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Correlation vs. causality - how can you prove the latter?
Thirith
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I've read a couple of documents at work over the last few months that used correlation to suggest causality. For instance, since there's a correlation between a country's investment in research and its economic success, these documents imply that investing in research will benefit a country's economy. I always come away from such arguments thinking that it may just as well be the other way around: economically successful countries are more likely to have more money that they can invest in research. There needs to be more evidence to show that A causes B.
Mathematically, how would one go about trying to prove a degree of causality in such a case? Is it even possible? I'm not asking for an extremely detailed description so much as being pointed in the general direction of the principles applied when trying to show that A isn't just correlated with B, it's actually one of the causes of B. Any explanations would be much appreciated.
Mathematically, how would one go about trying to prove a degree of causality in such a case? Is it even possible? I'm not asking for an extremely detailed description so much as being pointed in the general direction of the principles applied when trying to show that A isn't just correlated with B, it's actually one of the causes of B. Any explanations would be much appreciated.
"Nothing is gonna save us forever but a lot of things can save us today." - Night in the Woods
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I don't understand how that relates to causality being shown though. All that can really say is two events are well correlated or not.
For causality in Thirith's question above, wouldn't you have to show that the investment in research happens first, before growth? And then have an observable or testable method by which research causes economic growth? A then B, instead of "A and B like to show up together"?
In a general non-mathy sense you need to answer the following question: why would this factor influence this other factor? A case needs to be built to argue why investments in research lead to economic success. This will be a super nuanced answer, because everyone can see that if you would spend 100% of your GDP on research you wouldn't suddenly become the richest country. There are obviously many other factors in play and there are also many factors influencing the research budget as well.
I think this is the first episode on his Prof Leonard's classes on causation.
Doc: That's right, twenty five years into the future. I've always dreamed on seeing the future, looking beyond my years, seeing the progress of mankind. I'll also be able to see who wins the next twenty-five world series.
"Nothing is gonna save us forever but a lot of things can save us today." - Night in the Woods
1. Strong correlation with a high degree of consistency.
2. Rigorus method of analysis.
3. Establishing a logical chain of causation.
4. Coherent with known facts.
So far the opinion of the scientific community is that in stable countries with low corruption a public investment into research tends to pay off economicly within 5-10 years (more money back than invested).
-Antje Jackelén, Archbishop of the Church of Sweden
1. A theory explaining what's going on that lets you make a list of possible causes.
2. Some sort of experimental setup that lets you control for the possible causes.
"Experiment" doesn't necessarily mean something in a lab - "experiment" can also mean what scientists call a "natural experiment," which means you have enough observations in the real world that you can control for variables with those. So for instance if you think countries that do A rather than B are successful, and you have 20 countries that did A and 20 that did B and they are the same with respect to everything else, you can control for everything else and just test the A/B thing.
Of course, you never have 40 identical countries, so natural experiments are not always easy or possible. Artificial experiments are not always easy or possible either. But that's what you'd want to do in order to show causation in a case like this.
Also, remember that you need a theory explaining what's going on, and an experimental setup that lets you control for things. Neither of these can be obtained via some rote procedure. Judgment calls need to be made here. So as @kaliyama points out, it's not a matter of just doing objective number crunching. You have to be an experienced researched who understands the context in order to design these statistical analyses in the first place. The math that some of these other posters are talking about is just a tool that lets you run the experiment once you have #1 and #2, but getting #1 and #2 is not a matter of doing math, it's a matter of being a good scientist.