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'''Correlation''' describes the relationship of two factors to one another (see [[cause and effect]]). In common usage, it denotes an association of one variable with another in quite general terms; for example, one might say, "success is correlated with hard work". In mathematics, however, and in science and engineering, which make use of mathematical concepts, correlation is a technical term with a precise definition.
'''Correlation''' describes the relationship of two factors to one another (see [[cause and effect]]). When two factors are found to go together, there are only three explanations. First, the two things may be entirely unrelated. Second, they may both be caused by a another factor. Third, one of the factors might be causing the other. It is the task of [[statistics]] to point out the existence of a correlation, but it is the task of science to discover what relationship, if any, exists.
==Unrelated factors==
Often [[cancer clusters]] have been said to indicate the existence of a biological hazard, but by the laws of chance in any group of people who get a rare disease (or win the lottery) there will always be some who live close together. This does not mean that something in their environment caused their tragedy or good fortune.
If you flip coins or throw dice, from time to time you will get runs of similar results like 4 heads in a row. You might try to find the cause for these runs in what you were thinking about at the time, hoping to find that you could influence the toss or roll. But this is nonsense.
When unrelated events occur, it is dismissed as a matter of coincidence.
==Factors which have a common cause==
Two commuters might happen to see each other on a train, not because either intended to meet the other, but simply because each happens to dislike crowded trains and prefer trains with dining cars. When the regular train is crowded or lacks a dining car, both may independently decide to take a later train. Seeing each other in the dining car of one would not be merely a coincidence, but would stem from the conditions on the earlier train.
Cases of shark attacks correlate with sales of ice cream, but no one thinks that the bites make people buy ice cream, or that eating ice cream makes you vulnerable to sharks. Both things go up and down in an annual cycle, because people go to the beach more in the summer. They swim and buy ice cream because it's hot. Swimming exposes them to (rare) shark attacks.
==One thing causes another==
In scientific subjects like chemistry, physics and astronomy many laws of cause and effect have been discovered. Put two chemicals together, and they form a compound. Push something, and its momentum increases. The [[scientific method]] is useful in describing the relationship between events, especially when despite their best efforts, no one has been able to find an exception (see [[independent review]]).
==Terminology==
In common usage, it denotes an association of one variable with another in quite general terms; for example, one might say, "success is correlated with hard work". In mathematics, however, and in science and engineering, which make use of mathematical concepts, correlation is a technical term with a precise definition.
Correlation must be distinguished from causation (see article on [[correlation is not causation]]). When one factor changes and another factor changes with it, there is usually a direct relationship between the two factors, observed as a correlation. Alternatively, both changed could be the result of changes in a third factor. For example, the prices of two unrelated goods might increase during a period of [[inflation]]; the two price rises are correlated with each other but neither has caused the other.
Correlation must be distinguished from causation (see article on [[correlation is not causation]]). When one factor changes and another factor changes with it, there is usually a direct relationship between the two factors, observed as a correlation. Alternatively, both changed could be the result of changes in a third factor. For example, the prices of two unrelated goods might increase during a period of [[inflation]]; the two price rises are correlated with each other but neither has caused the other.