# Correlation implies causation

*This article is at an early stage of development.*

‘Correlation implies causation’ is a logical fallacy of the form:

- P is positively correlated with Q.
- Therefore, P causes Q.

An example of this error is:

- There’s a positive correlation between wealth and happiness.
- Therefore, wealth causes happiness.

This logic is invalid because it’s also possible that Q causes P, or that P and Q have a common cause, R. It’s also possible that a combination of these three possibilities is true, or that the correlation is just a coincidence. In the example, it’s also possible that happiness causes wealth - by in some way making us more successful at earning money - or that a particular type of personality can cause both wealth and happiness. And it’s also possible that a combination of these three possibilities is true, or that the correlation is just a coincidence.

This consistent logical error is actually a form of availability bias, and can therefore be explained by credulism, the certainty of belief, and the speed of the brain. In the example, when we consider the positive correlation between wealth and happiness, it’s easy to think of how increasing wealth could increasingly contribute to happiness, by increasingly freeing us of money concerns, and increasingly enabling us to pay for, and do, things that give us pleasure, or that allow us to avoid displeasure. That is, these apparent ways in which wealth can contribute to happiness are readily available to our thought processes. And, upon considering these ways, and the correlation, an obvious possibility is that wealth causes happiness. However, the ways that happiness could contribute to wealth, or that there could be a common factor that contributes to both, or that a combination of these three possibilities could be true, or that the correlation could be just a coincidence, aren’t as easy to think of, and are therefore not as readily available to our thought processes. Therefore, the other possible causal possibilities, and the possibility that the correlation is just a coincidence, aren’t, upon considering the correlation, as obvious a possibility as wealth causing happiness. Therefore, given the speed of the brain, and the obviousness of the possibility that wealth causes happiness, it tends to enters our thought processes, via our reasoning or imagination, within moments of us learning of the correlation, and before any of the other possibilities. And, given credulism, this possibility will enter our thought processes as reality, and, as explained in Confirmation bias - in the section Belief is self-preserving - the certainty of belief will then effectively provide a degree of protection to our belief, directly and via the confirmation bias. Specifically, while our certainty exists, we’re unlikely to question our conclusion, and are therefore biased against realising the logical flaw in it - that is, that correlation doesn’t imply causation. Thus, we’re biased, due to availability bias, towards committing this logical error.