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Correlation CAN Imply Causation! | Statistics Misconceptions

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 – you just need more than
one, together with something called causal networks. 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 excited to introduce the very relevant sponsor
for this video: Brilliant.org. Brilliant is a problem solving website designed
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and understand much of math and physics is to actively work through the material yourself
– videos only get you so far. And Brilliant does a brilliant job of making
that easy, sneakily enticing you into doing math and physics problems by means of intriguing
questions structured for all ability and knowledge levels. I say this from experience, because if you
haven’t done a problem for a few days, Brilliant will send you an attention-grabbing puzzle
, and I’ve been sucked in by quite a few of them. If you want to try out Brilliant (which I
recommend), heading to brilliant.org/minutephysics will let them know you came from here, and
you can check out their courses on Probability, the Physics of the Everyday, Classical Mechanics,
Gravitational Physics and so on. 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.
Video source: https://www.youtube.com/watch?v=HUti6vGctQM

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