Speaker A
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.
Explores how correlation can imply causation using causal networks, debunking misconceptions and highlighting exceptions in quantum mechanics.
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Key Takeaways
- Correlation alone does not prove causation but can guide causal inference when combined with additional data and models.
- Multiple correlations and causal networks allow elimination of many possible cause-effect relationships.
- Common statistical misconceptions include both overestimating and underestimating what correlations can reveal.
- Quantum mechanics challenges classical causal assumptions, showing limits of correlation-based causality.
- Active learning through problem-solving is essential for understanding complex concepts in math and science.
What the video covers
- Correlation does not necessarily imply causation, but this common phrase can lead to misunderstandings about inferring causality.
- Knowing a correlation alone cannot determine the direction or existence of causality between two variables.
- Using additional information and multiple correlations, causal relationships can be narrowed down significantly.
- The example of height, cat ownership, and islands illustrates how 19 possible causal models can be reduced to 2 with more data.
- Causal networks and temporal information help infer causality from statistical data.
- Correlation can imply causation if used to evaluate causal models rather than relying on single correlations.
- Quantum mechanics presents cases where correlations defy all classical cause-and-effect explanations.
- The video promotes Brilliant.org as a resource for learning math and science through active problem-solving.
- A follow-up video covers additional topics like feedback loops and chance correlations.
- The video encourages critical thinking about statistics beyond the oversimplified mantra that correlation never implies causation.
Chapters
- 00:00Misconception: Correlation Implies Causation
- 00:23Example: Cats, Height, and Islands
- 00:39Common Refrain and Its Misinterpretation
- 00:58Inferring Causality Beyond Single Correlations
- 01:1819 Possible Causal Relationships Explained
- 01:41Using Additional Information to Narrow Options
- 02:07Two Remaining Causal Explanations
- 02:26Generalizing Causal Inference from Correlations
- 02:47Quantum Mechanics and Causality Limits
- 02:57Sponsor Introduction: Brilliant.org
Full Transcript — Download SRT & Markdown
Speaker A
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
Speaker A
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.
Speaker A
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.
Speaker A
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.
Speaker A
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.
Speaker A
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
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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.
Speaker A
If we don’t know anything else, then there are 19 – yes 19! – different causal relationships that could explain the situation.
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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.
Speaker A
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
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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
Speaker A
an abundance of cats turned the island into a paradise, thereby influencing the height of future cat owners).
Speaker A
So, starting with 19 possible causal relationships, we used correlations to narrow things down to just 2 options – not bad!
Speaker A
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.
Speaker A
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.
Speaker A
We’ll have to save the details for a later video, but until then, may I suggest a new version of the famous refrain?
Speaker A
“Correlation doesn’t necessarily imply causation, but it can if you use it to evaluate causal models.
Speaker A
…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.
Speaker A
Brilliant is a problem-solving website designed to help you practice and learn math and science via guided problems, puzzles, and quizzes. I know that sounds kind of nerdy, but the truth is that the only way to truly learn and understand much of math and physics is
Speaker A
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
Speaker A
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.
Speaker A
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.
Speaker A
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.
Speaker A
The link’s on screen and in the video description.
Topics:correlationcausationstatistics misconceptionscausal networkscausal inferencequantum mechanicsdata analysisstatistical reasoningminutephysicsBrilliant.org
