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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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• Brilliant is a problem solving website designed to help you practice and learn math and science

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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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