Editing Correlation (section)

===Correlation and causality===
{{Main|Correlation does not imply causation}} {{See also|Normally distributed and uncorrelated does not imply independent}}
The conventional dictum that "[[correlation does not imply causation]]" means that correlation cannot be used by itself to infer a causal relationship between the variables.<ref>{{cite journal | last=Aldrich | first=John | journal=Statistical Science | volume=10 | issue=4 | year=1995 | pages=364–376 | title=Correlations Genuine and Spurious in Pearson and Yule | jstor=2246135 | doi=10.1214/ss/1177009870| doi-access=free }}</ref> This dictum should not be taken to mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown, and high correlations also overlap with [[identity (mathematics)|identity]] relations ([[tautology (logic)|tautologies]]), where no causal process exists (e.g., between two variables measuring the same construct). Consequently, a correlation between two variables is not a sufficient condition to establish a causal relationship (in either direction).

A correlation between age and height in children is fairly causally transparent, but a correlation between mood and health in people is less so. Does improved mood lead to improved health, or does good health lead to good mood, or both? Or does some other factor underlie both? In other words, a correlation can be taken as evidence for a possible causal relationship, but cannot indicate what the causal relationship, if any, might be.