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Man, for all the critics out there quick to point out that correlation is not equal to causation, nobody ever seems to explain what needs to be in place to actu

by porter 12y ago

Man, for all the critics out there quick to point out that correlation is not equal to causation, nobody ever seems to explain what needs to be in place to actually show causation. To establish causation you need 3 things: 1) Correlation 2) Temporal precedence. That is, you have to show that the cause occurs in time before the effect 3) A lack of other plausible explanations If more people knew the above the world would be a better place. Even the Udacity statistics course failed to mention the above, even though they hammered home that correlation does not imply causation.

alok-g 12y ago
Even when all three are satisfied, there may still not be a causal relationship since correlation may have been by way of coincidence. For example, if Google shows that the stock market change on a given day seems to correlate surprisingly well with search volume for a particular phrase on the day before, that may be just because the particular phrase was chosen from amongst a million others based on its correlation. Causation can still cannot be established (though a link cannot be denied either). Note: If I recall correctly, Google did show one such study.
- srean 12y ago
  But coincidences are covered by his (3). By definition coincidences are low probability events, if one does not account for coincidences, then yes, with low probability it will get it wrong. I think this gets more into the probably approximately correct (PAC) learning domain.
  - alok-g 12y ago
    I was thinking also if they were covered by #3, but I am not sure: >> 3) A lack of other plausible explanations This means that there are not other parameters involved, satisfying the other two criteria, that can also plausibly "explain" the measured effect. In the example I gave, there may not be any such other available correlation. That the analyst picked the plausible cause by hunting though a large number of others is by itself not a plausible explanation asked for by #3.
msellout 12y ago
The definition of cause is more of a philosophy/epistemology question than a statistics question. I'm not sure those 3 points are necessary. Even temporal precedence is called into question by quantum mechanics. Positrons are just electrons traveling backwards in time and all that. Most troubling is point 3 -- a lack of other plausible explanations. There are many things, such as smoking cigarettes causing cancer, that have other plausible explanations. It is clear that Americans understand causality to be some form of influence, and not necessarily the only possible influence for an event. It is the degree of influence that matters.
czr80 12y ago
When I get a cold I pray to Zeus. It always clears up in a few days. Can't think of any other reason for it getting better, therefore by your 3 criteria I'm justified in thinking Zeus cures my colds. Actually, to establish causation, in as much as this is possible at all [1], you need a predictive model and controlled experiments. [1] following Hume, you can never definitively show causation.
- tel 12y ago
  What's Hume's objection to proving causality? (Not that I intend to challenge it, I would just like to hear it characterized).
  - snowwrestler 12y ago
    You can never rule out hidden variables. Edit to add: because they are hidden.
tel 12y ago
This isn't really a great system for reporting causation. It's at best OK and is used from time to time (see any literature on Granger Causality). As I linked elsewhere in this thread, if you really want to prove causality then you need to be making counterfactuality arguments. Judea Pearl's framework of causal networks is a good system for doing this. At the end of the day, your claim of causality rests upon a network of assumptions about causality (and this is a formal description of your point (3), basically) and someone accepts this proof by accepting your assumption network and the strength of your new data.

by porter 12y ago

alok-g 12y ago

Even when all three are satisfied, there may still not be a causal relationship since correlation may have been by way of coincidence. For example, if Google shows that the stock market change on a given day seems to correlate surprisingly well with search volume for a particular phrase on the day before, that may be just because the particular phrase was chosen from amongst a million others based on its correlation. Causation can still cannot be established (though a link cannot be denied either). Note: If I recall correctly, Google did show one such study.

srean 12y ago
But coincidences are covered by his (3). By definition coincidences are low probability events, if one does not account for coincidences, then yes, with low probability it will get it wrong. I think this gets more into the probably approximately correct (PAC) learning domain.
- alok-g 12y ago
  I was thinking also if they were covered by #3, but I am not sure: >> 3) A lack of other plausible explanations This means that there are not other parameters involved, satisfying the other two criteria, that can also plausibly "explain" the measured effect. In the example I gave, there may not be any such other available correlation. That the analyst picked the plausible cause by hunting though a large number of others is by itself not a plausible explanation asked for by #3.

msellout 12y ago

The definition of cause is more of a philosophy/epistemology question than a statistics question. I'm not sure those 3 points are necessary. Even temporal precedence is called into question by quantum mechanics. Positrons are just electrons traveling backwards in time and all that. Most troubling is point 3 -- a lack of other plausible explanations. There are many things, such as smoking cigarettes causing cancer, that have other plausible explanations. It is clear that Americans understand causality to be some form of influence, and not necessarily the only possible influence for an event. It is the degree of influence that matters.

czr80 12y ago

When I get a cold I pray to Zeus. It always clears up in a few days. Can't think of any other reason for it getting better, therefore by your 3 criteria I'm justified in thinking Zeus cures my colds. Actually, to establish causation, in as much as this is possible at all [1], you need a predictive model and controlled experiments. [1] following Hume, you can never definitively show causation.

tel 12y ago
What's Hume's objection to proving causality? (Not that I intend to challenge it, I would just like to hear it characterized).
- snowwrestler 12y ago
  You can never rule out hidden variables. Edit to add: because they are hidden.

tel 12y ago

This isn't really a great system for reporting causation. It's at best OK and is used from time to time (see any literature on Granger Causality). As I linked elsewhere in this thread, if you really want to prove causality then you need to be making counterfactuality arguments. Judea Pearl's framework of causal networks is a good system for doing this. At the end of the day, your claim of causality rests upon a network of assumptions about causality (and this is a formal description of your point (3), basically) and someone accepts this proof by accepting your assumption network and the strength of your new data.