Here's a simple rule about causal inference:

• If everything related[1] to A is also related to B, we can conclude that A is causally upstream of B.
• Conversely, if we find even a single thing X which is related to A but independent of B, we can conclude that A is not causally upstream of B.

For example, consider the claim "rain causes me to carry an umbrella":

• It should be impossible to think of a thing that is correlated with rain that isn't also correlated with me carrying an umbrella.[2]
• Whereas it should be possible to find things that are correlated with umbrella-carrying but not rain.  For example, my level of laziness on a given day might be negatively correlated with carrying an umbrella even if my laziness isn't correlated with rain.

The rule has some exceptions which I discuss in the last section.

Derivation of the rule

Suppose A and B are related (non-independent). We want to distinguish the following three possibilities:

• A causes B
• B causes A
• neither causes the other (there is only common cause)

Now suppose we want to distinguish these using purely observational data. In particular, we can look at the [...]

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Outline:

(00:59) Derivation of the rule

(03:25) A visual derivation of the table

(03:39) Exceptions

The original text contained 4 footnotes which were omitted from this narration.

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