But it is difficult to imagine a mechanism where the lead could be caused by the crime and easy to imagine one where the crime is caused by the lead. A separate independent cause that affects crime and lead is easy to imagine, but if you control for location where people live, or lived when young (which is largely a measure of poverty) and still saw the correlation between lead and crime, then I would say that was quite strong evidence that lead poisoning (which is known to have mental effects) causes behavior patterns that lead to crime.
One causing the other is not the only possibility.
Maybe it's a complete coincidence.
Or maybe (keeping in mind that somoene above suggested the correlation has been shown in different countries at different times) -- societies that work to reduce lead also tend to be societies that work on other social issues, and those other social issues reduce crime. So the lead is correlated to crime historically, even though neither causes the other directly.
Now, i think the study showing lead/crime correlation is _awfully_ interesting, and I don't dismiss it.
But "correlation does not prove causation" does not just mean "B could have caused A instead of A causing B." And this is important to understand in order to evaluate statistical findings properly. There are all sorts of things that can cause correlation rather than either A or B causing the other -- including things nobody's actually even thought of yet, but may still be what happened. And complete coincidence is always possible as well.
The word "correlated" means that it is NOT just a complete coincidence. One might not cause the other, they might be correlated because of a separate factor that interacts with both, but if they are "correlated" then complete coincidence can be ruled out.
> [...] So the lead is correlated to crime historically, even though neither causes the other directly.
Yes, this is what I mean by a third factor affecting both. But lead is a physical effect -- there are only certain sorts of things that can cause it. Things like eating lead, breathing lead, or having a diet that causes one to incorporate less lead into neurons. Thinking happy thoughts cannot change your lead levels (directly). So there are only certain categories of separate factors, C, that could be the cause of both A (lead) and B (crime). Where your name comes in the alphabet might conceivably cause crime, but it simply cannot cause lead. C, if it exists, must be a physical effect.
That's why I mentioned controlling for location where people live. That is a likely candidate for C: it is plausible to correlate with crime and it is possible to correlate with lead. If you control for it and still find an effect, then either A causes B, B causes A (not reasonable), or there is a different C'. Perhaps a genetic mutation that increases lead absorption and also alters brain chemistry to increase propensity to crime? That one is already a bit of a stretch.
I guess what I am saying is that it is true that correlation does not imply causation, but that there are reasonableness constraints on the kinds of interactions one can hypothesize, and after a certain point Occam's razor implores us to consider causation.
The word "correlated" means that it is NOT just a complete coincidence.
How do you figure? The word 'correlated' means that a relationship has been shown to be statistically _unlikely_ to have happened purely by chance. It can never be shown to be impossible however. And there can (and often are) subtle mistakes in the calculations that mean even the correlation isn't what one first thought.
And obviously statistics alone can never prove (or rule out)_ a causation, I think we agree there.
I haven't examined the research under discussion in detail enough to know if they controlled for all the things you suggest would be good to control for, etc., I have no idea.
But yeah, in the end we use our judgement as to what statistical correlations actually mean (such as a causation, and what sort through what mechanism). We can also do experiments or analysis to try and rule out (or confirm) other plausible alternate explanations. That's science, yep.
I think we mostly agree. I still object to what I think was an overly facile implication on your part that a few minutes of thinking of alternate explanations and deciding they are implausible -- on your own without seeing what other people's responses to the study in the literature have been, without an in depth analysis and consideration of the original research -- is sufficient to determine that there's "quite strong evidence" for correlation. That's not science.
