We know correlation does not imply causality. What does?

You always need to make some assumption about the causal process before you can infer causality from evidence.

For example, take a randomized trial, where half of patients are given a drug, and half a placebo. If we define Y to be the outcome of interest, and X to be 0 when the patient received the placebo and 1 when they received the drug, then a positive outcome would be a correlation between X and Y. A person might object that "correlation does not imply causation", however, we know enough about the causal process involved, to infer that if Y and X are correlated, this must be because X caused Y.

There are many other ways that causation can be inferred, such as instrumental variables, regression discontinuity, or panel regressions. However all these methods require making an assumption about the causal process underlying the statistical distribution. Whether these assumptions are correct is often a matter for debate.

We keep falling back on Hume as if no one has thought critically about the subject since science became more mature. For the curious, Mackie's "The Cement of the Universe" from 1974 provides a more recent analysis of causation. http://books.google.com/books/about/The_Cement_of_the_Univer...

For a sample, suppose a barn burns down right after someone chucks a lighted match in the barn. You can't say that the match was "necessary," the barn could have been struck by lightning or arson and still burned. And the match wasn't "sufficient," because the match probably also needed to fall upon something flammable, like dry hay; there had to be oxygen; etc.

Mackie comes up with a fancy acronym, INUS, but I'll leave unpacking all that aside. One of the more provocative suggestions is that a "cause" is highly contingent on context (that might only be relevant to human observers).

If people harmlessly throw matches into a concrete-floored barn every day, if it's widely accepted as hot match disposal, but one day some joker uses it to store a bunch of oily rags... well, the unusual factor tends to get the blame.

The book Causality by Judea Pearl is kind of an extended answer to this question.

Err ... reliable experimental repetition of the hypothesized results against a control (and/or variety of controls) in carefully isolated environments using carefully controlled and documented methods that effectively remove all other plausible explanations?

Yes, we will never know for sure because https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_p... ... but we can be pretty certain.

Hmm, this seems to assume that we only have access to collected data (e.g. epidemiological studies) rather than being able to generate the data ourselves (many other types of scientific studies).

There is a key difference. A million surveys of smokers and cancer patients will never definitively prove causality. But if we could (legally and ethically) construct a randomized experiment in which we assigned a random half of the participants to smoke, we could easily conclude with very high confidence that smoking causes cancer.

(If this is not self-evident to you, the reason is straightforward probability. Suppose smoking does not cause cancer. Then when you take any given person and have them start smoking, their probability of getting cancer does not go up. Then the rates of cancer in the smoking group are exactly what they would have been had they not smoked. Then, since the people were placed in groups at random, with very high probability the rate of cancer in the smoking group will be almost the same as in the nonsmoking group. So if we find in our experiment that the rates of cancer are much higher in the smoking group, we must reject the hypothesis that smoking does not cause cancer.)

>But, in the end, we'll never be absolutely sure that one thing causes another.

Maybe so, but in the same pedantic sense that we'll never be "absolutely sure" that the universe didn't pop into existence five seconds ago with our memories already programmed in. This level of pedantry is great for impressing your fellow freshman philosophy students, but not actually useful for real life.

For actual practical day-to-day purposes knowing whether something causes something else is really useful, so what can we do? Controlled experiments. If you want to know whether cyanide is poisonous, get a hundred undergrads, randomly select half of them, feed 'em cyanide and see which ones drop dead. If you observe a strong correlation between the variable you're interested in and the one you think you're controlling then you've established causation for all practical purposes.

The pedant will point out there are two other possible explanations:

1. A massive coincidence -- those fifty undergrads just happened to drop dead for unrelated reasons. You can compute the probability of this as something like the average rate of spontaneous and inexplicable human death in undergrads to the power of fifty and multiplied by 1/(100 choose 50) [or something].

2. A slightly less massive combined with a reverse-causal process. Fifty of your undergrads just happened to be about to die anyway, and some aura emanating from them affected your coin-flipping process. The probability of this is harder to quantify, though since the scenario still requires fifty cases of spontaneous undergraduate death in a short space of time we can put an upper bound on it.

Oh, correlation does point to causality. What you don't immediately know is where to put the causal arrows. A and B occur together with a high probability: does A cause B, or B cause A? Or do they have a common cause?

Mere statistics cannot do that detective work for us, I'm afraid. But when a pure cause-and-effect relationship is uncovered and reproduced, the correlation will be 100%: remove the cause, the effect disappears. Restore the cause, and the effect appears reliably.

For instance, if we stop the flow of electric current through a coil, the magnetic field will collapse soon afterward. If we start the current again, the field comes back. Moreover, if we place a coil into a similar magnetic field, that field doesn't produce current. These things are 100% reproducible. It's not some weak statistic like "in coils where current was present, the magnetic field was observed to be 3.5% stronger on average". That kind of situation shows that some effects which are not being controlled for are masking the underlying causes and effects.

May not, not does not.

Correlation and causation can be implied if you have a control. Or if you can rule out external factors. Saying it does not is not accurate.

The parrot wakes and sleeps with the sunrise and sunset. Does the Parrot Cause the sunrise? No. This happened BEFORE the parrot was born. Does the sunset cause the sleep? Throw a blanket over it's cage it goes to sleep. TADA! Causation!

When you have two things which you can't control, and that have been going on longer than you can observe it gets to be harder. Proving the Moon phase causes the Tides, not the Tides cause the moon phase. That's a bit trickier. Not in today's age, but at one point. There is a reason we thought the Earth was flat, and that you could throw a stone in to a pond and get a Turtle.

> But, in the end, we'll never be absolutely sure that one thing causes another.

This is incorrect, because all knowledge is contextual.

For instance, it will always be true that gravity causes things to fall to the Earth. Future knowledge can't invalidate that, in can only expand the context.

Another example: Suppose a primitive tribesman climbes a tall tree, looks all around as far as he can see, and proclaims, "The land is flat." The eventual discovery that Earth is round does not invalidate his claim; it expands the context. The context of "the land [I can see]" is not the same as the context of "the entire Earth."

Correlation provides a starting point to investigate causality. To establish causality what you do is develop hypothesis for mechanisms of causality, identify intermediate events that may be observable if the mechanism hypothesis is valid and observe for those events. If these are observed, you have a much higher likelihood of causality. You'll typically do this if the return on investment from establishing causality is high enough since it's much more work - eg. You're trying to get a drug approval from FDA or you're trying to justify a major investment decision.

4. It does not account for Selection Bias. Just because some particular sample show a correlation does not mean the true distribution is correlated. This is almost certainly true if you look at lots (say 10+) relationships.

It's just too easy to fool yourself. For every time someone claimed no causality there are dozens, perhaps hundreds, of cases of false claims of causality. There is a huge bias.

The true test of causality is reproducible experiments. If X causes Y then making X happen should make Y much more likely. Unfortunately reality is not so easy to arrange.

I have been privately lumping causation and correlation together for decades now. It freed my thinking. While the two are certainly different, it is also true that causation does not have the set-in-stoneness/invariability that is commonly taken for granted. Witness the recent discussion about nasa's impossible-space-propulsion.

In terms of a human acquiring knowledge, correlation certainly is the first step. It is also called observation. Causation just seems to be a subsequent underpinning with context and concepts.

Wants to be smart, but uses "begs the question" in the first couple of paragraphs. What else didn't get caught in editing?

You know correlation implies causality when you can make money from the correlation.