The strength of the correlation or its time-scale have no bearing on whether the correlation should be considered evidence of causation. The fatal flaw of a correlation is that it can be specious — it can appear to explain reality, but really there's a third variable responsible for driving the phenomenon you're interested in.
In this case, lead exposure and crime rate are correlated, but maybe lead doesn't cause crime at all: maybe something else causes crime that also happens to correlate with lead exposure. Who knows, maybe a certain pesticide was used at the same time that lead gasoline came into vogue, and that's really the true cause of the rise in crime rates.
In research like this, when you can't do a manually controlled experiment, you have to control for hidden variables by some other means. And that's precisely what the investigators in this article did: they varied the input data to try to "shake out" other variables that might be behind the correlation. They looked at different time scales, different geographies, and different demographics, in an attempt to control for hidden variables that might be related to any one of those things. Every time you vary the input data and keep finding a correlation, your evidence of a causative relationship goes up.
The gold standard, of course, would be to expose two random, double-blind sets of infants to lead and to a control substance and see what happens. But since that would be unethical (as we have reason to think lead is bad for you), we're stuck with animal studies or retrospective studies. Personally, I find the evidence in this article impressive, but it would take quite a lot of looking into their specific methods to come to any real conclusion.
> The fatal flaw of a correlation is that it can be specious — it can appear to explain reality, but really there's a third variable responsible for driving the phenomenon you're interested in.
But in the case of lead, the causal chain from lead exposure to worse behaviour is fairly well understood.
That's the high level view of the problem of correlation and causation. What I'm really saying is how unlikely should we consider these correlations - especially correlations over very broad average trends in human behaviour. Now I'm sure there are some statistical tools that would give some sense of how surprising the correlation of these trends is but I'd like to know out of all the things about human society we track how many of them correlate and how closely.
In this case, lead exposure and crime rate are correlated, but maybe lead doesn't cause crime at all: maybe something else causes crime that also happens to correlate with lead exposure. Who knows, maybe a certain pesticide was used at the same time that lead gasoline came into vogue, and that's really the true cause of the rise in crime rates.
In research like this, when you can't do a manually controlled experiment, you have to control for hidden variables by some other means. And that's precisely what the investigators in this article did: they varied the input data to try to "shake out" other variables that might be behind the correlation. They looked at different time scales, different geographies, and different demographics, in an attempt to control for hidden variables that might be related to any one of those things. Every time you vary the input data and keep finding a correlation, your evidence of a causative relationship goes up.
The gold standard, of course, would be to expose two random, double-blind sets of infants to lead and to a control substance and see what happens. But since that would be unethical (as we have reason to think lead is bad for you), we're stuck with animal studies or retrospective studies. Personally, I find the evidence in this article impressive, but it would take quite a lot of looking into their specific methods to come to any real conclusion.