<P> As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not imply that the resulting conclusion is false . In the instance above, if the trials had found that hormone replacement therapy does in fact have a negative incidence on the likelihood of coronary heart disease the assumption of causality would have been correct, although the logic behind the assumption would still have been flawed . Indeed, a few go further, using correlation as a basis for testing a hypothesis to try to establish a true causal relationship; examples are the Granger causality test and convergent cross mapping . </P> <P> In logic, the technical use of the word "implies" means "is a sufficient circumstance for". This is the meaning intended by statisticians when they say causation is not certain . Indeed, p implies q has the technical meaning of the material conditional: if p then q symbolized as p → q . That is "if circumstance p is true, then q follows ." In this sense, it is always correct to say "Correlation does not imply causation ." </P> <P> However, in casual use, the word "implies" loosely means suggests rather than requires . The idea that correlation and causation are connected is certainly true; where there is causation, there is a likely correlation . Indeed, correlation is used when inferring causation; the important point is that such inferences are made after correlations are confirmed as real and all causational relationship are systematically explored using large enough data sets . </P> <P> For any two correlated events, A and B, the different possible relationships include: </P>

When does correlation allow you to infer causation