Correlation coefficients per se are no values expressing a causal link, yes. Cum hoc ergo propter hoc.
But:
A causal link between number of carrier poermits and crime rate could be imagined. A link between temperature and number of pirates - well, needs much, much more imagination.
If correlations would be completely meaningless, nobody in science would calculate them. The art lies in understanding what kind of two variable get correlated to each other. And that is the problem with that famous temperature-pirate- "argument".
A correlation never is a sufficient argument in itself, but it can be a supportive one, or not (depending on the kind of variables compared, like said above).
If an intellectual analysis of the nature of two variables you compare implies the possebility or results in the conclusion they have a relation of causal nature of some sort and amount, THEN a correlation coefficient is expected to describe the intensity, the total effectiveness of a causal link indeed. THIS IS OFTEN OVERSEEN.
That is why the correlation in the permits-crime relation bears much more reasons and is more likely to hint at a causal link, then the temperature-piracy example. A high correlation alone is no argument for causality yes or no. The decision on causality assumed or not has to be made by content of the variables, their quality, what they mean and stand for. And only then you take a high correlation as an argument for a strong causal effect.
Confounding variables always have to be taken into account. The possibility for confounding variables being effective in the permits-crime-relation needs further examination. The existence of confounding variables in the temperature-piracy-relation can be taken almost for granted. And this again is an argument why the one can be assumed to have a higher probability for a causal link than the other.
And just to show what a bean counter I can be: a correlation different than zero ALWAYS is the description of a link between two variables. Its just that that link can not only be huge or small, or causal, but also one of chance (probability). Statistics then speak of stochastic or non-deterministic links.
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Last edited by Skybird; 07-14-14 at 07:07 AM.
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