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

Still, numbers are important.

What's most? 50.1%? 70%? 99.9999%?

The point is well made. Any sort of deviation from control that exhibits a pattern will directly influence the outcome of your results.

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.

> 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

Right.. but when you find correlation, you just see that two things are obviously related in some way - there is a common factor. It could be direct causation, or it could be any number of other things. The question is whether or not you have a theory that can be analyzed to see if this is a CAUSE or not... and we can't test every correlated thing out there exhaustively.

Plausibility is a measure based on less than exact knowledge of the world. I indeed don't know with certainty the relationship between Greek debt and Facebook value. Not all less-than-perfect knowledge of the world is subjective however - subjective involves personal prejudice but there's more than personal prejudice operating in the judgement that Facebook prices won't affect Greek Debt - there's an understanding of finance, a doubt about action at a distance, etc.

Also, if you read my post, I'm not "disregarding" anything. I am simply saying that some things have a higher bar than others.

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.

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.

It is probably the ability to make the abstract jump from the data and its correlations to generalised laws that marks the chief difference between people on one hand and animals and machines on the other. Correlation is only useful up to a point. It shows that there may be some relationship between the variables but it says nothing about its nature. Was X caused by Y or was Y caused by X or were X,Y both caused by some unknown Z, was it all just an accidental data sample, was it significant, with how much doubt? Does the assigned significance in fact rely on an unwarranted assumption of some underlying population distribution? Just too many questions and no answers. Besides, causality is problematic enough (see non-aristotelian philosophies and/or quantum mechanics) even without trying to demonstrate it with statistics.

> 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.

They also are often... racist. Or hold whatever other stereotypes to heart. Racism is just a good example of an extreme position to hold which is often due to assumptions of causality.

"Lots of minorities are in prison. There is a high correlation between being a minority and being in prison. Therefore being a minority leads to being a criminal."

This completely ignores external reasons why minorities might end up in prison more often than others. For instance, it could be that minorities have an equal amount of criminal activity as the general population, but are more likely to end up in prison because of it. Correlation does not imply causation.

I think the number of social issues that arise due to assumptions of causation is quite high, actually, and often leads to poor decision making in policy. That is why it is "dangerous."

"Through what technique did they discern the difference between mere correlation, and a correlation with exploitable causality?"

Evolution - that is, assumptions that are accurate are favoured since they are more likely to lead to the animal surviving, vs embracing spurious correlations which are likely to get you killed.

Of course, this can break down if we try to apply the cognitive rules of thumb we've evolved to new domains outside our original evolutionary scope - our difficulties in thinking about statistics and probability are a great example of this. The math is trivial, but it just doesn't fit our brains very well without a great deal of cultural scaffolding.

> But why is it dangerous, on balance, to make assumptions of causality from data and statistics alone?

Well it all depends on the actions you take based upon those assumptions. If the action is low risk, low cost then it may be the wise choice. You need to remain aware of the uncertainty and that you are basically guessing until a better understanding is achieved.

One of the dangers is that initial uncertainty is forgotten and wrong information becomes "common knowledge".

Another danger is where there is there actually is causation but running the opposite way to that assumed. For example if a chemical substance is a useful form of self medication for sufferers of a condition there may be a correlation between the use of the chemical and the condition but banning/withdrawing/warning about the chemical would actually worsen the situation.

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.

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.

Depends what you mean by 'imply'.

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)".

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.