Correlation vs. Causation

I decided to write a response to one of the many excellent posts written by a fellow blogger.  It became long enough and I thought a worthy enough to be a blog post of it’s own!  If you are interested in the idea of correlation vs. causation you can read his blog here first.

In your last paragraph I was reminded of Dawkins’ argument in the God Delusion when he is talking about miracles.  Since miracles are by definition unique and rare events there is no way to really disprove a divine explanation.  This is of course if the same thing doesn’t keep happening again and again, which if it does, you really don’t have a miracle on your hands anymore.  He uses the example of the one documented miracle in Catholicism in which some 100,000 witness near Fatima, Portugal reported the Sun doing some odd things including zigzagging towards them and crashing to the Earth.  Dawkins argues that in looking for a natural explanation for the event, all of them, including the possibility that all 100,000 people are lying are actually more probable than the laws of physics being thwarted for a group of people in one part of the world (no other people reported seeing anything other than those at the event).  So I think that you are very correct that we the “correlation does not mean causation” argument does not negate a particular postulation for why a correlation exists.   However I would go a step further and say that it is not even an argument in of itself.

It is of course the responsibility of anybody who poses a correlation to provide a reason why such a correlation exists.  Provided you have done that, then the “correlation does not mean causation” response isn’t a logical argument in response to yours.  The person on the other side of the debate must either address why your reasons why are not valid, or must present something else that correlates better and why their reason for x causing y is more probable.  So I think you might be giving a little too much weight to the argument in how much it actually negates a correlation between two variables.

In many areas in science we can say why pretty easily because there are usually physical laws that explain why quite easily, and those things are testable and repeatable.  In social science this may be harder to do.  Especially since it is not always clear what all the variables are.  For instance it is clear that there is a positive correlation between gun deaths (accidental, homicide, and suicides) the amount of guns per capita in a population.  There are plenty of psychological factors of course to consider here on why would a person own a gun or why would someone choose to kill themselves?  There are practical questions like how to we get people to be more responsible about locking up their guns so their kid doesn’t pick it up, how to we make sure that more people remember to store their guns unloaded, how can make guns safer from accidental misfires, and how can we make sure that people who buy again are well trained in how to use it? There are likely even bigger questions like how does income disparity lead to increased crime in general? What are other ways that don’t involve firearms where people can be made safe?  All of these and plenty more are likely part and parcel of explaining gun violence, but that doesn’t change the fact that reducing access to guns would result a lowering of the number of gun deaths.  So making some laws that create a national gun registry, that do better background checks, and limit the type of weapon the general public could buy, would make some sense even though it clearly won’t eliminate gun deaths completely.  If by a counter-argument someone says “correlation does not mean causation” they haven’t actually addressed the argument being made.  They actually have to find an example with all other variables relatively constant between the U.S. and that country, except gun control laws, and show that an opposite correlation exists. i.e. Restrictive gun control laws and increased gun deaths, or high gun ownership and low gun deaths.  And that would be for a country with similar economies, democratic, with a high standard of living, and that doesn’t have mandatory military service in which the high amount of gun ownership isn’t because they keep their piece given to them in the military (Switzerland the example always used here).

So in the classic humorous example that has been around for awhile is that graph between global temperature and the number of pirates.  I can’t just show that graph and say see…look how the number of pirates is impacting global temperature?  I actually have to provide a reason why pirates might impact temperatures.  I can say there is less plundering and razing of towns so the urban heat island effect has increased thus raising global

From Wikipedia.org

temperatures.  Obviously this is a silly argument, but a response of “correlation and causation are different”, while a true statement, does not negate my assertion.  There are many ways to disprove my assertion but pointing out a correlation is not causation does not. Because the truth is, “correlation does not always mean causation” so one has to go past this statement to further argue one’s point.  This is true for many arguments that contain logical fallacies.  You could take the classic argument used against gay marriage.  Well if we let gays marry, pretty soon we’ll have to let people marry their pets.  Well this is of course the slippery slope logical fallacy.  Slippery slope arguments may not be incorrect, but are very often wrong.  So it’s not enough for me to counter your slippery slope argument with “Hey that’s a slippery slope argument”.  I would be quite wrong to think the argument was done, because they could actually be right.  Some events do lead to a chain of events that are far from where things started.  To win the argument I would actually need to argue that there has never been a push for legislation to marry a pet, that if anybody has tried this they were a crazy person, that this is not a psychological drive of human beings as a species, etc.  I could also point to many other marriage related laws or other laws that have not led to a hyperbolic slippery slope situations.

To say that “correlation and causation are not necessarily the same thing” is actually a Straw Man argument (which is fallacious) because the argument assumes a position that you have not taken in the argument.  Correlating variables is a valid method for discovering relationships, and by presenting that correlation, one’s assertion is not that correlation is a valid method, but rather that two variables are related to each other.  And to say two things are correlated doesn’t imply that this is the only important variable, or that even it is the primary or secondary cause of a particular event.  One has simply said there is a relationship and a counter argument must challenge the relationship.  A correlation must be presented along with some sound reasons why there is a correlation, and an argument in response must challenge those reasons.  The art of argumentation isn’t easy and few people can actually argue well. 🙂