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Correlation is usually not causation. But why not?

gwern.net

41–50 of 74 posts

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

#41

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 "…

The arrow of time. Randomised experiments.

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

#42

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 "…

What? Your comment is pure nonsense. Of course you can prove that striking a match causes it to ignite. There's a long chain of events, each of which trivially physically verifiable, which starts with you moving the match head while applying a given amount of pressure against the material lining the matchbox, which then, due to friction, flakes off (both head and lining), the two react together to produce a spark and a flame starts. You can cut the chain down to micro-events and you'll find each one to be consistently verifiable.

Or do an experiment - grab a mug and lift it. I claim that your arm motion while your hand had grabbed the mug caused it to ascend. We can again examine the basic physical events, cutting them as fine as you'd like, and we'll see that it really was you with your arm, who caused the mug to ascend.

This is a cause-and-effect link -- when you can show how event A lead to event B via a chain of events, each of which directly causes the next. At the least you need to show that there is a sensible progression from the cause to the effect, in order to claim a causation.

Correlation on the other hand is a description of past observations. You can observe that each time it snows people increase their energy expenditure in order to heat their homes. Does the increase in heating cause the snow? That doesn't seem likely, knowing how heating works. It could be that increased energy demands leads to more coal being burned, leading to larger clouds being formed and lowering the outside temperature. However, even though increased coal burning does lead to such effects, they're pretty small from just increased heating, so we can discount this hypothesis. On the other hand, you can show that cold weather causes snow. Water that falls in cold air crystallises and becomes snow. So there is a definite causative relationship between cold weather and snow. Could there also be a causative relationship between cold weather and heating? Well, assuming that people wish to live at a constant surrounding air temperature of about 20-30 degrees, that seems very likely. There are of course individuals who don't fit that profile, but they are very few (I can't actually provide a study which supports that claim, but just assume it for the purposes of this demonstration). In the end, we can say that while snow and heating are correlated, heating does not cause snow. They simply have a common cause - cold weather.

And finally, if you keep your home at a constant temperature, the setting on your heater does not correlate with the temperature inside your home, because the temperature is constant, while you have to change the setting up and down to counteract the more or less cold weather outside. It does correlate perfectly with the outside temperature, but I'll leave proving that putting your heater on high doesn't make the temperature outside drop by 10 degrees as an exercise.

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

#44
post #35
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.

No: The bad winter weather, say, ice on the roads, is the cause of the accidents. If happen to have a winter with little or no snow or ice, then the number of auto accidents will go down no matter what the latitude: So, latitude can't be the cause; ice and snow on the roads is the cause. So, if live in a lower latitude, say, closer to the equator, and get a freak winter snow storm with a lot of ice and snow on the roads, the we will see auto accidents in spite of the latitude.

For indirect causation, I just said winter weather to try to be brief. But, sure, the cause is the ice and snow on the roads, not just the weather in some vague sense. I was trying to keep the explanation simple, avoid discussing indirect causation, and concentrate on the OP issue of causation versus correlation.

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

#45

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…

> it's fair to say that experiment shows causation

No, that experiment doesn't show causation.

> I do think 'perhaps' we could use correlation more to assume causation. I think we are too cautious

Why do you think that? Is it because you think that science is moving too slowly (thus wasting time and money)? Is it because you think that good results are mistakenly discarded?

"using correlation more to assume causation" should produce results more quickly, both correct and incorrect. Do you understand the costs of incorrect results? First, incorrect results can have negative consequences for the consumers: for example, drugs that have harmful impacts and no beneficial ones for the people taking them (in addition to the cost of the drug, and the opportunity cost of not doing something else known to be beneficial). Second, time is wasted following up incorrect results and work based on incorrect results would be worthless. Third, the incorrect results would have to be overturned (and this communicated to everybody who had taken them as correct).

I think deciding whether to "use correlation more to assume causation" needs to take into account the costs and benefits of incorrect results, as well as the costs and benefits of correct results. Do you have any data on this? (unfortunately, I do not)

> certainly the haters always bring in correlation to stop science articles they think don't follow their beliefs

Can you support this accusation with examples of it happening to articles that actually do a good job of showing their result is something more than a correlation? Or are you saying that this happened to articles that just present a correlation?

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

#46

Another cracking article from gwern. For those wondering, that snazzy looking `choose` combinatorial function is from clojure, and I assume other lisps: http://clojuredocs.org/incanter/incanter.core/choose

No, it's just binomial coefficient. It's common to say "10 choose 2", it's the standard way of reading binomial coefficients out loud. See http://www.wolframalpha.com/input/?i=10+choose+2.

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

#47
post #22

Earlier quoted context omitted.

> 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.

Well, that's like "gun's don't kill people, bullets (or holes in vital organs) kill people".

Technically correct, but doesn't really take away from the first thing.

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

#48
post #32
post #13

Earlier quoted context omitted.

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 als…

> 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.

How would you want it addressed? A large part of the article is exactly about how the - to some - "intuitive" idea of 3 evenly split categories is incorrect. E.g. later in the article he writes:

"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."

Presumably this is why two people separately assumed you did not read the whole article.

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

#49
post #26

Because you can find things that are correlated, but have no practical relationship - many (frequently humorous) examples here: http://tylervigen.com

Datamining correlations like that confuses two issues: sampling error and 'everything is correlated'. When you find a correlation like that, it's unclear whether it's a spurious correlation which will disappear if you just collect more data (and caused by slicing the data in a thousand ways without any compensation by this) or whether there genuinely is some sort of opaque correlation which will persist no matter how much data you collect (maybe 'US spending on science, space, and technology' really does correlate with 'Suicides by hanging, strangulation and suffocation' through something like government stimuluses and economic growth).

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

#50

All I know about causation and correlation I learnt hunting bugs in large legacy software systems. In that environment I got the impression that correlation almost never equalled causation, but that's only because the hardest bugs, the ones I remembered, were hard because the obvious correlations did not help identify the root cause. A similar argument might be made for scientific studies: most of the easy causes tha…

I think this low-hanging-fruit idea is generally true for all of science: after centuries of science as a profession, pretty much all the easy stuff has already been done.

It's actually an argument for more cojones in science-- being willing to do bold stuff and explore "crazy" hypotheses. If all the easy stuff is done already, then picking methodically and timidly among the dregs is unlikely to ever yield anything.

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