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A common misconception in statistics is to think that correlation implies causation – like,
if more tall people have cats, you might think that means being tall makes people more likely
to get a cat.
However, simply knowing a correlation between height and cat ownership can’t tell us which
way the causality goes – it may instead be that having a cat causes people to grow
taller – or perhaps the real cause is something else altogether, like that the people and
cats live on two separate islands, one a lush paradise with enough food for growing tall
and feeding pet cats, and the other a wasteland that limits both height and cat ownership.
The point of examples like this is that noticing a correlation between two things doesn’t
imply that one of those things causes the other.
Hence the common refrain: correlation doesn’t imply causation.
And it’s true – it doesn’t!
But this oft-repeated mantra leads to another common misconception – the idea that you
can’t infer any causality from statistics.
You can!
I mean, it’s quite reasonable to think that, if two things are correlated, there’s likely
some reason, , even if a single correlation can’t tell you.
Sometimes you can infer the causality from additional information – like knowing that
one thing happened before the other – but you can also infer causality directly from
correlations –\hyou just need more than one, together with something called causal
Like, in our cat-height-island example, we know that cat ownership and height are correlated,
but we don’t know what the cause of that correlation is.
If we don’t know anything else, then there are 19 – yes 19! – different causal relationships
that could explain the situation.
20 if you think the correlation is just an accident.
However, perhaps we know two other things: first, suppose people born on a particular
island stay there, so their height doesn’t influence what island they live on, and we
can rule out the relationships where height influences island.
Second, suppose that on either island, taken by itself, there isn’t any correlation between
height and cat ownership; then we can rule out all the options where height and cats
influence each other directly . This leaves us with just two options: either the islands
are the causal explanation for both height and cat ownership (maybe, as before, one island
is a lush, healthy paradise for both people and cats), or else cat ownership is the causal
explanation for the islands which are the causal explanation for height, (like, maybe
an abundance of cats turned the island into a paradise, thereby influencing the height
of future cat owners).
So, starting with 19 possible causal relationships, we used correlations to narrow things down
to just 2 options – not bad!
Of course, this is just a simple example, but for any group of things, you can use the
various correlations between them (or lack of correlations) to eliminate some of the
possible cause-and-effect relationships.
And that’s how correlations CAN imply causation.
There is one problem, though… some experiments in quantum mechanics have correlations that
rule out ALL possible cause and effect relationships.
We’ll have to save the details for a later video, but until then, may I suggest a new
version of the famous refrain?
“Correlation doesn’t necessarily imply causation, but it can if you use it to evaluate
causal models.
…Except in quantum mechanics.”
I’ve got a little more about statistics and causality after this, but first I’m
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Hey, glad you’re still here – in case you’re interested, there’s a footnotes
video covering a few things that got cut out of this one, like feedback loops and correlations
that arise just by chance.
The link’s on screen and in the video description.