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'''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.
'''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 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.
* correlation '''does not imply causation'''. This is the most frequent mistake made by people. There are set of principles of [[causal inference]] that need to be satisfied in order to imply cause and effect. [http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/node46.html]
==Unrelated factors==
==Unrelated factors==
Additionally, correlation estimates a linear relationship between X and Y. Thus, an increase in variable X is assumed to exert the same influence on Y across all values of X and Y.
Additionally, correlation estimates a linear relationship between X and Y. Thus, an increase in variable X is assumed to exert the same influence on Y across all values of X and Y.
===Example===
Suppose a polling firm was hired to talk to voters as they voted. Each voter was asked "Are you a Republican?", "Are you a blue collar worker?", "Are you male?", "Do you live in West Virginia?", and "Did you vote for Donald Trump?" We can record that data on a spreadsheet using one for yes and zero for no:
{| class="wikitable"
|Person||Republican?||Blue collar?||Male?||WVa?||Trump?
|-
|A||1||1||1||1||1
|-
|B||1||1||1||1||1
|-
|C||1||1||1||0||1
|-
|D||0||1||1||1||1
|-
|E||0||0||1||0||0
|-
|F||0||0||0||0||0
|-
|G||0||0||0||1||0
|-
|correlation coeff||0.75||1||0.73||0.42
|}
Whether the person voted for Trump is the dependent variable, and each of the other questions are independent variables. The correlation coefficient can then be computed comparing the column of each dependent variable with the Trump column. What this data tells us is that being blue collar is a perfect predictor of voting for Trump—the correlation coefficient is 1. The next best predictive factor would be whether the voter was a Republican, where they match 6 out of 7 times. Then comes gender and West Virginia residence. Assuming that the data sample was large enough to be statistically significant, we could build a model to predict whether other voters would vote for Trump by asking the same questions and computing a score using the formula:
.75*Republican + 1*Blue collar + .73*Male + .42*WVa
A perfect score would be 2.897, and someone with a 0 score would be most unlikely to vote for Trump. Of course, the polling firm would be using many more questions and would experiment to fine-tune the questions to get the best predictive scores. They would also use much larger data samples.
This fine-tuning process is a form of learning. When a computer does this by itself it is called [[machine learning]].
==Correlation and Causation==
==Correlation and Causation==
{{Main|Correlation is not causation}}
Correlation is a linear statistic and makes no mathematical distinction between [[independent variable|independent]] and [[dependent variable]]s. As a consequence, it is impossible to assert [[causation]] based on a correlation even if that correlation is statistically significant. Therefore, when a significant correlation has been identified it is possible that X -> Y (i.e. X causes Y), Y -> X (i.e. Y causes X), or that X <- Z -> Y (i.e. Both X and Y are caused by an additional variable, Z). Caution must be exercised in asserting causation using correlation and claims to this effect must be viewed with considerable skepticism.
Correlation is a linear statistic and makes no mathematical distinction between [[independent variable|independent]] and [[dependent variable]]s. As a consequence, it is impossible to assert [[causation]] based on a correlation even if that correlation is statistically significant. Therefore, when a significant correlation has been identified it is possible that X -> Y (i.e. X causes Y), Y -> X (i.e. Y causes X), or that X <- Z -> Y (i.e. Both X and Y are caused by an additional variable, Z). Caution must be exercised in asserting causation using correlation and claims to this effect must be viewed with considerable skepticism.
Aron, Arthur, Elaine N. Aron and Elliot J. Coups. 2008. ''Statistics for the Behavioral and Social Sciences: A Brief Course.'' 4/e. Upper Saddle River, New Jersey: Prentice Hall.
Aron, Arthur, Elaine N. Aron and Elliot J. Coups. 2008. ''Statistics for the Behavioral and Social Sciences: A Brief Course.'' 4/e. Upper Saddle River, New Jersey: Prentice Hall.
[[Category:statistics]]
[[Category:Statistics]]