Example:

The faster that windmills are observed to rotate, the more wind is observed.

Therefore, wind is caused by the rotation of windmills.

In this example, the correlation (simultaneity) between windmill activity and wind velocity does not imply that wind is caused by windmills. It is rather the other way around, as suggested by the fact that wind does not need windmills to exist, while windmills need wind to rotate. Wind can be observed in places where there are no windmills or non-rotating windmills—and there are good reasons to believe that wind existed before the invention of windmills.

For example:

Children that watch a lot of TV are the most violent. Clearly, TV makes children more violent.

This could easily be the other way round; that is, violent children like watching more TV than less violent ones.

The two variables are not related at all, but correlate by chance. The more things are examined, the more likely it is that two unrelated variables will appear to be related. For example:

The result of the last home game by the Washington Commanders prior to the presidential election predicted the outcome of every presidential election from 1936 to 2000 inclusive, despite the fact that the outcomes of football games had nothing to do with the outcome of the popular election. This streak was finally broken in 2004 (or 2012 using an alternative formulation of the original rule).

Correlation is a valuable type of scientific evidence in fields such as medicine, psychology, and sociology. Correlations must first be confirmed as real, every possible causative relationship must be systematically explored. In the end correlation alone cannot be used as evidence for a cause-and-effect relationship between a treatment and benefit, a risk factor and a disease, or a social or economic factor and various outcomes. It's one of the most abused types of evidence, because it is easy and tempting to come to premature conclusions based upon the preliminary appearance of a correlation.

“Cars with flames painted on the hood might get more speeding tickets. Are the flames making the car go fast? No. Certain things just go together. And when they do, they are correlated. It is the darling of all human errors to assume, without proper testing, that one is the cause of the other.”

-Barbara Kingsolver, Flight Behavior

“Causality = Correlation + Assumptions”

-J.N. Berkemeijer