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originally posted by: Sinter Klaas
a reply to: rickymouse
I do not like using roundup,
It is an illegal substance out here. There are no non toxic substances to kill plants. If it kills a plant, it will get in the soil directly or when the plant is decomposing.
You can add fertilizer though, if it is from a biological source, the only issue is that the oceans get over run by algae from all the fertilizer that gets in streams and canals and rivers and eventually the oceans. It isn't so weird if you consider it to be closely related to plants.
The point I was trying to make (and will elaborate here) is that the usual mantra, "Correlation does not imply causation," is true only in a trivial sense, so we need to think about it more carefully. And as regular readers might expect, I'll take a Bayesian approach.
It is true that correlation doesn't imply causation in the mathematical sense of "imply;" that is, finding a correlation between A and B does not prove that A causes B. However, it does provide evidence that A causes B. It also provides evidence that B causes A, and if there is a hypothetical C that might cause A and B, the correlation is evidence for that hypothesis, too.
In Bayesian terms, a dataset, D, is evidence for a hypothesis, H, if the probability of H is higher after seeing D. That is, if P(H|D) > P(H).
For any two variables, A and B, we should consider 4 hypotheses:
A: A causes B
B: B causes A
C: C causes A and B
N: there are no causal relationships among A, B, and C
And there might be multiple versions of C, for different hypothetical factors. If I have no prior evidence of any causal relationships among these variables, I would assign a high probability (in the sense of a subjective degree of belief) to the null hypothesis, N, and low probabilities to the others. If I have background information that makes A, B, or C more plausible, I might assign prior probabilities accordingly. Otherwise I would assign them equal priors.
The correlation phrase has become so common and so irritating that a minor backlash has now ensued against the rhetoric if not the concept. No, correlation does not imply causation, but it sure as hell provides a hint. Does email make a man depressed? Does sadness make a man send email? Or is something else again to blame for both? A correlation can't tell one from the other; in that sense it's inadequate. Still, if it can frame the question, then our observation sets us down the path toward thinking through the workings of reality, so we might learn new ways to tweak them. It helps us go from seeing things to changing them.
Pearson’s work suggested that causation might be irrelevant to science and that it could in certain ways be indistinguishable from perfect correlation. "The higher the correlation, the more certainly we can predict from one member what the value of the associated member will be," he wrote in one of his major works, The Grammar of Science. "This is the transition of correlation into causation."
Correlation and Causation
Much of scientific evidence is based upon a correlation of variables – they tend to occur together. Scientists are careful to point out that correlation does not necessarily mean causation. The assumption that A causes B simply because A correlates with B is a logical fallacy – it is not a legitimate form of argument. However, sometimes people commit the opposite fallacy – dismissing correlation entirely, as if it does not imply causation. This would dismiss a large swath of important scientific evidence.
For example, the tobacco industry abused this fallacy to argue that simply because smoking correlates with lung cancer that does not mean that smoking causes lung cancer. The simple correlation is not enough to arrive at a conclusion of causation, but multiple correlations all triangulating on the conclusion that smoking causes lung cancer, combined with biological plausibility, does.