{pdf download} Cause and Correlation in Biology: Path Analysis, Structural Equations and D-separatio

In everyday language, dependence, association and correlation are used interchangeably. Technically, however, association is synonymous with dependence and is different from correlation (Fig. 1a). Association is a very general relationship: one variable provides information about another. Correlation is more specific: two variables are correlated when they display an increasing or decreasing trend. For example, in an increasing trend, observing that X > μX implies that it is more likely that Y > μY. Because not all associations are correlations, and because causality, as discussed above, can be connected only to association, we cannot equate correlation with causality in either direction.

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Because P depends on both r and the sample size, it should never be used as a measure of the strength of the association. It is possible for a smaller r, whose magnitude can be interpreted as the estimated effect size, to be associated with a smaller P merely because of a large sample size3. Statistical significance of a correlation coefficient does not imply substantive and biologically relevant significance. 2ff7e9595c