Taking "correlation does not imply causation" back from the internet

If you don't drink water, you still die - that sounds pretty uncorrelated to me.

Only to score points at the expense of the audience's vocabulary would one say "there is no variance in either variable" as opposed to saying "there are no people who avoid drinking water, nor people who don't end up dead, to compare to".

Let's not encourage this.

Disagree. Our target audience - humans - rarely if ever thinks of 'correlation' in terms of its mathematical definition and I suspect would be put off by an attempt to do so.

Correlate water consumption rate with lifespan, to get a correlation. My guess is it will be negative.

I had intended on tackling this, but the original still works as a Steel Man of the general case.

They can also be completely independant and have causation, but that's not something that would happen by chance. The only time I know of where something like that will happen is if the cause is designed to regulate whatever it's independant of. For example, the temperature doesn't correlate to the power going through the heater or air conditioner, since it's always constant, which is because the heater and air conditioner keep it constant.

That sounds like a bite-sized refutation of the Worst Argument in the World.

Aren't comics like that the source of the cached thought we're trying to improve on here?

I go to some lengths to avoid innumerate discussion online, but it still happens in real life with reasonable frequency. The flavours I seem to encounter most:

1) an all-purpose attempt to refute any statistical finding, even if said finding is not showing correlation, or proposing causation

2) dogged adherence to the belief that the direction of causal relationships are completely impossible to establish

3) the most perverse, that establishing an association between two variables is evidence against a causal relationship

Look at almost any reporting of a scientific finding (even something like CNN gets this wrong usually). Chances are, the reporter will claim causality, while the original paper will claim association. This sort of thing is extremely common. Our good friend from slate was not immune to this, sadly.

if variables A and B are correlated, then we can be pretty damn sure that either: a) A causes B b) B causes A c) there's a third variable affecting both A and B.

There is in fact a d) A and not-B both can cause some condition C that defines our sample.

Example: Sexy people are more likely to be hired as actors. Good actors are also more likely to be hired as actors. So if we look at "people who are actors," then we'll get people who are sexy but can't really act, people who are sexy and can act, and people who can act and aren't really sexy. If sexiness and acting ability are independent, these three groups will be about equally full.

Thus if we look at actors in general in our simple model, 2/3 of them will be sexy and 2/3 of them will be good actors. But of the ones who are sexy, only 1/2 will be good actors. So being sexy is correlated with being a bad actor! Not because sexiness rots your brain (a), or because acting well makes you ugly (b), and not because acting classes cause both good acting and ugliness, or diet pills cause both beauty and bad acting (c). Instead, it's just because how we picked actors made sexiness and acting ability "compete for the same niche."

Similar examples would be sports and academics in college, different sorts of skills in people promoted in the workplace, UI design versus functionality in popular programs, and so on and so on.

There's also e): A causes B within our sample, but A does not cause B generally, or in the sense that we care about.

For example, suppose a teacher gives out a gold star whenever a pupil does a good piece of work, and this causes the pupil to work harder. Suppose also that this effect is greatest on mediocre pupils and least on the best pupils - but the best pupils get most of the gold stars, naturally.

Now suppose an educational researcher observes the class, and notes the correlation between receiving a gold star, and increased effort. This is genuine causation. He then concludes that the teacher should give out more gold stars, regardless of whether the pupil does a good piece of work or not, and focus the stars on mediocre pupils. This change made, the gold stars no longer cause increased effort. The causation disappears! Changing the way the teacher hands out the gold stars changes the relationship between gold stars and effort. So although there was genuine causation in the original sample, there is no general causation, or causation in the sense we care about; we can't treat the gold stars as an exogenous variable.

See also the Lucas Critique.

I like how this guy complains about "internet blowhards" abusing this phrase, but then gets basic reporting of correlation in scientific papers wrong (by reporting causation in articles he wrote about those papers). There was a comment on that slate article calling him out on this.

Since it was the response to a quote from this article that gave me the idea, I'm going to infer that it's causal.