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  • A common misconception in statistics is to think that correlation implies causationlike,

  • 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 goesit may instead be that having a cat causes people to grow

  • talleror 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 trueit doesn't!

  • But this oft-repeated mantra leads to another common misconceptionthe 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 informationlike knowing that

  • one thing happened before the otherbut 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 optionsnot 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, thoughsome 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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  • And Brilliant does a brilliant job of making that easy, sneakily enticing you into doing

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  • I say this from experience, because if you haven't done a problem for a few days, Brilliant

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  • If you want to try out Brilliant (which I recommend), heading to brilliant.org/minutephysics

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  • Hey, glad you're still herein 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.

A common misconception in statistics is to think that correlation implies causationlike,

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Correlation CAN Imply Causation! | Statistics Misconceptions

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    Summer posted on 2021/03/21
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