The many possible interactions of correlation and non-correlation, causation and non-causation, and the need to pursue (and rule out or fail to rule out) ALL of them is lost on many people who can recite the mantra.
For example, it is also true (especially when looking for small effects in large samples) that "non-correlation does not prove non-causation". This is especially worth understanding when reading papers that are making a claim based entirely on the presence or absence of "statistical significance" (the Evidence Based Medicine way of talking about correlations and whether they can be assumed to be causative or not).
Re: The Club of Raving Lunatics
The many possible interactions of correlation and non-correlation, causation and non-causation, and the need to pursue (and rule out or fail to rule out) ALL of them is lost on many people who can recite the mantra.
For example, it is also true (especially when looking for small effects in large samples) that "non-correlation does not prove non-causation". This is especially worth understanding when reading papers that are making a claim based entirely on the presence or absence of "statistical significance" (the Evidence Based Medicine way of talking about correlations and whether they can be assumed to be causative or not).