# CorrelationsAndCausality

Some things happen together more frequently than chance would suggest: clouds and rain, smoke and fire, smoking and cancer, etc. Other things are less often associated with each other than a random roll of the dice might imply.

There's a mathematical concept, the correlation, that quantifies the linkage between two variables. A correlation of 0 means that knowing one thing tells you absolutely nothing about the other. If a (fair) coin comes up "heads" that doesn't imply anything about the result of the next toss; the two events are totally independent. A correlation of 1, on the other hand, means that a pair of quantities are rigidly linked. Knowing one of them gives you absolute predictive power over the other. When a (normal) coin has come up heads, then the bottom side is sure to be tails. In between 0 and 1, the correlation identifies the fraction of the story that one variable tells about the other.

But being correlated doesn't imply a cause-and-effect relationship among variables. Both may be moved in parallel by an outside force. Or the correlation may be only a statistical artifact, the result of analyzing an incomplete data set. If you take enough observations, and try out enough hypotheses, then some of them will appear to fit ... until you do further measurements, when the effect fades away. Correlations are clues --- leads to pursue, not proofs.

Sunday, April 09, 2000 at 06:44:23 (EDT) = 2000-04-09

(correlates: InMyJournal, GorillaPhilosopher, PullPush, ...)