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Correlation only shows how well two variables vary together; it does not show the causation of the effect - there is often a third factor (or variable) which causes both, or causes one and influences the other.

An example:

A survey of all the inhabitants in a village found a strong (but not perfect) correlation between foot (shoe) size and mathematical ability - the larger the foot size the better they were at mathematics. Does this mean that foot size causes the mathematical ability of someone?

In this case no; there is a third factor which causes the first (foot size) and has some influence over the second (mathematical ability): the survey was of all the inhabitants of the village which includes babies and young children.

The third factor here (the real cause of the "apparent" correlation) is the age of the inhabitant: the older someone gets (from being a baby to a teenager) the larger their foot size will become, but also the better their mathematical ability is (likely) to get. The babies with the smaller feet will have very limited mathematical ability, the 7 year olds with larger feet will have better mathematical ability, the teenagers with even larger feet will have better mathematical ability again. The correlation need not be perfect as there will be older people with less mathematical ability, but "on average" (sic) the older someone is the better their mathematical ability (along with the larger their feet).

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Q: Why with two variables such as strength and running speed which are correlated meaning they are associated with each other does one not cause the other?
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