How can it be explained that causal statements cannot be made from correlational data? This is about correlation in Statistics.

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Correlational data cannot tell us that causation has occurred.  We should also note, though, that correlation does not mean that causation has notoccurred.  All that correlation can tell us is that the two variables are related to one another.  We have to hypothesize the nature of the causal relationship between the two (if any).

For example, let us look at the fact that there is a correlation between watching violence on TV and behaving violently in real life.  People who watch violent TV are more likely to be violent.  This is correlational data, but it cannot tell us about causation.  

In this case, there are three possible stories that can be told.  It could be that watching violence on TV causes violent behavior.  It could be that behaving violently causes one to watch violence on TV.  It could also be that something else causes both things.  Perhaps a lack of parental attention causes children to watch violence on TV and to actually be violent.  

The fact that there is a correlation between two variables cannot (on its own) tell us whether there is causation or (if there is causation) which variable is the causal factor.

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