does not mean "the abstract 'we' mathematically expect 33%", but indeed "the generic person-on-the-street has an intuitive belief that we should get 33%". If you check the context I think you'll see this fits. [1] So far as I know, anyhow.

@jerf Why did you assume I did not read the article? I read it, and I find the writing to be unclear. Maybe "you'd expect" means what you think; maybe not.

Independent of my or your opinion, (or precisely because reasonable people may disagree over something so simple) the writing is unnecessarily unclear. It would be simple to add a quick note saying, more-or-less, that the author will revisit the point later.

I also disagree with another commenter who says that the later writing clears up this issue. The point about 33% not being a fair assumption isn't addressed head on in the way that I think matters most.

Here is my main point, which was not received in the spirit I intended. Many smart people, even programmers, sometimes incorrectly assume a discrete uniform distribution (e.g. 1/3, 1/3, 1/3 in the above example), probably because they think it makes the fewest assumptions.

I'll put it another way with a related example. Alexa gives Bart a two-sided coin, tells him it may or not be fair, and asks the expected probability of getting heads. Bart reasons as follows: "I know that the coin may be unfair, ranging from, say, 0%/100% to 50%/50% to 100%/0%. By symmetry, for each 1%/99% coin there is a 99%/1% coin. So, in the end, the coin will average out to 50/50, so the best answer is 50%."

Chuck comes along and says, "Bart got it wrong. Any point estimate must be incorrect, because we don't have enough information. The correct answer must be a distribution. Since we know nothing, the best answer is a flat (uniform) distribution ranging from 0% to 100%."

Danielle chimes in and adds "Yes, Bart was wrong, and Chuck improved on the analysis, but Chuck did not go far enough. Both Bart and Chuck assumed symmetry, without justification. Chuck's act of assuming a uniform distribution is tantamount to knowing the process that generated the coin. Does Chuck really know the chances of a 0-10% coin are the same as a 10-20% coin, and so on? No, he does not. Therefore, even answering the question with a distribution is incorrect. The only correct answer is that the probability of heads ranges from 0 to 100%, but no distribution can be given."

Danielle is correct. The author may well know this, but it is not communicated clearly in the article.

I would be willing to wager that many people, when confronted with Alex's question, would answer like Bob or Chuck did.

Re: Correlation is usually not causation. But why not?

#33

Post by dj-wonk »

Jemaclus wrote: post #11
dj-wonk wrote: post #9

This article starts off with a common mistake. It is ok to create the 3 categories: > If I suspect that A→B, and I collect data and establish beyond doubt that A&B correlates r=0.7, how much evidence do I have that A→B? > you can divvy up the possibilities as: 1. A causes B 2. B causes A 3. both A and B are caused by a C So far so good, but here is the problem: > Even if we were guessing at random, you’d expect us to…

If you read the whole article, he addresses this about halfway down.

@Jemaclus I'm not sure why you assumed that I did not read the article. Maybe you disagreed with my conclusion and assumed I had not read the article?

To your question, I would ask: Where, exactly, does the author "address this"? (Maybe we are talking about different meaning of "this"? I explain the fallacy I'm talking about in a longer comment on a sister thread (by "sister" I mean up one level, over one, down one).

Did you mean this part?

> It turns out, we weren’t supposed to be reasoning ‘there are 3 categories of possible relationships, so we start with 33%’, but rather: ‘there is only one explanation “A causes B”, only one explanation “B causes A”, but there are many explanations of the form “C1 causes A and B”, “C2 causes A and B”, “C3 causes A and B”…’, and the more nodes in a field’s true causal networks (psychology or biology vs physics, say), the bigger this last category will be.

This is also fallacious, in my opinion. See my longer comment. In short, if you "count up" categories in this way, you are assuming information that you don't have; doing so is a matter of belief, not analysis.

Or did you mean this part?

> they might not be reasoning in a causal-net framework at all, but starting from the naive 33% base-rate you get when you treat all 3 kinds of causal relationships equally. > This could be shown by eliciting estimates and seeing whether the estimates tend to look like base rates of 33% and modifications thereof.

This chunk of text does not debunk the claim that a 33% base rate is reasonable as a starting point. My point is that the 33% starting point was not reasonable in the first place.

Re: Correlation is usually not causation. But why not?

#34

Post by a_bonobo »

nmjohn wrote: post #30
jrapdx3 wrote: post #7

This question is bound to be a can of worms. There has been a great deal written about the matter, particularly in regard to observational studies. Drawing causal inference is overwhelmingly likely to be wrong when there is a good chance that unknown variables are influencing the correlates observed. In health-related sciences that more often than not is the case. A few years ago there was a study correlating hours o…

> There was a great article published in PLOS several years ago (ATM I don't have the link) showing mathematically that the odds were about 1 in a million that an observational study like the above would turn out to be a "true" causal relationship, and the author concluded most published studies were junk. I very much doubt the second part of that, that most published studies are junk. The idea that not showing a cau…

This, I think, is the study the first poster meant, Ioannidis 2005, 'Why Most Published Research Findings Are False':

http://www.plosmedicine.org/article/info%3Adoi%2F10.1371%2Fj...

It's quite a famous paper. Many rebuttals, comments, blog-posts etc, have been published, have a look at the comments on the PLOS site, I especially like this blog post summarizing more research:

http://simplystatistics.org/2013/09/25/is-most-science-false...

From the same author, here's a small overview of the discussion at the end of 2013:

http://simplystatistics.org/2013/12/16/a-summary-of-the-evid...

Quote on the Ioannidis paper:

>Under assumptions about the way people perform these tests and report them it is possible to construct a universe where most published findings are false positive results. Important drawback: The paper contains no real data, it is purely based on conjecture and simulation.

Re: Correlation is usually not causation. But why not?

#35

Post by lsd5you »

graycat wrote: post #10

Bad winter weather can cause auto accidents, and we expect a positive correlation between bad winter storms and winter auto accidents. Okay, but in the northern hemisphere, living in more northern latitudes also correlates with winter auto accidents but does not cause them. For heart disease, we know that the main causes have to do with aging. Well, then, since now the audience for TV news is comparatively old, we ca…

Your first example is wrong. If you move to a more northerly latitude then it will increase the risk of accidents for you (i.e. there is causation). It is indirect causation, but then ultimately (almost?) all causation is going to be indirect if you take the reduction far enough. That is bad weather doesn't directly cause accidents, but ice on the roads does ... etc.

Re: Correlation is usually not causation. But why not?

#36

Post by TheSpiceIsLife »

coldtea wrote: post #22
graycat wrote: post #10

Bad winter weather can cause auto accidents, and we expect a positive correlation between bad winter storms and winter auto accidents. Okay, but in the northern hemisphere, living in more northern latitudes also correlates with winter auto accidents but does not cause them. For heart disease, we know that the main causes have to do with aging. Well, then, since now the audience for TV news is comparatively old, we ca…

> Well, then, since now the audience for TV news is comparatively old, we can expect that watching TV news has positive correlation with heart disease. Still watching TV news does not cause heart disease. Well, I'm not so sure. All this sitting to watch TV news, plus all the stress from bad news and fear-mongering...

Watching (bad) fear monger news doesn't cause stress. Rather, the story you tell yourself about what the news means causes the stress. One person (say, me for example) can watch the (bad) news and have a good laugh (call that a , while another (one of my housemates, for example) will watch the same thing and have a negative response to it.

Re: Correlation is usually not causation. But why not?

#37

Post by sqrt17 »

Normally, causation has a couple confounders for correlation, such as

- inverse causation - common cause - random correlations

The first two should be relatively stable and reproducible, and we could then proceed to find out about causation with an intervention study (e.g. if "good education" directly causes "good job prospects", will it help if we give people good education that wouldn't normally get one? Or does it improve people's educational achievement when we give them better access to jobs?)

The third isn't reproducible, but should normally be relatively rare. Why we're seeing more and more non-reproducible results is usually

- People fishing around in data sets for correlations, or tweaking experiments until they find a correlation

Because of this, we end up with a great deal of correlations that have nothing to do with causation.

For a related but different perspective, see this article ("Language is never, ever random", Adam Kilgariff) http://www.kilgarriff.co.uk/Publications/2005-K-lineer.pdf

Re: Correlation is usually not causation. But why not?

#39

Post by mgregory22 »

The difference between correlation and causation is merely conventional. Does the striking of a match cause it to ignite? There is no way to prove that it does, only the correlation between the striking and the ignition makes us say they're causal. Correlation is the only way to determine what's causal and what's not.

On the other hand, if you want to look at it philosophically, then the only sensible definition of "causation" is "anything necessary for a thing to exist." So what's necessary for a thing to exist? Every other thing in the universe that is not that thing! Pluto causes us to exist right now because it hasn't turned into a giant space goat and swallowed the Earth. Yes, the fact that something DIDN'T prevent the existence of a thing is also ultimately a cause of that thing's existence. Causation in its purest form can help us understand the nature of reality, but it can't help us predict anything. It's only when we draw a line between causes that we can control and causes that we can't that it becomes a practical tool (not that understanding reality isn't practical).

So you can see, this whole correlation != causation discussion is pure nonsense. Get some philosophical skill before you try to discuss philosophical issues and stop embarrassing yourselves. Sheesh, it's ridiculous.

Re: Correlation is usually not causation. But why not?

#40

Post by return0 »

mgregory22 wrote: post #39

The difference between correlation and causation is merely conventional. Does the striking of a match cause it to ignite? There is no way to prove that it does, only the correlation between the striking and the ignition makes us say they're causal. Correlation is the only way to determine what's causal and what's not. On the other hand, if you want to look at it philosophically, then the only sensible definition of "…

Apart from semantic acrobatics, there is a practical need for defining causation in science and technology. The cause has to have a temporal precedence and be necessary.

> Causation in its purest form can help us understand the nature of reality, but it can't help us predict anything

huh?

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