Do You Really Understand Correlation?

[DBTrek]

Digging into correlation as part of a Data Analysis certification and ran across the following, surprisingly good, Wikipedia entry. The top takeaway was a short list of the ways two variables could be correlated:

For any two correlated events, A and B, the different possible relationships include:

A causes B (direct causation);
B causes A (reverse causation);
A and B are consequences of a common cause, but do not cause each other;
A and B both cause C, which is (explicitly or implicitly) conditioned on;
A causes B and B causes A (bidirectional or cyclic causation);
A causes C which causes B (indirect causation);
There is no connection between A and B; the correlation is a coincidence.

https://en.wikipedia.org/wiki/Correlati ... _causation

So what, right? Well, if you understand how humans tend to take any correlation and immediately assume causation, then you can see how many socio-political dogmas are parading around as fact based on nothing more than a correlation. Reading through the examples of the A/B correlation relationships is a worthwhile endeavor for anyone interested in seeing how little we actually know about anything.

I'll include a couple of my favorites below, but they're all worth a read:

When a country's debt rises above 90% of GDP, growth slows.
Therefore, high debt causes slow growth.

This argument by Carmen Reinhart and Kenneth Rogoff was refuted by Paul Krugman on the basis that they got the causality backwards: in actuality, slow growth causes debt to increase.

In other cases it may simply be unclear which is the cause and which is the effect. For example:
Children that watch a lot of TV are the most violent. Clearly, TV makes children more violent.

This could easily be the other way round; that is, violent children like watching more TV than less violent ones.

The relationship between A and B is coincidental

Alternating bald–hairy Russian leaders: A bald (or obviously balding) state leader of Russia has succeeded a non-bald ("hairy") one, and vice versa, for nearly 200 years.

Everyone is familiar with the catchphrase "correlation doesn't equal causation", but you should really take a look at how often we still act as if it does.

"Minorities are disproportionately imprisoned because police are racist"
"Global temperatures are up because we create more CO2"
"We all have less because the 1% have more"
etc.

[Zlaxer]

Everyone is familiar with the catchphrase "correlation doesn't equal causation", but you should really take a look at how often we still act as if it does.

"Minorities are disproportionately imprisoned because police are racist"
"Global temperatures are up because we create more CO2"
"We all have less because the 1% have more"
etc.

Why so surprised? Those statements are good at conditioning proles. Proles will always be proles - history shows that. It's wasted energy to try and change them.

[DBTrek]

David Hume argued that beliefs about causality are based on experience, and experience similarly based on the assumption that the future models the past, which in turn can only be based on experience – leading to circular logic. In conclusion, he asserted that causality is not based on actual reasoning: only correlation can actually be perceived.

Hume makes a strong argument that we can't ever reach causality through reasoning - a fancy way of saying "When people tell you that A causes B because they're correlated and they've reasoned the relationship out, that shit is literally impossible".

But you can't appreciate Hume's argument without understanding how often we base our entire worldviews on misperceptions about correlation and causality. How often has medical science bumped into some variation of this story:

For example, in a widely studied case, numerous epidemiological studies showed that women taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD. But randomized controlled trials showed that HRT caused a small but statistically significant increase in risk of CHD. Re-analysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher socio-economic groups (ABC1), with better-than-average diet and exercise regimens. The use of HRT and decreased incidence of coronary heart disease were coincident effects of a common cause (i.e. the benefits associated with a higher socioeconomic status), rather than a direct cause and effect, as had been supposed.

"Look everybody, we discovered a drug that protects you from coronary heart disease!!!"
... "Oh shit, it actually increases your risk of coronary heart disease. Oops."

They didn't understand correlation and causation.