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from: http://en.wikipedia.org/wiki/Correlatio ... _causation
The cum hoc ergo propter hoc logical fallacy can be expressed as follows:
A occurs in correlation with B.
Therefore, A causes B.
In this type of logical fallacy, one makes a premature conclusion about causality after observing only a correlation between two or more factors. Generally, if one factor (A) is observed to only be correlated with another factor (B), it is sometimes taken for granted that A is causing B even when no evidence supports it. This is a logical fallacy because there are at least five possibilities:
- A may be the cause of B.
- B may be the cause of A.
-some unknown third factor C may actually be the cause of both A and B.
-there may be a combination of the above three relationships. For example, B may be the cause of A at the same time as A is the cause of B (contradicting that the only relationship between A and B is that A causes B). This describes a self-reinforcing system.
-the "relationship" is a coincidence or so complex or indirect that it is more effectively called a coincidence (i.e. two events occurring at the same time that have no direct relationship to each other besides the fact that they are occurring at the same time). A larger sample size helps to reduce the chance of a coincidence, unless there is a systematic error in the experiment.
In other words, there can be no conclusion made regarding the existence or the direction of a cause and effect relationship only from the fact that A and B are correlated. Determining whether there is an actual cause and effect relationship requires further investigation, even when the relationship between A and B is statistically significant, a large effect size is observed, or a large part of the variance is explained.
If you assume dependence (as we have done in this conversation), i.e. that the correlation between two sampled data sets is not by chance, then at least one of:
-A causes B
-B causes A
-C causes A and B
Now, we can rule out that being prone to HIV causes homosexuality (since we already know the methods of transmission of HIV). So either there is some unknown C which causes people to be gay and causes them to get HIV, or being gay causes them (probabilistically) to get HIV.
There is no candidate for C, it is entirely unreasonable to suppose that a predilection for anal sex causes
men to want to have sex with men. The reasonable conclusion is that being gay causally increases the risk of HIV amongst men.