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, ...)*