Causal Blocks
Correlation isn't causation. So what is?
You've probably heard it: correlation isn't causation. Two things going up together doesn't prove one causes the other. But hardly anyone tells you what to do next. That's what this site is for.
Two things going up together
On hot summer days, ice cream sales go up. So do shark attacks. A newspaper could print "Ice cream causes shark attacks!" and the numbers would seem to back it up.
That pattern is a correlation: when one thing is high, the other tends to be high too. A cause is different. It means that if you changed one thing, the other would change because of it. Banning ice cream wouldn't save a single swimmer.
Who's really behind it?
When two things go together, one of these is usually behind it.
Confounder: a hidden cause
Something else causes both. Hot weather sells ice cream and sends people into the sea, where the sharks are. It pulls two strings at once, so two things rise together without ever touching.
The arrow points the other way
Towns with more police have more crime. The police don't cause the crime: police get sent to where the crime is. The link is real, but it runs backwards.
Collider: only looking at some people
A club's bouncer lets you in if you're rich or good-looking. Inside, the rich people seem less good-looking. Out in the town there's no link at all. Only looking at who got in made one up.
Mediator: how a real cause travels
It isn't a trick. Revision club helps you understand the topic, and understanding helps you pass. The effect is real, and the mediator carries it. Stop it and the effect stops too.
So how do you find out what really causes what?
If you can, do an experiment
The fairest test is to pick a random half of people, change one thing for them (say, send them to revision club), and compare them with everyone else. Because the groups were picked at random, nothing else is different between them. If the result changes, you've found a cause.
If you can't, draw a map
Often you can't experiment. You can't make half the world's summers hotter. So you draw your best guess as boxes and arrows, where each arrow means "this causes that". Scientists call this a causal diagram (or a DAG). Then you make a fair comparison: compare hot days with hot days, so the weather can't fool you. That's called controlling for the weather.
The catch is knowing what to hold fixed. Get it wrong and the answer gets worse, not better:
| If it's… | Hold it fixed? |
|---|---|
| Confounder | Yes. Then it can't fool you. |
| Mediator | No. You'd block the real effect. |
| Collider | Never. You'd make up a link that isn't there. |
The numbers can't tell you which character is which. Your map can. That's why you draw it first.
Why it matters
Headlines, adverts and even school decisions are full of claims like "pupils who eat breakfast get better grades". Is it the breakfast, or something else about those pupils? Asking "what else could cause this?" is one of the most useful habits you can have in a world full of numbers. Real researchers use exactly these ideas, with tools like DoWhy.
Try it yourself
- Play the game: read the headline, draw your map and catch the culprit.
Want to go further? Reading for older students and teachers
- The Book of Why Judea Pearl and Dana Mackenzie, 2018 The best place to start. A non-technical history and explanation of causal thinking from the person who formalised much of it.
- Thinking Clearly About Correlations and Causation Julia Rohrer, 2018, Advances in Methods and Practices in Psychological Science A short, readable paper on causal graphs for observational data. Good for a single sitting.
- The Effect Nick Huntington-Klein, 2021 Free online A friendly textbook on research design and causal inference, with causal graphs throughout.
- Causal Inference: The Mixtape Scott Cunningham, 2021 Free online An economist's introduction, with code in R, Stata and Python.
- Causal Inference: What If Miguel Hernán and James Robins, 2020 Free online The standard text from epidemiology. More formal, and very clear.
- Statistical Rethinking Richard McElreath, 2nd edition, 2020 A statistics course that puts causal graphs at its centre. The recorded lectures are free.
- Introduction to Causal Inference Brady Neal Free course Lecture videos and notes, from the machine-learning side of the field.
- DAGitty Johannes Textor and colleagues Free tool Draw a causal graph in the browser and get the adjustment sets. The academic standard.
- Spurious Correlations Tyler Vigen Hundreds of real correlations with no causal link at all. A good reminder, and funny.
Get in touch
Causal Blocks is made by George Lindley. I'd like to hear from you if you:
- teach (at any level) and would like to use it with your students,
- have a dataset or example that would make a good lesson,
- want to collaborate on teaching causal thinking, or have ideas for what it should do next.
- george.j.lindley+causalblocks@gmail.com
- linkedin.com/in/georgelindley
- Website
- georgelindley.com
- Code
- github.com/george-lindley/causal-blocks. Bugs and suggestions are welcome as issues there.