Statistics

How to tell causation?

Here we continue to discuss the problem of wrong interpretation of correlation.

Q: How to test causation?
If it was all simple, no-one would ever make false conclusions. But the problem exists: the thing is, there are statistical methods to test correlation (a bunch of them, actually), while there isn’t a method to test causation, at all. All so called causation tests are in fact tests for correlation.

Explanation: say, I want to know if the presence/absence of tail in lizards affects their sprint performance. What I normally do then is establish two trial groups: one – with whole tail, the other – with cut tail. And then make both groups sprint, while measuring their speed. I find the correlation: tailed lizards are faster than cut.  Does it mean a true relationship? Perhaps, but… any factors could have affected the trials. Probably, unrelated to tails at all.

Firstly, individuals in both groups are not the same. Who knows how are they different? Maybe those without tails got high before the trials, and never mentioned it in their patient cards Okay, we could use the same lizards. Make the first trial, then, on the next day, cut their tails and run the second trial. There will be a correlation. Yet, what if they just got tired on the next day? Let’s wait for a month then, rather than for a day. Then… what if they become old and not so quick? There always will be contaminating factors, it’s unavoidable. Thus, we can never identify causation with 100% certainty using correlation tests.

Probably, the best solution would be to test a lizard with a tail, then run a time machine, jump back into the moment right before the experiment, cut the lizards tail and repeat the trial. That’ll be much closer: we are testing the same lizard, in exactly the same physiological state (except it’ll have no tail), at exactly the same age down to a second. The very idea of testing causation is answering the “what if” question. “What if that lizard didn’t have a tail?”

And still, it’s hardly possible to cut a tail without contaminating anything else. Even with time machine. There will be pain at least. Won’t it affect the lizards’ performance? Then we’ll do the surgery under anesthesia. But what if it causes headaches in lizards?

Q: So, basically, causation is impossible to determine?
Perhaps, but don’t let it trouble you. Experimental designers are working hard to eliminate as many contaminators from their trials as possible, and selecting huge samples for results to be as close to perfect as possible. Modern experiments with good samples are more than 99,9999% precise. A condom is 30000 times less reliable, yet people use them. Reliability over 99% (sometimes, even over 95%) is more than enough to make serious decisions. There is no better option. In your daily life, you accept even less probable hypotheses as truth – you do it every day. For decades people have been making meds; building cars, houses, rocket ships; studying all sciences in the world. There always’ve been some doubt. We cannot prove things with 100% certainty: there is no guarantee that your next glass of water won’t kill you. Yet, everyone drinks.

Yet, from my perspective, there is a way to identify causation with de facto 100% certainty. Prove by explanation. People love stats and numbers so much that they are forgetting about observation and description. There is a correlation: the darker is the room, the easier people mistake colours. How to prove that lack of light affects our colour perception? Simple: explain it. What exactly happens to our eyes in the dark and in the light? How exactly are colours identified, and what’s the role of light in all of this? Show me the structures inside an eye that are responsible for colour perception.

The way I see it, the more precise and fundamental the science is, the less it is grounded by statistics.

Q: What if causation is explained, but then we find out that it is in fact wrong?
It’s not impossible, but would probably mean that we are completely mistaken about the world around us. That something otherworldly affects the nature. Say, we have correlation between the light qty and colour perception. We have explained the mechanisms. But it is possible, that Odin the All-father has a remote controller that controls our colour perception, and light has nothing to do with it. He’s just careful enough to turn our colour vision off whenever it’s dark around. One day he might not be in the mood and we’ll find out that all our knowledge about colours is the lie – we’ll all suddenly see colours at night. And eye design… it’s all for decoration. Or maybe, we don’t even exist: we are all holographic.

But as far as we know nothing of Odin, and everything suggests that we are not holographic, there is no point in even suggesting that we are wrong. We never pretend to understand the utter reality, we merely describe the world that makes sense to us, that we can see around us. We study our world. There’s only one alternative: to accept our total ignorance and study nothing.

Why don’t you, say, stop earning money: what if Ra and Anubis decide to take them all away tomorrow? Or start to cross the road against the red light: what if Odin the All-father decides to switch colour perception in all the drivers from red to green the moment you’ll be crossing the road next time? Could save your life, you know. Or don’t come home ever again: what is an asteroid falls on your house while you’re inside?

Skepticism is fine, but… we gotta live our lives somehow

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Further reads

Previous Article: The Magical Correlation
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