### Correlation does not imply causation

I got up in them middle of the night to write this and it was all muddled. Then I got up in the middle of another night thinking 'This makes no sense!' And it didn't, because I had written P(causation|corrrelation) = P(causation) - P(correlation|no causation)

. Stupid me. I'll correct it later. In short: They're not independent, as correlation is a prerequisite for causation. P(correlation) is not 0 or we wouldn't be discussing P(correlation) with such fascination. I'll explain it with more rigor when I'm not really tired and needing to get up in seven hours.

----

I occasionally see misuse of the mantra 'Correlation does not imply causation'. So I don't have to write all this every time I see it, here's a concise explanation:

(Note on notation for non-mathy people: P(x) is the probability that x is true. P(y|x) means the probability that y is true given that x is true.)

The source of the confusion with this statement is that 'imply' can mean either 'entail' or 'suggest'. 'x entails y' means P(y|x)=1). 'x suggests y' means P(y|x)>P(y).

In 'correlation does not imply causation', the word 'imply' is being used to mean entail. Correlation *does suggest* causation.

Also, if you've ever been tempted to claim that 'lack of evidence is not evidence of lack', I encourage you to apply the same [deleted because I muddled it] reasoning, keeping in mind that the terms 'evidence' and 'proof' are not typically considered interchangeable.